Line_Integral_Greens_Theorem.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    120655,       2539]
NotebookOptionsPosition[    115838,       2451]
NotebookOutlinePosition[    116170,       2466]
CellTagsIndexPosition[    116127,       2463]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{"(*", " ", 
  RowBox[{
   RowBox[{
   "Compute", " ", "the", " ", "line", " ", "integral", "\[IndentingNewLine]", 
    RowBox[{
     SubscriptBox["\[Integral]", "C"], 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"x", " ", 
        SuperscriptBox["y", "2"], 
        RowBox[{"\[DifferentialD]", "y"}]}], " ", "-", " ", 
       RowBox[{
        SuperscriptBox["x", "2"], "y", " ", 
        RowBox[{"\[DifferentialD]", "x"}]}]}], ")"}]}]}], " ", ",", " ", 
   RowBox[{
    RowBox[{
    "where", " ", "C", " ", "is", " ", "the", " ", "cardioid", " ", "r"}], 
    " ", "=", " ", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "+", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ")"}], " ", 
     "\[IndentingNewLine]", 
     ButtonBox[
      RowBox[{
       RowBox[{"https", ":"}], "//", 
       RowBox[{
        RowBox[{
         RowBox[{"www", ".", "quora", ".", "com"}], "/", "How"}], "-", "do", 
        "-", "you", "-", "evaluate", "-", "the", "-", "line", "-", "integral",
         "-", "int_C", "-", "xy", "-", "2", "-", "dy", "-", "x", "-", 
        RowBox[{"2", "y"}], "-", "dx", "-", "where", "-", "C", "-", "is", "-",
         "the", "-", "cardioid", "-", "r", "-", "a", "-", "1", "-", "cos", 
        "-", "theta"}]}],
      BaseStyle->"Hyperlink",
      ButtonData->{
        URL[
        "https://www.quora.com/How-do-you-evaluate-the-line-integral-int_C-xy-\
2-dy-x-2y-dx-where-C-is-the-cardioid-r-a-1-cos-theta"], None},
      ButtonNote->
       "https://www.quora.com/How-do-you-evaluate-the-line-integral-int_C-xy-\
2-dy-x-2y-dx-where-C-is-the-cardioid-r-a-1-cos-theta"]}]}]}], 
  "\[IndentingNewLine]", "*)"}]], "Input",
 CellChangeTimes->{{3.8163100703687267`*^9, 3.816310161194888*^9}, 
   3.816315426358858*^9, {3.8163156179567137`*^9, 
   3.816315650419203*^9}},ExpressionUUID->"d9a963c7-af47-4c7b-be6d-\
ef7222b8b9f9"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Cardioid", ":"}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"c", "[", "\[Theta]_", "]"}], ":=", " ", 
   RowBox[{"a", 
    RowBox[{"(", 
     RowBox[{"1", "+", 
      RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ")"}]}]}]}]], "Input",
 CellChangeTimes->{{3.816310377142457*^9, 3.8163103954328823`*^9}, {
  3.816310556293763*^9, 3.816310559322358*^9}, {3.816315270078664*^9, 
  3.816315278346942*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"9dac9486-7675-4d75-9f41-1f3228cf0215"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Use", " ", 
    RowBox[{"Green", "'"}], "s", " ", 
    RowBox[{"theorem", ":", " ", 
     RowBox[{
      SubscriptBox["\[Integral]", "C"], 
      RowBox[{
       RowBox[{"v", "[", 
        RowBox[{"x", ",", "y"}], "]"}], 
       RowBox[{"\[Integral]", 
        RowBox[{
         SubscriptBox["\[Integral]", "R"], 
         RowBox[{"curl", " ", 
          RowBox[{"v", "[", 
           RowBox[{"x", ",", "y"}], "]"}]}]}]}]}]}]}]}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{" ", "1", ")"}], " ", "Vector", " ", 
    RowBox[{"field", ":"}]}], " ", "*)"}], 
  RowBox[{
   RowBox[{"v", "[", 
    RowBox[{"x_", ",", "y_"}], "]"}], ":=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       SuperscriptBox["x", "2"]}], "y"}], " ", ",", 
     RowBox[{"x", " ", 
      SuperscriptBox["y", "2"]}]}], "}"}]}]}]], "Input",
 CellChangeTimes->{{3.816310185557372*^9, 3.816310202990904*^9}, {
  3.816310333222149*^9, 3.816310338165669*^9}, {3.816315431855113*^9, 
  3.816315453727457*^9}, {3.816315675903129*^9, 3.816315723278336*^9}, {
  3.8163183354426517`*^9, 3.8163183538554173`*^9}},
 CellLabel->
  "In[135]:=",ExpressionUUID->"6b5d85f4-dd9b-4ff4-ba7d-177082207cd1"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Visualize", " ", "the", " ", "vector", " ", "field", " ", 
    RowBox[{"(", 
     RowBox[{"and", " ", "cardioid"}], ")"}], " ", "for", " ", "the", " ", 
    "line", " ", 
    RowBox[{"integral", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"VectorPlot", "[", 
   RowBox[{
    RowBox[{"v", "[", 
     RowBox[{"x", ",", "y"}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", 
      RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"y", ",", 
      RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", 
    RowBox[{"PlotRangePadding", "->", "None"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.81631023359063*^9, 3.816310296979602*^9}, {
  3.816310359524692*^9, 3.816310370805648*^9}, {3.8163104051822367`*^9, 
  3.816310406186249*^9}, {3.816310459749834*^9, 3.8163105070155478`*^9}, {
  3.8163105504547377`*^9, 3.816310614334094*^9}, {3.8163154772487793`*^9, 
  3.816315479334496*^9}, {3.816318443910656*^9, 3.81631844514264*^9}},
 CellLabel->
  "In[137]:=",ExpressionUUID->"98adb345-ac70-4a54-8b92-4c4c3f3a637c"],

Cell[BoxData[
 GraphicsBox[{{}, 
   {RGBColor[0.2947336, 0.4054232, 0.5678384000000001], 
    {Arrowheads[{{0.04098360655737703, 1.}}], 
     ArrowBox[{{-2.142857142857143, -1.3928571428571428`}, \
{-1.8571428571428572`, -1.607142857142857}}]}, 
    {Arrowheads[{{0.03340913411259937, 1.}}], 
     ArrowBox[{{-2.122448979591837, -1.206997084548105}, \
{-1.8775510204081631`, -1.3644314868804666`}}]}, 
    {Arrowheads[{{0.026568049806404453`, 1.}}], 
     ArrowBox[{{-2.1020408163265305`, -1.0167638483965016`}, \
{-1.8979591836734695`, -1.1260932944606417`}}]}, 
    {Arrowheads[{{0.020383467663737456`, 1.}}], 
     ArrowBox[{{-2.0816326530612246`, -0.8221574344023326}, \
{-1.9183673469387756`, -0.8921282798833822}}]}, 
    {Arrowheads[{{0.014759559554887298`, 1.}}], 
     ArrowBox[{{-2.061224489795918, -0.6231778425655978}, \
{-1.9387755102040818`, -0.6625364431486882}}]}, 
    {Arrowheads[{{0.0095803419627142, 1.}}], 
     ArrowBox[{{-2.0408163265306123`, -0.4198250728862975}, \
{-1.9591836734693877`, -0.4373177842565599}}]}, 
    {Arrowheads[{{0.0047106483239640895`, 1.}}], 
     ArrowBox[{{-2.020408163265306, -0.21209912536443165`}, \
{-1.9795918367346939`, -0.21647230320699726`}}]}, 
    {Arrowheads[{{0.00471064832396414, 1.}}], 
     ArrowBox[{{-1.9795918367346939`, 
      0.2164723032069969}, {-2.0204081632653064`, 0.21209912536443132`}}]}, 
    {Arrowheads[{{0.009580341962714197, 1.}}], 
     ArrowBox[{{-1.9591836734693877`, 
      0.4373177842565596}, {-2.0408163265306123`, 0.4198250728862972}}]}, 
    {Arrowheads[{{0.01475955955488737, 1.}}], 
     ArrowBox[{{-1.9387755102040816`, 
      0.6625364431486879}, {-2.0612244897959187`, 0.6231778425655975}}]}, 
    {Arrowheads[{{0.020383467663737404`, 1.}}], 
     ArrowBox[{{-1.9183673469387756`, 
      0.8921282798833817}, {-2.081632653061224, 0.8221574344023322}}]}, 
    {Arrowheads[{{0.026568049806404447`, 1.}}], 
     ArrowBox[{{-1.8979591836734695`, 
      1.1260932944606412`}, {-2.1020408163265305`, 1.0167638483965014`}}]}, 
    {Arrowheads[{{0.033409134112599305`, 1.}}], 
     ArrowBox[{{-1.8775510204081634`, 
      1.3644314868804661`}, {-2.1224489795918364`, 1.2069970845481046`}}]}, 
    {Arrowheads[{{0.04098360655737703, 1.}}], 
     ArrowBox[{{-1.8571428571428572`, 
      1.6071428571428565`}, {-2.142857142857143, 1.3928571428571423`}}]}, 
    {Arrowheads[{{0.03200779936922443, 1.}}], 
     ArrowBox[{{-1.8192419825072887`, -1.4081632653061225`}, \
{-1.60932944606414, -1.5918367346938775`}}]}, 
    {Arrowheads[{{0.025808918415141234`, 1.}}], 
     ArrowBox[{{-1.8042482299042066`, -1.2182423990004165`}, \
{-1.624323198667222, -1.3531861724281549`}}]}, 
    {Arrowheads[{{0.02029007078060255, 1.}}], 
     ArrowBox[{{-1.7892544773011247`, -1.0245730945439402`}, \
{-1.6393169512703043`, -1.118284048313203}}]}, 
    {Arrowheads[{{0.015389465600533857`, 1.}}], 
     ArrowBox[{{-1.7742607246980426`, -0.8271553519366932}, \
{-1.6543107038733862`, -0.8871303623490214}}]}, 
    {Arrowheads[{{0.01102557478007806, 1.}}], 
     ArrowBox[{{-1.7592669720949605`, -0.6259891711786757}, \
{-1.6693044564764683`, -0.6597251145356103}}]}, 
    {Arrowheads[{{0.007094193113905074, 1.}}], 
     ArrowBox[{{-1.7442732194918786`, -0.42107455226988766`}, \
{-1.6842982090795504`, -0.4360683048729697}}]}, 
    {Arrowheads[{{0.00346796920779464, 1.}}], 
     ArrowBox[{{-1.7292794668887965`, -0.21241149521032918`}, \
{-1.6992919616826323`, -0.2161599333610997}}]}, 
    {Arrowheads[{{0.003467969207794614, 1.}}], 
     ArrowBox[{{-1.6992919616826323`, 
      0.21615993336109937`}, {-1.7292794668887963`, 
      0.21241149521032887`}}]}, 
    {Arrowheads[{{0.007094193113905074, 1.}}], 
     ArrowBox[{{-1.6842982090795504`, 
      0.4360683048729694}, {-1.7442732194918786`, 0.4210745522698873}}]}, 
    {Arrowheads[{{0.01102557478007806, 1.}}], 
     ArrowBox[{{-1.6693044564764683`, 
      0.65972511453561}, {-1.7592669720949605`, 0.6259891711786754}}]}, 
    {Arrowheads[{{0.015389465600533857`, 1.}}], 
     ArrowBox[{{-1.6543107038733862`, 
      0.8871303623490211}, {-1.7742607246980426`, 0.8271553519366929}}]}, 
    {Arrowheads[{{0.02029007078060253, 1.}}], 
     ArrowBox[{{-1.6393169512703043`, 
      1.1182840483132026`}, {-1.7892544773011245`, 1.0245730945439397`}}]}, 
    {Arrowheads[{{0.025808918415141213`, 1.}}], 
     ArrowBox[{{-1.6243231986672222`, 
      1.3531861724281546`}, {-1.8042482299042066`, 1.2182423990004163`}}]}, 
    {Arrowheads[{{0.032007799369224425`, 1.}}], 
     ArrowBox[{{-1.60932944606414, 1.591836734693877}, {-1.8192419825072887`, 
      1.4081632653061222`}}]}, 
    {Arrowheads[{{0.02425560388089663, 1.}}], 
     ArrowBox[{{-1.5014577259475221`, -1.4234693877551021`}, \
{-1.3556851311953355`, -1.576530612244898}}]}, 
    {Arrowheads[{{0.01929019363438374, 1.}}], 
     ArrowBox[{{-1.4910453977509375`, -1.2294877134527282`}, \
{-1.3660974593919204`, -1.3419408579758434`}}]}, 
    {Arrowheads[{{0.014935716675428949`, 1.}}], 
     ArrowBox[{{-1.4806330695543526`, -1.0323823406913788`}, \
{-1.376509787588505, -1.1104748021657644`}}]}, 
    {Arrowheads[{{0.011147449017531539`, 1.}}], 
     ArrowBox[{{-1.470220741357768, -0.832153269471054}, \
{-1.3869221157850897`, -0.8821324448146608}}]}, 
    {Arrowheads[{{0.007861580150836885, 1.}}], 
     ArrowBox[{{-1.459808413161183, -0.6288004997917536}, \
{-1.3973344439816744`, -0.6569137859225325}}]}, 
    {Arrowheads[{{0.0049898707206952, 1.}}], 
     ArrowBox[{{-1.4493960849645984`, -0.42232403165347787`}, \
{-1.4077467721782593`, -0.43481882548937956`}}]}, 
    {Arrowheads[{{0.002416449411670975, 1.}}], 
     ArrowBox[{{-1.4389837567680135`, -0.21272386505622673`}, \
{-1.418159100374844, -0.21584756351520215`}}]}, 
    {Arrowheads[{{0.002416449411670975, 1.}}], 
     ArrowBox[{{-1.4181591003748442`, 
      0.21584756351520182`}, {-1.4389837567680137`, 0.2127238650562264}}]}, 
    {Arrowheads[{{0.0049898707206952, 1.}}], 
     ArrowBox[{{-1.4077467721782593`, 
      0.4348188254893792}, {-1.4493960849645984`, 0.42232403165347754`}}]}, 
    {Arrowheads[{{0.00786158015083688, 1.}}], 
     ArrowBox[{{-1.3973344439816746`, 
      0.6569137859225321}, {-1.4598084131611833`, 0.6288004997917533}}]}, 
    {Arrowheads[{{0.011147449017531516`, 1.}}], 
     ArrowBox[{{-1.3869221157850897`, 
      0.8821324448146604}, {-1.4702207413577677`, 0.8321532694710535}}]}, 
    {Arrowheads[{{0.014935716675428949`, 1.}}], 
     ArrowBox[{{-1.376509787588505, 1.110474802165764}, {-1.4806330695543526`,
       1.0323823406913784`}}]}, 
    {Arrowheads[{{0.019290193634383758`, 1.}}], 
     ArrowBox[{{-1.3660974593919202`, 
      1.341940857975843}, {-1.4910453977509373`, 1.2294877134527276`}}]}, 
    {Arrowheads[{{0.024255603880896613`, 1.}}], 
     ArrowBox[{{-1.3556851311953355`, 
      1.5765306122448974`}, {-1.5014577259475221`, 1.4234693877551017`}}]}, 
    {Arrowheads[{{0.01766527772826241, 1.}}], 
     ArrowBox[{{-1.189504373177843, -1.4387755102040816`}, \
{-1.0962099125364435`, -1.5612244897959182`}}]}, 
    {Arrowheads[{{0.013812468092100322`, 1.}}], 
     ArrowBox[{{-1.1828404831320287`, -1.2407330279050397`}, \
{-1.1028738025822578`, -1.330695543523532}}]}, 
    {Arrowheads[{{0.010482106867782505`, 1.}}], 
     ArrowBox[{{-1.1761765930862145`, -1.0401915868388174`}, \
{-1.109537692628072, -1.102665556018326}}]}, 
    {Arrowheads[{{0.007647086937819628, 1.}}], 
     ArrowBox[{{-1.1695127030404002`, -0.8371511870054146}, \
{-1.1162015826738863`, -0.8771345272803001}}]}, 
    {Arrowheads[{{0.005264319576739231, 1.}}], 
     ArrowBox[{{-1.162848812994586, -0.6316118284048314}, \
{-1.1228654727197005`, -0.6541024573094545}}]}, 
    {Arrowheads[{{0.0032668369718749837`, 1.}}], 
     ArrowBox[{{-1.1561849229487717`, -0.42357351103706803`}, \
{-1.1295293627655147`, -0.4335693461057894}}]}, 
    {Arrowheads[{{0.0015560694542942899`, 1.}}], 
     ArrowBox[{{-1.1495210329029575`, -0.21303623490212426`}, \
{-1.136193252811329, -0.2155351936693046}}]}, 
    {Arrowheads[{{0.0015560694542942899`, 1.}}], 
     ArrowBox[{{-1.136193252811329, 
      0.21553519366930426`}, {-1.1495210329029575`, 
      0.21303623490212392`}}]}, 
    {Arrowheads[{{0.0032668369718749837`, 1.}}], 
     ArrowBox[{{-1.1295293627655147`, 
      0.43356934610578907`}, {-1.1561849229487717`, 0.4235735110370677}}]}, 
    {Arrowheads[{{0.005264319576739231, 1.}}], 
     ArrowBox[{{-1.1228654727197005`, 
      0.6541024573094543}, {-1.162848812994586, 0.6316118284048312}}]}, 
    {Arrowheads[{{0.007647086937819628, 1.}}], 
     ArrowBox[{{-1.1162015826738863`, 
      0.8771345272802997}, {-1.1695127030404002`, 0.8371511870054142}}]}, 
    {Arrowheads[{{0.010482106867782488`, 1.}}], 
     ArrowBox[{{-1.109537692628072, 
      1.1026655560183254`}, {-1.1761765930862145`, 1.040191586838817}}]}, 
    {Arrowheads[{{0.013812468092100322`, 1.}}], 
     ArrowBox[{{-1.1028738025822578`, 
      1.3306955435235315`}, {-1.1828404831320287`, 1.2407330279050393`}}]}, 
    {Arrowheads[{{0.01766527772826241, 1.}}], 
     ArrowBox[{{-1.0962099125364435`, 1.561224489795918}, {-1.189504373177843,
       1.4387755102040813`}}]}, 
    {Arrowheads[{{0.01213789222728119, 1.}}], 
     ArrowBox[{{-0.8833819241982511, -1.4540816326530612`}, \
{-0.830903790087464, -1.5459183673469388`}}]}, 
    {Arrowheads[{{0.009305537871005862, 1.}}], 
     ArrowBox[{{-0.8796334860474806, -1.2519783423573512`}, \
{-0.8346522282382344, -1.3194502290712204`}}]}, 
    {Arrowheads[{{0.006885737960246569, 1.}}], 
     ArrowBox[{{-0.8758850478967102, -1.048000832986256}, \
{-0.8384006663890049, -1.0948563098708872`}}]}, 
    {Arrowheads[{{0.004866576327049797, 1.}}], 
     ArrowBox[{{-0.8721366097459397, -0.8421491045397752}, \
{-0.8421491045397755, -0.8721366097459393}}]}, 
    {Arrowheads[{{0.003226114801892654, 1.}}], 
     ArrowBox[{{-0.8683881715951691, -0.6344231570179094}, \
{-0.8458975426905461, -0.6512911286963767}}]}, 
    {Arrowheads[{{0.0019236832000667393`, 1.}}], 
     ArrowBox[{{-0.8646397334443986, -0.4248229904206582}, \
{-0.8496459808413165, -0.43231986672219924`}}]}, 
    {Arrowheads[{{0.0008867741392381375, 1.}}], 
     ArrowBox[{{-0.8608912952936281, -0.2133486047480218}, \
{-0.853394418992087, -0.21522282382340707`}}]}, 
    {Arrowheads[{{0.0008867741392381375, 1.}}], 
     ArrowBox[{{-0.853394418992087, 
      0.21522282382340674`}, {-0.8608912952936281, 0.21334860474802148`}}]}, 
    {Arrowheads[{{0.0019236832000667247`, 1.}}], 
     ArrowBox[{{-0.8496459808413165, 
      0.4323198667221989}, {-0.8646397334443985, 0.4248229904206579}}]}, 
    {Arrowheads[{{0.003226114801892654, 1.}}], 
     ArrowBox[{{-0.845897542690546, 0.6512911286963763}, {-0.868388171595169, 
      0.634423157017909}}]}, 
    {Arrowheads[{{0.0048665763270497875`, 1.}}], 
     ArrowBox[{{-0.8421491045397755, 0.872136609745939}, {-0.8721366097459395,
       0.8421491045397749}}]}, 
    {Arrowheads[{{0.006885737960246581, 1.}}], 
     ArrowBox[{{-0.838400666389005, 
      1.0948563098708868`}, {-0.8758850478967102, 1.0480008329862553`}}]}, 
    {Arrowheads[{{0.009305537871005862, 1.}}], 
     ArrowBox[{{-0.8346522282382345, 1.31945022907122}, {-0.8796334860474807, 
      1.2519783423573507`}}]}, 
    {Arrowheads[{{0.01213789222728119, 1.}}], 
     ArrowBox[{{-0.830903790087464, 
      1.5459183673469383`}, {-0.8833819241982511, 1.4540816326530608`}}]}, 
    {Arrowheads[{{0.007518302125876299, 1.}}], 
     ArrowBox[{{-0.5830903790087468, -1.469387755102041}, \
{-0.559766763848397, -1.5306122448979593`}}]}, 
    {Arrowheads[{{0.005648630388641839, 1.}}], 
     ArrowBox[{{-0.5814244064972932, -1.2632236568096626`}, \
{-0.5614327363598505, -1.3082049146189088`}}]}, 
    {Arrowheads[{{0.0040625149357166705`, 1.}}], 
     ArrowBox[{{-0.5797584339858397, -1.0558100791336944`}, \
{-0.5630987088713041, -1.0870470637234486`}}]}, 
    {Arrowheads[{{0.002757196406223957, 1.}}], 
     ArrowBox[{{-0.5780924614743861, -0.847147022074136}, \
{-0.5647646813827576, -0.8671386922115787}}]}, 
    {Arrowheads[{{0.001726558511512545, 1.}}], 
     ArrowBox[{{-0.5764264889629326, -0.6372344856309873}, \
{-0.5664306538942112, -0.6484798000832989}}]}, 
    {Arrowheads[{{0.0009558858672274535, 1.}}], 
     ArrowBox[{{-0.574760516451479, -0.42607246980424834`}, \
{-0.5680966264056647, -0.43107038733860903`}}]}, 
    {Arrowheads[{{0.00040835462148437355`, 1.}}], 
     ArrowBox[{{-0.5730945439400255, -0.21366097459391936`}, \
{-0.5697625989171183, -0.21491045397750955`}}]}, 
    {Arrowheads[{{0.0004083546214843724, 1.}}], 
     ArrowBox[{{-0.5697625989171182, 
      0.21491045397750919`}, {-0.5730945439400253, 0.21366097459391903`}}]}, 
    {Arrowheads[{{0.0009558858672274535, 1.}}], 
     ArrowBox[{{-0.5680966264056647, 0.4310703873386087}, {-0.574760516451479,
       0.426072469804248}}]}, 
    {Arrowheads[{{0.001726558511512545, 1.}}], 
     ArrowBox[{{-0.5664306538942111, 
      0.6484798000832984}, {-0.5764264889629325, 0.6372344856309868}}]}, 
    {Arrowheads[{{0.002757196406223957, 1.}}], 
     ArrowBox[{{-0.5647646813827576, 
      0.8671386922115784}, {-0.5780924614743861, 0.8471470220741356}}]}, 
    {Arrowheads[{{0.0040625149357166705`, 1.}}], 
     ArrowBox[{{-0.563098708871304, 
      1.0870470637234484`}, {-0.5797584339858396, 1.0558100791336942`}}]}, 
    {Arrowheads[{{0.005648630388641839, 1.}}], 
     ArrowBox[{{-0.5614327363598505, 
      1.3082049146189085`}, {-0.5814244064972932, 1.2632236568096624`}}]}, 
    {Arrowheads[{{0.007518302125876299, 1.}}], 
     ArrowBox[{{-0.5597667638483969, 
      1.5306122448979587`}, {-0.5830903790087467, 1.4693877551020402`}}]}, 
    {Arrowheads[{{0.0035760385290117187`, 1.}}], 
     ArrowBox[{{-0.28862973760932986`, -1.4846938775510203`}, \
{-0.28279883381924237`, -1.5153061224489797`}}]}, 
    {Arrowheads[{{0.0026438496747004515`, 1.}}], 
     ArrowBox[{{-0.2882132444814665, -1.2744689712619743`}, \
{-0.2832153269471058, -1.2969596001665975`}}]}, 
    {Arrowheads[{{0.0018549173990656347`, 1.}}], 
     ArrowBox[{{-0.2877967513536031, -1.063619325281133}, \
{-0.2836318200749692, -1.0792378175760102`}}]}, 
    {Arrowheads[{{0.0012091106094416215`, 1.}}], 
     ArrowBox[{{-0.2873802582257397, -0.8521449396084966}, \
{-0.2840483132028326, -0.862140774677218}}]}, 
    {Arrowheads[{{0.0007060787985802283, 1.}}], 
     ArrowBox[{{-0.2869637650978763, -0.6400458142440651}, \
{-0.28446480633069593`, -0.6456684714702209}}]}, 
    {Arrowheads[{{0.0003446495507779973, 1.}}], 
     ArrowBox[{{-0.28654727197001295`, -0.42732194918783856`}, \
{-0.2848812994585594, -0.4298209079550189}}]}, 
    {Arrowheads[{{0.00011948573340343375`, 1.}}], 
     ArrowBox[{{-0.28613077884214955`, -0.2139733444398169}, \
{-0.28529779258642274`, -0.21459808413161197`}}]}, 
    {Arrowheads[{{0.00011948573340343375`, 1.}}], 
     ArrowBox[{{-0.28529779258642274`, 
      0.21459808413161166`}, {-0.28613077884214955`, 0.21397334443981658`}}]}, 
    {Arrowheads[{{0.0003446495507779973, 1.}}], 
     ArrowBox[{{-0.28488129945855933`, 
      0.42982090795501854`}, {-0.2865472719700129, 0.42732194918783817`}}]}, 
    {Arrowheads[{{0.0007060787985802283, 1.}}], 
     ArrowBox[{{-0.284464806330696, 
      0.6456684714702206}, {-0.28696376509787636`, 0.6400458142440648}}]}, 
    {Arrowheads[{{0.0012091106094416215`, 1.}}], 
     ArrowBox[{{-0.2840483132028326, 
      0.8621407746772177}, {-0.2873802582257397, 0.8521449396084964}}]}, 
    {Arrowheads[{{0.0018549173990656347`, 1.}}], 
     ArrowBox[{{-0.2836318200749692, 
      1.0792378175760098`}, {-0.2877967513536031, 1.0636193252811326`}}]}, 
    {Arrowheads[{{0.0026438496747004515`, 1.}}], 
     ArrowBox[{{-0.28321532694710577`, 
      1.2969596001665968`}, {-0.28821324448146646`, 1.2744689712619737`}}]}, 
    {Arrowheads[{{0.003576038529011694, 1.}}], 
     ArrowBox[{{-0.2827988338192424, 
      1.5153061224489792`}, {-0.2886297376093299, 1.4846938775510201`}}]}, 
    {Arrowheads[{{0.0035760385290116927`, 1.}}], 
     ArrowBox[{{0.28279883381924154`, -1.5153061224489797`}, {
      0.288629737609329, -1.4846938775510206`}}]}, 
    {Arrowheads[{{0.0026438496747004264`, 1.}}], 
     ArrowBox[{{0.28321532694710494`, -1.2969596001665973`}, {
      0.2882132444814656, -1.2744689712619743`}}]}, 
    {Arrowheads[{{0.001854917399065633, 1.}}], 
     ArrowBox[{{0.2836318200749683, -1.0792378175760102`}, {
      0.28779675135360216`, -1.063619325281133}}]}, 
    {Arrowheads[{{0.0012091106094416215`, 1.}}], 
     ArrowBox[{{0.2840483132028317, -0.862140774677218}, {
      0.2873802582257388, -0.8521449396084966}}]}, 
    {Arrowheads[{{0.0007060787985802257, 1.}}], 
     ArrowBox[{{0.2844648063306951, -0.6456684714702209}, {
      0.2869637650978754, -0.6400458142440651}}]}, 
    {Arrowheads[{{0.000344649550777992, 1.}}], 
     ArrowBox[{{0.2848812994585585, -0.42982090795501887`}, {
      0.28654727197001206`, -0.42732194918783856`}}]}, 
    {Arrowheads[{{0.00011948573340342866`, 1.}}], 
     ArrowBox[{{0.28529779258642185`, -0.214598084131612}, {
      0.2861307788421486, -0.21397334443981691`}}]}, 
    {Arrowheads[{{0.00011948573340342866`, 1.}}], 
     ArrowBox[{{0.28613077884214866`, 0.21397334443981655`}, {
      0.2852977925864219, 0.21459808413161163`}}]}, 
    {Arrowheads[{{0.000344649550777992, 1.}}], 
     ArrowBox[{{0.286547271970012, 0.4273219491878382}, {0.28488129945855845`,
       0.42982090795501854`}}]}, 
    {Arrowheads[{{0.0007060787985802257, 1.}}], 
     ArrowBox[{{0.2869637650978754, 0.6400458142440648}, {0.2844648063306951, 
      0.6456684714702206}}]}, 
    {Arrowheads[{{0.0012091106094416215`, 1.}}], 
     ArrowBox[{{0.2873802582257388, 0.8521449396084964}, {0.2840483132028317, 
      0.8621407746772177}}]}, 
    {Arrowheads[{{0.0018549173990656084`, 1.}}], 
     ArrowBox[{{0.2877967513536022, 1.0636193252811326`}, {
      0.28363182007496834`, 1.0792378175760096`}}]}, 
    {Arrowheads[{{0.0026438496747004264`, 1.}}], 
     ArrowBox[{{0.28821324448146557`, 1.274468971261974}, {0.2832153269471049,
       1.2969596001665968`}}]}, 
    {Arrowheads[{{0.0035760385290116927`, 1.}}], 
     ArrowBox[{{0.288629737609329, 1.48469387755102}, {0.28279883381924154`, 
      1.515306122448979}}]}, 
    {Arrowheads[{{0.007518302125876276, 1.}}], 
     ArrowBox[{{0.5597667638483961, -1.530612244897959}, {
      0.5830903790087459, -1.469387755102041}}]}, 
    {Arrowheads[{{0.005648630388641839, 1.}}], 
     ArrowBox[{{0.5614327363598496, -1.308204914618909}, {
      0.5814244064972923, -1.2632236568096629`}}]}, 
    {Arrowheads[{{0.0040625149357166705`, 1.}}], 
     ArrowBox[{{0.5630987088713032, -1.0870470637234488`}, {
      0.5797584339858388, -1.0558100791336946`}}]}, 
    {Arrowheads[{{0.002757196406223957, 1.}}], 
     ArrowBox[{{0.5647646813827567, -0.8671386922115787}, {
      0.5780924614743852, -0.847147022074136}}]}, 
    {Arrowheads[{{0.001726558511512545, 1.}}], 
     ArrowBox[{{0.5664306538942103, -0.6484798000832988}, {
      0.5764264889629317, -0.6372344856309872}}]}, 
    {Arrowheads[{{0.0009558858672274535, 1.}}], 
     ArrowBox[{{0.5680966264056638, -0.43107038733860903`}, {
      0.5747605164514781, -0.42607246980424834`}}]}, 
    {Arrowheads[{{0.00040835462148437355`, 1.}}], 
     ArrowBox[{{0.5697625989171174, -0.21491045397750952`}, {
      0.5730945439400246, -0.21366097459391933`}}]}, 
    {Arrowheads[{{0.0004083546214843724, 1.}}], 
     ArrowBox[{{0.5730945439400245, 0.21366097459391903`}, {
      0.5697625989171173, 0.21491045397750919`}}]}, 
    {Arrowheads[{{0.0009558858672274535, 1.}}], 
     ArrowBox[{{0.5747605164514781, 0.42607246980424807`}, {
      0.5680966264056638, 0.43107038733860875`}}]}, 
    {Arrowheads[{{0.0017265585115125355`, 1.}}], 
     ArrowBox[{{0.5764264889629316, 0.637234485630987}, {0.5664306538942102, 
      0.6484798000832984}}]}, 
    {Arrowheads[{{0.002757196406223957, 1.}}], 
     ArrowBox[{{0.5780924614743852, 0.8471470220741356}, {0.5647646813827567, 
      0.8671386922115784}}]}, 
    {Arrowheads[{{0.0040625149357166705`, 1.}}], 
     ArrowBox[{{0.5797584339858387, 1.055810079133694}, {0.5630987088713031, 
      1.0870470637234482`}}]}, 
    {Arrowheads[{{0.005648630388641839, 1.}}], 
     ArrowBox[{{0.5814244064972923, 1.2632236568096624`}, {0.5614327363598496,
       1.3082049146189085`}}]}, 
    {Arrowheads[{{0.0075183021258762705`, 1.}}], 
     ArrowBox[{{0.5830903790087458, 1.4693877551020404`}, {0.5597667638483961,
       1.5306122448979587`}}]}, 
    {Arrowheads[{{0.012137892227281183`, 1.}}], 
     ArrowBox[{{0.8309037900874631, -1.5459183673469388`}, {
      0.8833819241982501, -1.4540816326530612`}}]}, 
    {Arrowheads[{{0.009305537871005855, 1.}}], 
     ArrowBox[{{0.8346522282382336, -1.3194502290712204`}, {
      0.8796334860474797, -1.2519783423573512`}}]}, 
    {Arrowheads[{{0.0068857379602465735`, 1.}}], 
     ArrowBox[{{0.8384006663890041, -1.0948563098708872`}, {
      0.8758850478967092, -1.0480008329862558`}}]}, 
    {Arrowheads[{{0.004866576327049797, 1.}}], 
     ArrowBox[{{0.8421491045397747, -0.8721366097459393}, {
      0.8721366097459388, -0.8421491045397752}}]}, 
    {Arrowheads[{{0.003226114801892654, 1.}}], 
     ArrowBox[{{0.8458975426905452, -0.6512911286963766}, {
      0.8683881715951682, -0.6344231570179093}}]}, 
    {Arrowheads[{{0.0019236832000667247`, 1.}}], 
     ArrowBox[{{0.8496459808413156, -0.43231986672219924`}, {
      0.8646397334443976, -0.42482299042065824`}}]}, 
    {Arrowheads[{{0.0008867741392381375, 1.}}], 
     ArrowBox[{{0.8533944189920861, -0.21522282382340707`}, {
      0.8608912952936272, -0.2133486047480218}}]}, 
    {Arrowheads[{{0.0008867741392381375, 1.}}], 
     ArrowBox[{{0.8608912952936272, 0.21334860474802148`}, {
      0.8533944189920861, 0.21522282382340674`}}]}, 
    {Arrowheads[{{0.0019236832000667247`, 1.}}], 
     ArrowBox[{{0.8646397334443977, 0.42482299042065785`}, {
      0.8496459808413157, 0.43231986672219885`}}]}, 
    {Arrowheads[{{0.003226114801892654, 1.}}], 
     ArrowBox[{{0.8683881715951681, 0.6344231570179091}, {0.8458975426905451, 
      0.6512911286963764}}]}, 
    {Arrowheads[{{0.0048665763270497875`, 1.}}], 
     ArrowBox[{{0.8721366097459387, 0.842149104539775}, {0.8421491045397747, 
      0.8721366097459391}}]}, 
    {Arrowheads[{{0.0068857379602465735`, 1.}}], 
     ArrowBox[{{0.8758850478967092, 1.0480008329862556`}, {0.8384006663890041,
       1.094856309870887}}]}, 
    {Arrowheads[{{0.009305537871005834, 1.}}], 
     ArrowBox[{{0.8796334860474797, 1.2519783423573507`}, {0.8346522282382336,
       1.3194502290712198`}}]}, 
    {Arrowheads[{{0.012137892227281183`, 1.}}], 
     ArrowBox[{{0.8833819241982502, 1.4540816326530608`}, {0.8309037900874632,
       1.5459183673469383`}}]}, 
    {Arrowheads[{{0.01766527772826239, 1.}}], 
     ArrowBox[{{1.0962099125364426`, -1.5612244897959184`}, {
      1.1895043731778419`, -1.4387755102040818`}}]}, 
    {Arrowheads[{{0.013812468092100322`, 1.}}], 
     ArrowBox[{{1.1028738025822569`, -1.330695543523532}, {
      1.1828404831320278`, -1.2407330279050397`}}]}, 
    {Arrowheads[{{0.010482106867782488`, 1.}}], 
     ArrowBox[{{1.1095376926280711`, -1.1026655560183258`}, {
      1.1761765930862136`, -1.0401915868388174`}}]}, 
    {Arrowheads[{{0.007647086937819628, 1.}}], 
     ArrowBox[{{1.1162015826738854`, -0.8771345272803001}, {
      1.1695127030403993`, -0.8371511870054146}}]}, 
    {Arrowheads[{{0.005264319576739231, 1.}}], 
     ArrowBox[{{1.1228654727196996`, -0.6541024573094546}, {
      1.162848812994585, -0.6316118284048315}}]}, 
    {Arrowheads[{{0.0032668369718749837`, 1.}}], 
     ArrowBox[{{1.1295293627655139`, -0.4335693461057894}, {
      1.1561849229487708`, -0.42357351103706803`}}]}, 
    {Arrowheads[{{0.0015560694542942899`, 1.}}], 
     ArrowBox[{{1.136193252811328, -0.21553519366930463`}, {
      1.1495210329029566`, -0.21303623490212428`}}]}, 
    {Arrowheads[{{0.0015560694542942899`, 1.}}], 
     ArrowBox[{{1.1495210329029566`, 0.21303623490212395`}, {
      1.136193252811328, 0.2155351936693043}}]}, 
    {Arrowheads[{{0.0032668369718749837`, 1.}}], 
     ArrowBox[{{1.1561849229487708`, 0.4235735110370677}, {
      1.1295293627655139`, 0.43356934610578907`}}]}, 
    {Arrowheads[{{0.005264319576739231, 1.}}], 
     ArrowBox[{{1.162848812994585, 0.6316118284048312}, {1.1228654727196996`, 
      0.6541024573094543}}]}, 
    {Arrowheads[{{0.0076470869378196206`, 1.}}], 
     ArrowBox[{{1.1695127030403993`, 0.8371511870054142}, {
      1.1162015826738854`, 0.8771345272802996}}]}, 
    {Arrowheads[{{0.010482106867782488`, 1.}}], 
     ArrowBox[{{1.1761765930862136`, 1.040191586838817}, {1.1095376926280711`,
       1.1026655560183254`}}]}, 
    {Arrowheads[{{0.013812468092100304`, 1.}}], 
     ArrowBox[{{1.1828404831320278`, 1.2407330279050393`}, {1.102873802582257,
       1.3306955435235315`}}]}, 
    {Arrowheads[{{0.01766527772826239, 1.}}], 
     ArrowBox[{{1.189504373177842, 1.4387755102040813`}, {1.0962099125364428`,
       1.561224489795918}}]}, 
    {Arrowheads[{{0.024255603880896596`, 1.}}], 
     ArrowBox[{{1.3556851311953346`, -1.5765306122448979`}, {
      1.501457725947521, -1.4234693877551021`}}]}, 
    {Arrowheads[{{0.01929019363438374, 1.}}], 
     ArrowBox[{{1.3660974593919195`, -1.3419408579758434`}, {
      1.4910453977509364`, -1.229487713452728}}]}, 
    {Arrowheads[{{0.014935716675428949`, 1.}}], 
     ArrowBox[{{1.3765097875885042`, -1.1104748021657644`}, {
      1.4806330695543517`, -1.0323823406913788`}}]}, 
    {Arrowheads[{{0.011147449017531516`, 1.}}], 
     ArrowBox[{{1.3869221157850888`, -0.8821324448146607}, {
      1.4702207413577668`, -0.8321532694710538}}]}, 
    {Arrowheads[{{0.007861580150836855, 1.}}], 
     ArrowBox[{{1.3973344439816737`, -0.6569137859225325}, {
      1.4598084131611822`, -0.6288004997917537}}]}, 
    {Arrowheads[{{0.0049898707206952, 1.}}], 
     ArrowBox[{{1.4077467721782584`, -0.43481882548937956`}, {
      1.4493960849645975`, -0.42232403165347787`}}]}, 
    {Arrowheads[{{0.002416449411670975, 1.}}], 
     ArrowBox[{{1.4181591003748433`, -0.21584756351520215`}, {
      1.4389837567680128`, -0.21272386505622673`}}]}, 
    {Arrowheads[{{0.002416449411670975, 1.}}], 
     ArrowBox[{{1.4389837567680126`, 0.2127238650562264}, {1.418159100374843, 
      0.21584756351520182`}}]}, 
    {Arrowheads[{{0.004989870720695175, 1.}}], 
     ArrowBox[{{1.4493960849645975`, 0.42232403165347754`}, {
      1.4077467721782586`, 0.4348188254893792}}]}, 
    {Arrowheads[{{0.007861580150836855, 1.}}], 
     ArrowBox[{{1.4598084131611822`, 0.6288004997917532}, {
      1.3973344439816737`, 0.656913785922532}}]}, 
    {Arrowheads[{{0.01114744901753151, 1.}}], 
     ArrowBox[{{1.4702207413577668`, 0.8321532694710536}, {
      1.3869221157850888`, 0.8821324448146604}}]}, 
    {Arrowheads[{{0.014935716675428949`, 1.}}], 
     ArrowBox[{{1.4806330695543517`, 1.0323823406913784`}, {
      1.3765097875885042`, 1.110474802165764}}]}, 
    {Arrowheads[{{0.01929019363438372, 1.}}], 
     ArrowBox[{{1.4910453977509364`, 1.2294877134527278`}, {
      1.3660974593919195`, 1.341940857975843}}]}, 
    {Arrowheads[{{0.024255603880896596`, 1.}}], 
     ArrowBox[{{1.501457725947521, 1.4234693877551017`}, {1.3556851311953346`,
       1.5765306122448974`}}]}, 
    {Arrowheads[{{0.03200779936922443, 1.}}], 
     ArrowBox[{{1.6093294460641392`, -1.5918367346938775`}, {
      1.8192419825072879`, -1.4081632653061225`}}]}, 
    {Arrowheads[{{0.025808918415141213`, 1.}}], 
     ArrowBox[{{1.6243231986672213`, -1.353186172428155}, {
      1.8042482299042057`, -1.2182423990004168`}}]}, 
    {Arrowheads[{{0.02029007078060255, 1.}}], 
     ArrowBox[{{1.6393169512703034`, -1.118284048313203}, {
      1.7892544773011239`, -1.0245730945439402`}}]}, 
    {Arrowheads[{{0.015389465600533834`, 1.}}], 
     ArrowBox[{{1.6543107038733853`, -0.8871303623490214}, {
      1.7742607246980415`, -0.8271553519366932}}]}, 
    {Arrowheads[{{0.01102557478007806, 1.}}], 
     ArrowBox[{{1.6693044564764674`, -0.6597251145356103}, {
      1.7592669720949596`, -0.6259891711786757}}]}, 
    {Arrowheads[{{0.007094193113905074, 1.}}], 
     ArrowBox[{{1.6842982090795495`, -0.4360683048729697}, {
      1.7442732194918777`, -0.42107455226988766`}}]}, 
    {Arrowheads[{{0.0034679692077946144`, 1.}}], 
     ArrowBox[{{1.6992919616826314`, -0.2161599333610997}, {
      1.7292794668887954`, -0.21241149521032918`}}]}, 
    {Arrowheads[{{0.003467969207794614, 1.}}], 
     ArrowBox[{{1.7292794668887956`, 0.21241149521032884`}, {
      1.6992919616826316`, 0.21615993336109934`}}]}, 
    {Arrowheads[{{0.007094193113905047, 1.}}], 
     ArrowBox[{{1.7442732194918775`, 0.4210745522698874}, {
      1.6842982090795495`, 0.4360683048729694}}]}, 
    {Arrowheads[{{0.011025574780078054`, 1.}}], 
     ArrowBox[{{1.7592669720949596`, 0.6259891711786754}, {
      1.6693044564764674`, 0.6597251145356099}}]}, 
    {Arrowheads[{{0.015389465600533827`, 1.}}], 
     ArrowBox[{{1.7742607246980417`, 0.8271553519366929}, {
      1.6543107038733855`, 0.887130362349021}}]}, 
    {Arrowheads[{{0.020290070780602517`, 1.}}], 
     ArrowBox[{{1.7892544773011236`, 1.0245730945439397`}, {
      1.6393169512703034`, 1.1182840483132024`}}]}, 
    {Arrowheads[{{0.025808918415141213`, 1.}}], 
     ArrowBox[{{1.8042482299042057`, 1.2182423990004163`}, {
      1.6243231986672213`, 1.3531861724281546`}}]}, 
    {Arrowheads[{{0.032007799369224404`, 1.}}], 
     ArrowBox[{{1.8192419825072876`, 1.4081632653061222`}, {
      1.6093294460641392`, 1.591836734693877}}]}, 
    {Arrowheads[{{0.04098360655737703, 1.}}], 
     ArrowBox[{{1.8571428571428563`, -1.607142857142857}, {
      2.142857142857142, -1.3928571428571428`}}]}, 
    {Arrowheads[{{0.03340913411259935, 1.}}], 
     ArrowBox[{{1.8775510204081625`, -1.3644314868804666`}, {
      2.122448979591836, -1.206997084548105}}]}, 
    {Arrowheads[{{0.026568049806404453`, 1.}}], 
     ArrowBox[{{1.8979591836734686`, -1.1260932944606417`}, {
      2.1020408163265296`, -1.0167638483965016`}}]}, 
    {Arrowheads[{{0.02038346766373741, 1.}}], 
     ArrowBox[{{1.9183673469387748`, -0.8921282798833821}, {
      2.0816326530612232`, -0.8221574344023325}}]}, 
    {Arrowheads[{{0.014759559554887298`, 1.}}], 
     ArrowBox[{{1.938775510204081, -0.6625364431486882}, {
      2.0612244897959173`, -0.6231778425655978}}]}, 
    {Arrowheads[{{0.009580341962714197, 1.}}], 
     ArrowBox[{{1.9591836734693868`, -0.4373177842565599}, {
      2.0408163265306114`, -0.41982507288629756`}}]}, 
    {Arrowheads[{{0.004710648323964141, 1.}}], 
     ArrowBox[{{1.979591836734693, -0.21647230320699723`}, {
      2.0204081632653055`, -0.21209912536443162`}}]}, 
    {Arrowheads[{{0.004710648323964064, 1.}}], 
     ArrowBox[{{2.020408163265305, 0.21209912536443132`}, {
      1.9795918367346932`, 0.2164723032069969}}]}, 
    {Arrowheads[{{0.009580341962714173, 1.}}], 
     ArrowBox[{{2.0408163265306114`, 0.4198250728862972}, {1.959183673469387, 
      0.4373177842565596}}]}, 
    {Arrowheads[{{0.01475955955488732, 1.}}], 
     ArrowBox[{{2.0612244897959173`, 0.6231778425655975}, {
      1.9387755102040807`, 0.6625364431486879}}]}, 
    {Arrowheads[{{0.020383467663737453`, 1.}}], 
     ArrowBox[{{2.0816326530612237`, 0.8221574344023322}, {
      1.9183673469387748`, 0.8921282798833817}}]}, 
    {Arrowheads[{{0.026568049806404447`, 1.}}], 
     ArrowBox[{{2.1020408163265296`, 1.0167638483965014`}, {
      1.8979591836734686`, 1.1260932944606412`}}]}, 
    {Arrowheads[{{0.033409134112599284`, 1.}}], 
     ArrowBox[{{2.1224489795918355`, 1.2069970845481046`}, {
      1.8775510204081625`, 1.364431486880466}}]}, 
    {Arrowheads[{{0.04098360655737702, 1.}}], 
     ArrowBox[{{2.142857142857142, 1.3928571428571426`}, {1.8571428571428563`,
       1.6071428571428565`}}]}}},
  AspectRatio->1,
  DisplayFunction->Identity,
  Frame->True,
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
    "TransparentPolygonMesh" -> True},
  PlotRange->{{-2.1785714285714284`, 
   2.1785714285714284`}, {-1.6785714285714286`, 1.6785714285714286`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{None, None}, {None, None}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.816310479034214*^9, 3.816310507975004*^9}, {
   3.816310564520734*^9, 3.816310614826962*^9}, 3.8163152809817467`*^9, 
   3.81631547980837*^9, {3.816318437441739*^9, 3.816318446681157*^9}},
 CellLabel->
  "Out[137]=",ExpressionUUID->"1c56aa61-0239-499e-a0c3-603bfa293c05"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"%", ",", " ", 
   RowBox[{"PolarPlot", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"c", "[", "\[Theta]", "]"}], "/.", 
      RowBox[{"a", "\[Rule]", " ", "1"}]}], ",", " ", 
     RowBox[{"{", 
      RowBox[{"\[Theta]", ",", " ", "0", ",", " ", 
       RowBox[{"2", "\[Pi]"}]}], "}"}]}], "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.816310511193996*^9, 3.816310534396007*^9}, {
  3.816310573750292*^9, 3.8163105756179523`*^9}},
 CellLabel->
  "In[138]:=",ExpressionUUID->"b3a56e8f-4120-4267-a7c3-fef7772e4aa9"],

Cell[BoxData[
 GraphicsBox[{{{}, 
    {RGBColor[0.2947336, 0.4054232, 0.5678384000000001], 
     {Arrowheads[{{0.04098360655737703, 1.}}], 
      ArrowBox[{{-2.142857142857143, -1.3928571428571428`}, \
{-1.8571428571428572`, -1.607142857142857}}]}, 
     {Arrowheads[{{0.03340913411259937, 1.}}], 
      ArrowBox[{{-2.122448979591837, -1.206997084548105}, \
{-1.8775510204081631`, -1.3644314868804666`}}]}, 
     {Arrowheads[{{0.026568049806404453`, 1.}}], 
      ArrowBox[{{-2.1020408163265305`, -1.0167638483965016`}, \
{-1.8979591836734695`, -1.1260932944606417`}}]}, 
     {Arrowheads[{{0.020383467663737456`, 1.}}], 
      ArrowBox[{{-2.0816326530612246`, -0.8221574344023326}, \
{-1.9183673469387756`, -0.8921282798833822}}]}, 
     {Arrowheads[{{0.014759559554887298`, 1.}}], 
      ArrowBox[{{-2.061224489795918, -0.6231778425655978}, \
{-1.9387755102040818`, -0.6625364431486882}}]}, 
     {Arrowheads[{{0.0095803419627142, 1.}}], 
      ArrowBox[{{-2.0408163265306123`, -0.4198250728862975}, \
{-1.9591836734693877`, -0.4373177842565599}}]}, 
     {Arrowheads[{{0.0047106483239640895`, 1.}}], 
      ArrowBox[{{-2.020408163265306, -0.21209912536443165`}, \
{-1.9795918367346939`, -0.21647230320699726`}}]}, 
     {Arrowheads[{{0.00471064832396414, 1.}}], 
      ArrowBox[{{-1.9795918367346939`, 
       0.2164723032069969}, {-2.0204081632653064`, 0.21209912536443132`}}]}, 
     {Arrowheads[{{0.009580341962714197, 1.}}], 
      ArrowBox[{{-1.9591836734693877`, 
       0.4373177842565596}, {-2.0408163265306123`, 0.4198250728862972}}]}, 
     {Arrowheads[{{0.01475955955488737, 1.}}], 
      ArrowBox[{{-1.9387755102040816`, 
       0.6625364431486879}, {-2.0612244897959187`, 0.6231778425655975}}]}, 
     {Arrowheads[{{0.020383467663737404`, 1.}}], 
      ArrowBox[{{-1.9183673469387756`, 
       0.8921282798833817}, {-2.081632653061224, 0.8221574344023322}}]}, 
     {Arrowheads[{{0.026568049806404447`, 1.}}], 
      ArrowBox[{{-1.8979591836734695`, 
       1.1260932944606412`}, {-2.1020408163265305`, 1.0167638483965014`}}]}, 
     {Arrowheads[{{0.033409134112599305`, 1.}}], 
      ArrowBox[{{-1.8775510204081634`, 
       1.3644314868804661`}, {-2.1224489795918364`, 1.2069970845481046`}}]}, 
     {Arrowheads[{{0.04098360655737703, 1.}}], 
      ArrowBox[{{-1.8571428571428572`, 
       1.6071428571428565`}, {-2.142857142857143, 1.3928571428571423`}}]}, 
     {Arrowheads[{{0.03200779936922443, 1.}}], 
      ArrowBox[{{-1.8192419825072887`, -1.4081632653061225`}, \
{-1.60932944606414, -1.5918367346938775`}}]}, 
     {Arrowheads[{{0.025808918415141234`, 1.}}], 
      ArrowBox[{{-1.8042482299042066`, -1.2182423990004165`}, \
{-1.624323198667222, -1.3531861724281549`}}]}, 
     {Arrowheads[{{0.02029007078060255, 1.}}], 
      ArrowBox[{{-1.7892544773011247`, -1.0245730945439402`}, \
{-1.6393169512703043`, -1.118284048313203}}]}, 
     {Arrowheads[{{0.015389465600533857`, 1.}}], 
      ArrowBox[{{-1.7742607246980426`, -0.8271553519366932}, \
{-1.6543107038733862`, -0.8871303623490214}}]}, 
     {Arrowheads[{{0.01102557478007806, 1.}}], 
      ArrowBox[{{-1.7592669720949605`, -0.6259891711786757}, \
{-1.6693044564764683`, -0.6597251145356103}}]}, 
     {Arrowheads[{{0.007094193113905074, 1.}}], 
      ArrowBox[{{-1.7442732194918786`, -0.42107455226988766`}, \
{-1.6842982090795504`, -0.4360683048729697}}]}, 
     {Arrowheads[{{0.00346796920779464, 1.}}], 
      ArrowBox[{{-1.7292794668887965`, -0.21241149521032918`}, \
{-1.6992919616826323`, -0.2161599333610997}}]}, 
     {Arrowheads[{{0.003467969207794614, 1.}}], 
      ArrowBox[{{-1.6992919616826323`, 
       0.21615993336109937`}, {-1.7292794668887963`, 0.21241149521032887`}}]}, 
     {Arrowheads[{{0.007094193113905074, 1.}}], 
      ArrowBox[{{-1.6842982090795504`, 
       0.4360683048729694}, {-1.7442732194918786`, 0.4210745522698873}}]}, 
     {Arrowheads[{{0.01102557478007806, 1.}}], 
      ArrowBox[{{-1.6693044564764683`, 
       0.65972511453561}, {-1.7592669720949605`, 0.6259891711786754}}]}, 
     {Arrowheads[{{0.015389465600533857`, 1.}}], 
      ArrowBox[{{-1.6543107038733862`, 
       0.8871303623490211}, {-1.7742607246980426`, 0.8271553519366929}}]}, 
     {Arrowheads[{{0.02029007078060253, 1.}}], 
      ArrowBox[{{-1.6393169512703043`, 
       1.1182840483132026`}, {-1.7892544773011245`, 1.0245730945439397`}}]}, 
     {Arrowheads[{{0.025808918415141213`, 1.}}], 
      ArrowBox[{{-1.6243231986672222`, 
       1.3531861724281546`}, {-1.8042482299042066`, 1.2182423990004163`}}]}, 
     {Arrowheads[{{0.032007799369224425`, 1.}}], 
      ArrowBox[{{-1.60932944606414, 1.591836734693877}, {-1.8192419825072887`,
        1.4081632653061222`}}]}, 
     {Arrowheads[{{0.02425560388089663, 1.}}], 
      ArrowBox[{{-1.5014577259475221`, -1.4234693877551021`}, \
{-1.3556851311953355`, -1.576530612244898}}]}, 
     {Arrowheads[{{0.01929019363438374, 1.}}], 
      ArrowBox[{{-1.4910453977509375`, -1.2294877134527282`}, \
{-1.3660974593919204`, -1.3419408579758434`}}]}, 
     {Arrowheads[{{0.014935716675428949`, 1.}}], 
      ArrowBox[{{-1.4806330695543526`, -1.0323823406913788`}, \
{-1.376509787588505, -1.1104748021657644`}}]}, 
     {Arrowheads[{{0.011147449017531539`, 1.}}], 
      ArrowBox[{{-1.470220741357768, -0.832153269471054}, \
{-1.3869221157850897`, -0.8821324448146608}}]}, 
     {Arrowheads[{{0.007861580150836885, 1.}}], 
      ArrowBox[{{-1.459808413161183, -0.6288004997917536}, \
{-1.3973344439816744`, -0.6569137859225325}}]}, 
     {Arrowheads[{{0.0049898707206952, 1.}}], 
      ArrowBox[{{-1.4493960849645984`, -0.42232403165347787`}, \
{-1.4077467721782593`, -0.43481882548937956`}}]}, 
     {Arrowheads[{{0.002416449411670975, 1.}}], 
      ArrowBox[{{-1.4389837567680135`, -0.21272386505622673`}, \
{-1.418159100374844, -0.21584756351520215`}}]}, 
     {Arrowheads[{{0.002416449411670975, 1.}}], 
      ArrowBox[{{-1.4181591003748442`, 
       0.21584756351520182`}, {-1.4389837567680137`, 0.2127238650562264}}]}, 
     {Arrowheads[{{0.0049898707206952, 1.}}], 
      ArrowBox[{{-1.4077467721782593`, 
       0.4348188254893792}, {-1.4493960849645984`, 0.42232403165347754`}}]}, 
     {Arrowheads[{{0.00786158015083688, 1.}}], 
      ArrowBox[{{-1.3973344439816746`, 
       0.6569137859225321}, {-1.4598084131611833`, 0.6288004997917533}}]}, 
     {Arrowheads[{{0.011147449017531516`, 1.}}], 
      ArrowBox[{{-1.3869221157850897`, 
       0.8821324448146604}, {-1.4702207413577677`, 0.8321532694710535}}]}, 
     {Arrowheads[{{0.014935716675428949`, 1.}}], 
      ArrowBox[{{-1.376509787588505, 
       1.110474802165764}, {-1.4806330695543526`, 1.0323823406913784`}}]}, 
     {Arrowheads[{{0.019290193634383758`, 1.}}], 
      ArrowBox[{{-1.3660974593919202`, 
       1.341940857975843}, {-1.4910453977509373`, 1.2294877134527276`}}]}, 
     {Arrowheads[{{0.024255603880896613`, 1.}}], 
      ArrowBox[{{-1.3556851311953355`, 
       1.5765306122448974`}, {-1.5014577259475221`, 1.4234693877551017`}}]}, 
     {Arrowheads[{{0.01766527772826241, 1.}}], 
      ArrowBox[{{-1.189504373177843, -1.4387755102040816`}, \
{-1.0962099125364435`, -1.5612244897959182`}}]}, 
     {Arrowheads[{{0.013812468092100322`, 1.}}], 
      ArrowBox[{{-1.1828404831320287`, -1.2407330279050397`}, \
{-1.1028738025822578`, -1.330695543523532}}]}, 
     {Arrowheads[{{0.010482106867782505`, 1.}}], 
      ArrowBox[{{-1.1761765930862145`, -1.0401915868388174`}, \
{-1.109537692628072, -1.102665556018326}}]}, 
     {Arrowheads[{{0.007647086937819628, 1.}}], 
      ArrowBox[{{-1.1695127030404002`, -0.8371511870054146}, \
{-1.1162015826738863`, -0.8771345272803001}}]}, 
     {Arrowheads[{{0.005264319576739231, 1.}}], 
      ArrowBox[{{-1.162848812994586, -0.6316118284048314}, \
{-1.1228654727197005`, -0.6541024573094545}}]}, 
     {Arrowheads[{{0.0032668369718749837`, 1.}}], 
      ArrowBox[{{-1.1561849229487717`, -0.42357351103706803`}, \
{-1.1295293627655147`, -0.4335693461057894}}]}, 
     {Arrowheads[{{0.0015560694542942899`, 1.}}], 
      ArrowBox[{{-1.1495210329029575`, -0.21303623490212426`}, \
{-1.136193252811329, -0.2155351936693046}}]}, 
     {Arrowheads[{{0.0015560694542942899`, 1.}}], 
      ArrowBox[{{-1.136193252811329, 
       0.21553519366930426`}, {-1.1495210329029575`, 0.21303623490212392`}}]}, 
     {Arrowheads[{{0.0032668369718749837`, 1.}}], 
      ArrowBox[{{-1.1295293627655147`, 
       0.43356934610578907`}, {-1.1561849229487717`, 0.4235735110370677}}]}, 
     {Arrowheads[{{0.005264319576739231, 1.}}], 
      ArrowBox[{{-1.1228654727197005`, 
       0.6541024573094543}, {-1.162848812994586, 0.6316118284048312}}]}, 
     {Arrowheads[{{0.007647086937819628, 1.}}], 
      ArrowBox[{{-1.1162015826738863`, 
       0.8771345272802997}, {-1.1695127030404002`, 0.8371511870054142}}]}, 
     {Arrowheads[{{0.010482106867782488`, 1.}}], 
      ArrowBox[{{-1.109537692628072, 
       1.1026655560183254`}, {-1.1761765930862145`, 1.040191586838817}}]}, 
     {Arrowheads[{{0.013812468092100322`, 1.}}], 
      ArrowBox[{{-1.1028738025822578`, 
       1.3306955435235315`}, {-1.1828404831320287`, 1.2407330279050393`}}]}, 
     {Arrowheads[{{0.01766527772826241, 1.}}], 
      ArrowBox[{{-1.0962099125364435`, 
       1.561224489795918}, {-1.189504373177843, 1.4387755102040813`}}]}, 
     {Arrowheads[{{0.01213789222728119, 1.}}], 
      ArrowBox[{{-0.8833819241982511, -1.4540816326530612`}, \
{-0.830903790087464, -1.5459183673469388`}}]}, 
     {Arrowheads[{{0.009305537871005862, 1.}}], 
      ArrowBox[{{-0.8796334860474806, -1.2519783423573512`}, \
{-0.8346522282382344, -1.3194502290712204`}}]}, 
     {Arrowheads[{{0.006885737960246569, 1.}}], 
      ArrowBox[{{-0.8758850478967102, -1.048000832986256}, \
{-0.8384006663890049, -1.0948563098708872`}}]}, 
     {Arrowheads[{{0.004866576327049797, 1.}}], 
      ArrowBox[{{-0.8721366097459397, -0.8421491045397752}, \
{-0.8421491045397755, -0.8721366097459393}}]}, 
     {Arrowheads[{{0.003226114801892654, 1.}}], 
      ArrowBox[{{-0.8683881715951691, -0.6344231570179094}, \
{-0.8458975426905461, -0.6512911286963767}}]}, 
     {Arrowheads[{{0.0019236832000667393`, 1.}}], 
      ArrowBox[{{-0.8646397334443986, -0.4248229904206582}, \
{-0.8496459808413165, -0.43231986672219924`}}]}, 
     {Arrowheads[{{0.0008867741392381375, 1.}}], 
      ArrowBox[{{-0.8608912952936281, -0.2133486047480218}, \
{-0.853394418992087, -0.21522282382340707`}}]}, 
     {Arrowheads[{{0.0008867741392381375, 1.}}], 
      ArrowBox[{{-0.853394418992087, 
       0.21522282382340674`}, {-0.8608912952936281, 
       0.21334860474802148`}}]}, 
     {Arrowheads[{{0.0019236832000667247`, 1.}}], 
      ArrowBox[{{-0.8496459808413165, 
       0.4323198667221989}, {-0.8646397334443985, 0.4248229904206579}}]}, 
     {Arrowheads[{{0.003226114801892654, 1.}}], 
      ArrowBox[{{-0.845897542690546, 0.6512911286963763}, {-0.868388171595169,
        0.634423157017909}}]}, 
     {Arrowheads[{{0.0048665763270497875`, 1.}}], 
      ArrowBox[{{-0.8421491045397755, 
       0.872136609745939}, {-0.8721366097459395, 0.8421491045397749}}]}, 
     {Arrowheads[{{0.006885737960246581, 1.}}], 
      ArrowBox[{{-0.838400666389005, 
       1.0948563098708868`}, {-0.8758850478967102, 1.0480008329862553`}}]}, 
     {Arrowheads[{{0.009305537871005862, 1.}}], 
      ArrowBox[{{-0.8346522282382345, 1.31945022907122}, {-0.8796334860474807,
        1.2519783423573507`}}]}, 
     {Arrowheads[{{0.01213789222728119, 1.}}], 
      ArrowBox[{{-0.830903790087464, 
       1.5459183673469383`}, {-0.8833819241982511, 1.4540816326530608`}}]}, 
     {Arrowheads[{{0.007518302125876299, 1.}}], 
      ArrowBox[{{-0.5830903790087468, -1.469387755102041}, \
{-0.559766763848397, -1.5306122448979593`}}]}, 
     {Arrowheads[{{0.005648630388641839, 1.}}], 
      ArrowBox[{{-0.5814244064972932, -1.2632236568096626`}, \
{-0.5614327363598505, -1.3082049146189088`}}]}, 
     {Arrowheads[{{0.0040625149357166705`, 1.}}], 
      ArrowBox[{{-0.5797584339858397, -1.0558100791336944`}, \
{-0.5630987088713041, -1.0870470637234486`}}]}, 
     {Arrowheads[{{0.002757196406223957, 1.}}], 
      ArrowBox[{{-0.5780924614743861, -0.847147022074136}, \
{-0.5647646813827576, -0.8671386922115787}}]}, 
     {Arrowheads[{{0.001726558511512545, 1.}}], 
      ArrowBox[{{-0.5764264889629326, -0.6372344856309873}, \
{-0.5664306538942112, -0.6484798000832989}}]}, 
     {Arrowheads[{{0.0009558858672274535, 1.}}], 
      ArrowBox[{{-0.574760516451479, -0.42607246980424834`}, \
{-0.5680966264056647, -0.43107038733860903`}}]}, 
     {Arrowheads[{{0.00040835462148437355`, 1.}}], 
      ArrowBox[{{-0.5730945439400255, -0.21366097459391936`}, \
{-0.5697625989171183, -0.21491045397750955`}}]}, 
     {Arrowheads[{{0.0004083546214843724, 1.}}], 
      ArrowBox[{{-0.5697625989171182, 
       0.21491045397750919`}, {-0.5730945439400253, 
       0.21366097459391903`}}]}, 
     {Arrowheads[{{0.0009558858672274535, 1.}}], 
      ArrowBox[{{-0.5680966264056647, 
       0.4310703873386087}, {-0.574760516451479, 0.426072469804248}}]}, 
     {Arrowheads[{{0.001726558511512545, 1.}}], 
      ArrowBox[{{-0.5664306538942111, 
       0.6484798000832984}, {-0.5764264889629325, 0.6372344856309868}}]}, 
     {Arrowheads[{{0.002757196406223957, 1.}}], 
      ArrowBox[{{-0.5647646813827576, 
       0.8671386922115784}, {-0.5780924614743861, 0.8471470220741356}}]}, 
     {Arrowheads[{{0.0040625149357166705`, 1.}}], 
      ArrowBox[{{-0.563098708871304, 
       1.0870470637234484`}, {-0.5797584339858396, 1.0558100791336942`}}]}, 
     {Arrowheads[{{0.005648630388641839, 1.}}], 
      ArrowBox[{{-0.5614327363598505, 
       1.3082049146189085`}, {-0.5814244064972932, 1.2632236568096624`}}]}, 
     {Arrowheads[{{0.007518302125876299, 1.}}], 
      ArrowBox[{{-0.5597667638483969, 
       1.5306122448979587`}, {-0.5830903790087467, 1.4693877551020402`}}]}, 
     {Arrowheads[{{0.0035760385290117187`, 1.}}], 
      ArrowBox[{{-0.28862973760932986`, -1.4846938775510203`}, \
{-0.28279883381924237`, -1.5153061224489797`}}]}, 
     {Arrowheads[{{0.0026438496747004515`, 1.}}], 
      ArrowBox[{{-0.2882132444814665, -1.2744689712619743`}, \
{-0.2832153269471058, -1.2969596001665975`}}]}, 
     {Arrowheads[{{0.0018549173990656347`, 1.}}], 
      ArrowBox[{{-0.2877967513536031, -1.063619325281133}, \
{-0.2836318200749692, -1.0792378175760102`}}]}, 
     {Arrowheads[{{0.0012091106094416215`, 1.}}], 
      ArrowBox[{{-0.2873802582257397, -0.8521449396084966}, \
{-0.2840483132028326, -0.862140774677218}}]}, 
     {Arrowheads[{{0.0007060787985802283, 1.}}], 
      ArrowBox[{{-0.2869637650978763, -0.6400458142440651}, \
{-0.28446480633069593`, -0.6456684714702209}}]}, 
     {Arrowheads[{{0.0003446495507779973, 1.}}], 
      ArrowBox[{{-0.28654727197001295`, -0.42732194918783856`}, \
{-0.2848812994585594, -0.4298209079550189}}]}, 
     {Arrowheads[{{0.00011948573340343375`, 1.}}], 
      ArrowBox[{{-0.28613077884214955`, -0.2139733444398169}, \
{-0.28529779258642274`, -0.21459808413161197`}}]}, 
     {Arrowheads[{{0.00011948573340343375`, 1.}}], 
      ArrowBox[{{-0.28529779258642274`, 
       0.21459808413161166`}, {-0.28613077884214955`, 
       0.21397334443981658`}}]}, 
     {Arrowheads[{{0.0003446495507779973, 1.}}], 
      ArrowBox[{{-0.28488129945855933`, 
       0.42982090795501854`}, {-0.2865472719700129, 
       0.42732194918783817`}}]}, 
     {Arrowheads[{{0.0007060787985802283, 1.}}], 
      ArrowBox[{{-0.284464806330696, 
       0.6456684714702206}, {-0.28696376509787636`, 0.6400458142440648}}]}, 
     {Arrowheads[{{0.0012091106094416215`, 1.}}], 
      ArrowBox[{{-0.2840483132028326, 
       0.8621407746772177}, {-0.2873802582257397, 0.8521449396084964}}]}, 
     {Arrowheads[{{0.0018549173990656347`, 1.}}], 
      ArrowBox[{{-0.2836318200749692, 
       1.0792378175760098`}, {-0.2877967513536031, 1.0636193252811326`}}]}, 
     {Arrowheads[{{0.0026438496747004515`, 1.}}], 
      ArrowBox[{{-0.28321532694710577`, 
       1.2969596001665968`}, {-0.28821324448146646`, 
       1.2744689712619737`}}]}, 
     {Arrowheads[{{0.003576038529011694, 1.}}], 
      ArrowBox[{{-0.2827988338192424, 
       1.5153061224489792`}, {-0.2886297376093299, 1.4846938775510201`}}]}, 
     {Arrowheads[{{0.0035760385290116927`, 1.}}], 
      ArrowBox[{{0.28279883381924154`, -1.5153061224489797`}, {
       0.288629737609329, -1.4846938775510206`}}]}, 
     {Arrowheads[{{0.0026438496747004264`, 1.}}], 
      ArrowBox[{{0.28321532694710494`, -1.2969596001665973`}, {
       0.2882132444814656, -1.2744689712619743`}}]}, 
     {Arrowheads[{{0.001854917399065633, 1.}}], 
      ArrowBox[{{0.2836318200749683, -1.0792378175760102`}, {
       0.28779675135360216`, -1.063619325281133}}]}, 
     {Arrowheads[{{0.0012091106094416215`, 1.}}], 
      ArrowBox[{{0.2840483132028317, -0.862140774677218}, {
       0.2873802582257388, -0.8521449396084966}}]}, 
     {Arrowheads[{{0.0007060787985802257, 1.}}], 
      ArrowBox[{{0.2844648063306951, -0.6456684714702209}, {
       0.2869637650978754, -0.6400458142440651}}]}, 
     {Arrowheads[{{0.000344649550777992, 1.}}], 
      ArrowBox[{{0.2848812994585585, -0.42982090795501887`}, {
       0.28654727197001206`, -0.42732194918783856`}}]}, 
     {Arrowheads[{{0.00011948573340342866`, 1.}}], 
      ArrowBox[{{0.28529779258642185`, -0.214598084131612}, {
       0.2861307788421486, -0.21397334443981691`}}]}, 
     {Arrowheads[{{0.00011948573340342866`, 1.}}], 
      ArrowBox[{{0.28613077884214866`, 0.21397334443981655`}, {
       0.2852977925864219, 0.21459808413161163`}}]}, 
     {Arrowheads[{{0.000344649550777992, 1.}}], 
      ArrowBox[{{0.286547271970012, 0.4273219491878382}, {
       0.28488129945855845`, 0.42982090795501854`}}]}, 
     {Arrowheads[{{0.0007060787985802257, 1.}}], 
      ArrowBox[{{0.2869637650978754, 0.6400458142440648}, {0.2844648063306951,
        0.6456684714702206}}]}, 
     {Arrowheads[{{0.0012091106094416215`, 1.}}], 
      ArrowBox[{{0.2873802582257388, 0.8521449396084964}, {0.2840483132028317,
        0.8621407746772177}}]}, 
     {Arrowheads[{{0.0018549173990656084`, 1.}}], 
      ArrowBox[{{0.2877967513536022, 1.0636193252811326`}, {
       0.28363182007496834`, 1.0792378175760096`}}]}, 
     {Arrowheads[{{0.0026438496747004264`, 1.}}], 
      ArrowBox[{{0.28821324448146557`, 1.274468971261974}, {
       0.2832153269471049, 1.2969596001665968`}}]}, 
     {Arrowheads[{{0.0035760385290116927`, 1.}}], 
      ArrowBox[{{0.288629737609329, 1.48469387755102}, {0.28279883381924154`, 
       1.515306122448979}}]}, 
     {Arrowheads[{{0.007518302125876276, 1.}}], 
      ArrowBox[{{0.5597667638483961, -1.530612244897959}, {
       0.5830903790087459, -1.469387755102041}}]}, 
     {Arrowheads[{{0.005648630388641839, 1.}}], 
      ArrowBox[{{0.5614327363598496, -1.308204914618909}, {
       0.5814244064972923, -1.2632236568096629`}}]}, 
     {Arrowheads[{{0.0040625149357166705`, 1.}}], 
      ArrowBox[{{0.5630987088713032, -1.0870470637234488`}, {
       0.5797584339858388, -1.0558100791336946`}}]}, 
     {Arrowheads[{{0.002757196406223957, 1.}}], 
      ArrowBox[{{0.5647646813827567, -0.8671386922115787}, {
       0.5780924614743852, -0.847147022074136}}]}, 
     {Arrowheads[{{0.001726558511512545, 1.}}], 
      ArrowBox[{{0.5664306538942103, -0.6484798000832988}, {
       0.5764264889629317, -0.6372344856309872}}]}, 
     {Arrowheads[{{0.0009558858672274535, 1.}}], 
      ArrowBox[{{0.5680966264056638, -0.43107038733860903`}, {
       0.5747605164514781, -0.42607246980424834`}}]}, 
     {Arrowheads[{{0.00040835462148437355`, 1.}}], 
      ArrowBox[{{0.5697625989171174, -0.21491045397750952`}, {
       0.5730945439400246, -0.21366097459391933`}}]}, 
     {Arrowheads[{{0.0004083546214843724, 1.}}], 
      ArrowBox[{{0.5730945439400245, 0.21366097459391903`}, {
       0.5697625989171173, 0.21491045397750919`}}]}, 
     {Arrowheads[{{0.0009558858672274535, 1.}}], 
      ArrowBox[{{0.5747605164514781, 0.42607246980424807`}, {
       0.5680966264056638, 0.43107038733860875`}}]}, 
     {Arrowheads[{{0.0017265585115125355`, 1.}}], 
      ArrowBox[{{0.5764264889629316, 0.637234485630987}, {0.5664306538942102, 
       0.6484798000832984}}]}, 
     {Arrowheads[{{0.002757196406223957, 1.}}], 
      ArrowBox[{{0.5780924614743852, 0.8471470220741356}, {0.5647646813827567,
        0.8671386922115784}}]}, 
     {Arrowheads[{{0.0040625149357166705`, 1.}}], 
      ArrowBox[{{0.5797584339858387, 1.055810079133694}, {0.5630987088713031, 
       1.0870470637234482`}}]}, 
     {Arrowheads[{{0.005648630388641839, 1.}}], 
      ArrowBox[{{0.5814244064972923, 1.2632236568096624`}, {
       0.5614327363598496, 1.3082049146189085`}}]}, 
     {Arrowheads[{{0.0075183021258762705`, 1.}}], 
      ArrowBox[{{0.5830903790087458, 1.4693877551020404`}, {
       0.5597667638483961, 1.5306122448979587`}}]}, 
     {Arrowheads[{{0.012137892227281183`, 1.}}], 
      ArrowBox[{{0.8309037900874631, -1.5459183673469388`}, {
       0.8833819241982501, -1.4540816326530612`}}]}, 
     {Arrowheads[{{0.009305537871005855, 1.}}], 
      ArrowBox[{{0.8346522282382336, -1.3194502290712204`}, {
       0.8796334860474797, -1.2519783423573512`}}]}, 
     {Arrowheads[{{0.0068857379602465735`, 1.}}], 
      ArrowBox[{{0.8384006663890041, -1.0948563098708872`}, {
       0.8758850478967092, -1.0480008329862558`}}]}, 
     {Arrowheads[{{0.004866576327049797, 1.}}], 
      ArrowBox[{{0.8421491045397747, -0.8721366097459393}, {
       0.8721366097459388, -0.8421491045397752}}]}, 
     {Arrowheads[{{0.003226114801892654, 1.}}], 
      ArrowBox[{{0.8458975426905452, -0.6512911286963766}, {
       0.8683881715951682, -0.6344231570179093}}]}, 
     {Arrowheads[{{0.0019236832000667247`, 1.}}], 
      ArrowBox[{{0.8496459808413156, -0.43231986672219924`}, {
       0.8646397334443976, -0.42482299042065824`}}]}, 
     {Arrowheads[{{0.0008867741392381375, 1.}}], 
      ArrowBox[{{0.8533944189920861, -0.21522282382340707`}, {
       0.8608912952936272, -0.2133486047480218}}]}, 
     {Arrowheads[{{0.0008867741392381375, 1.}}], 
      ArrowBox[{{0.8608912952936272, 0.21334860474802148`}, {
       0.8533944189920861, 0.21522282382340674`}}]}, 
     {Arrowheads[{{0.0019236832000667247`, 1.}}], 
      ArrowBox[{{0.8646397334443977, 0.42482299042065785`}, {
       0.8496459808413157, 0.43231986672219885`}}]}, 
     {Arrowheads[{{0.003226114801892654, 1.}}], 
      ArrowBox[{{0.8683881715951681, 0.6344231570179091}, {0.8458975426905451,
        0.6512911286963764}}]}, 
     {Arrowheads[{{0.0048665763270497875`, 1.}}], 
      ArrowBox[{{0.8721366097459387, 0.842149104539775}, {0.8421491045397747, 
       0.8721366097459391}}]}, 
     {Arrowheads[{{0.0068857379602465735`, 1.}}], 
      ArrowBox[{{0.8758850478967092, 1.0480008329862556`}, {
       0.8384006663890041, 1.094856309870887}}]}, 
     {Arrowheads[{{0.009305537871005834, 1.}}], 
      ArrowBox[{{0.8796334860474797, 1.2519783423573507`}, {
       0.8346522282382336, 1.3194502290712198`}}]}, 
     {Arrowheads[{{0.012137892227281183`, 1.}}], 
      ArrowBox[{{0.8833819241982502, 1.4540816326530608`}, {
       0.8309037900874632, 1.5459183673469383`}}]}, 
     {Arrowheads[{{0.01766527772826239, 1.}}], 
      ArrowBox[{{1.0962099125364426`, -1.5612244897959184`}, {
       1.1895043731778419`, -1.4387755102040818`}}]}, 
     {Arrowheads[{{0.013812468092100322`, 1.}}], 
      ArrowBox[{{1.1028738025822569`, -1.330695543523532}, {
       1.1828404831320278`, -1.2407330279050397`}}]}, 
     {Arrowheads[{{0.010482106867782488`, 1.}}], 
      ArrowBox[{{1.1095376926280711`, -1.1026655560183258`}, {
       1.1761765930862136`, -1.0401915868388174`}}]}, 
     {Arrowheads[{{0.007647086937819628, 1.}}], 
      ArrowBox[{{1.1162015826738854`, -0.8771345272803001}, {
       1.1695127030403993`, -0.8371511870054146}}]}, 
     {Arrowheads[{{0.005264319576739231, 1.}}], 
      ArrowBox[{{1.1228654727196996`, -0.6541024573094546}, {
       1.162848812994585, -0.6316118284048315}}]}, 
     {Arrowheads[{{0.0032668369718749837`, 1.}}], 
      ArrowBox[{{1.1295293627655139`, -0.4335693461057894}, {
       1.1561849229487708`, -0.42357351103706803`}}]}, 
     {Arrowheads[{{0.0015560694542942899`, 1.}}], 
      ArrowBox[{{1.136193252811328, -0.21553519366930463`}, {
       1.1495210329029566`, -0.21303623490212428`}}]}, 
     {Arrowheads[{{0.0015560694542942899`, 1.}}], 
      ArrowBox[{{1.1495210329029566`, 0.21303623490212395`}, {
       1.136193252811328, 0.2155351936693043}}]}, 
     {Arrowheads[{{0.0032668369718749837`, 1.}}], 
      ArrowBox[{{1.1561849229487708`, 0.4235735110370677}, {
       1.1295293627655139`, 0.43356934610578907`}}]}, 
     {Arrowheads[{{0.005264319576739231, 1.}}], 
      ArrowBox[{{1.162848812994585, 0.6316118284048312}, {1.1228654727196996`,
        0.6541024573094543}}]}, 
     {Arrowheads[{{0.0076470869378196206`, 1.}}], 
      ArrowBox[{{1.1695127030403993`, 0.8371511870054142}, {
       1.1162015826738854`, 0.8771345272802996}}]}, 
     {Arrowheads[{{0.010482106867782488`, 1.}}], 
      ArrowBox[{{1.1761765930862136`, 1.040191586838817}, {
       1.1095376926280711`, 1.1026655560183254`}}]}, 
     {Arrowheads[{{0.013812468092100304`, 1.}}], 
      ArrowBox[{{1.1828404831320278`, 1.2407330279050393`}, {
       1.102873802582257, 1.3306955435235315`}}]}, 
     {Arrowheads[{{0.01766527772826239, 1.}}], 
      ArrowBox[{{1.189504373177842, 1.4387755102040813`}, {
       1.0962099125364428`, 1.561224489795918}}]}, 
     {Arrowheads[{{0.024255603880896596`, 1.}}], 
      ArrowBox[{{1.3556851311953346`, -1.5765306122448979`}, {
       1.501457725947521, -1.4234693877551021`}}]}, 
     {Arrowheads[{{0.01929019363438374, 1.}}], 
      ArrowBox[{{1.3660974593919195`, -1.3419408579758434`}, {
       1.4910453977509364`, -1.229487713452728}}]}, 
     {Arrowheads[{{0.014935716675428949`, 1.}}], 
      ArrowBox[{{1.3765097875885042`, -1.1104748021657644`}, {
       1.4806330695543517`, -1.0323823406913788`}}]}, 
     {Arrowheads[{{0.011147449017531516`, 1.}}], 
      ArrowBox[{{1.3869221157850888`, -0.8821324448146607}, {
       1.4702207413577668`, -0.8321532694710538}}]}, 
     {Arrowheads[{{0.007861580150836855, 1.}}], 
      ArrowBox[{{1.3973344439816737`, -0.6569137859225325}, {
       1.4598084131611822`, -0.6288004997917537}}]}, 
     {Arrowheads[{{0.0049898707206952, 1.}}], 
      ArrowBox[{{1.4077467721782584`, -0.43481882548937956`}, {
       1.4493960849645975`, -0.42232403165347787`}}]}, 
     {Arrowheads[{{0.002416449411670975, 1.}}], 
      ArrowBox[{{1.4181591003748433`, -0.21584756351520215`}, {
       1.4389837567680128`, -0.21272386505622673`}}]}, 
     {Arrowheads[{{0.002416449411670975, 1.}}], 
      ArrowBox[{{1.4389837567680126`, 0.2127238650562264}, {1.418159100374843,
        0.21584756351520182`}}]}, 
     {Arrowheads[{{0.004989870720695175, 1.}}], 
      ArrowBox[{{1.4493960849645975`, 0.42232403165347754`}, {
       1.4077467721782586`, 0.4348188254893792}}]}, 
     {Arrowheads[{{0.007861580150836855, 1.}}], 
      ArrowBox[{{1.4598084131611822`, 0.6288004997917532}, {
       1.3973344439816737`, 0.656913785922532}}]}, 
     {Arrowheads[{{0.01114744901753151, 1.}}], 
      ArrowBox[{{1.4702207413577668`, 0.8321532694710536}, {
       1.3869221157850888`, 0.8821324448146604}}]}, 
     {Arrowheads[{{0.014935716675428949`, 1.}}], 
      ArrowBox[{{1.4806330695543517`, 1.0323823406913784`}, {
       1.3765097875885042`, 1.110474802165764}}]}, 
     {Arrowheads[{{0.01929019363438372, 1.}}], 
      ArrowBox[{{1.4910453977509364`, 1.2294877134527278`}, {
       1.3660974593919195`, 1.341940857975843}}]}, 
     {Arrowheads[{{0.024255603880896596`, 1.}}], 
      ArrowBox[{{1.501457725947521, 1.4234693877551017`}, {
       1.3556851311953346`, 1.5765306122448974`}}]}, 
     {Arrowheads[{{0.03200779936922443, 1.}}], 
      ArrowBox[{{1.6093294460641392`, -1.5918367346938775`}, {
       1.8192419825072879`, -1.4081632653061225`}}]}, 
     {Arrowheads[{{0.025808918415141213`, 1.}}], 
      ArrowBox[{{1.6243231986672213`, -1.353186172428155}, {
       1.8042482299042057`, -1.2182423990004168`}}]}, 
     {Arrowheads[{{0.02029007078060255, 1.}}], 
      ArrowBox[{{1.6393169512703034`, -1.118284048313203}, {
       1.7892544773011239`, -1.0245730945439402`}}]}, 
     {Arrowheads[{{0.015389465600533834`, 1.}}], 
      ArrowBox[{{1.6543107038733853`, -0.8871303623490214}, {
       1.7742607246980415`, -0.8271553519366932}}]}, 
     {Arrowheads[{{0.01102557478007806, 1.}}], 
      ArrowBox[{{1.6693044564764674`, -0.6597251145356103}, {
       1.7592669720949596`, -0.6259891711786757}}]}, 
     {Arrowheads[{{0.007094193113905074, 1.}}], 
      ArrowBox[{{1.6842982090795495`, -0.4360683048729697}, {
       1.7442732194918777`, -0.42107455226988766`}}]}, 
     {Arrowheads[{{0.0034679692077946144`, 1.}}], 
      ArrowBox[{{1.6992919616826314`, -0.2161599333610997}, {
       1.7292794668887954`, -0.21241149521032918`}}]}, 
     {Arrowheads[{{0.003467969207794614, 1.}}], 
      ArrowBox[{{1.7292794668887956`, 0.21241149521032884`}, {
       1.6992919616826316`, 0.21615993336109934`}}]}, 
     {Arrowheads[{{0.007094193113905047, 1.}}], 
      ArrowBox[{{1.7442732194918775`, 0.4210745522698874}, {
       1.6842982090795495`, 0.4360683048729694}}]}, 
     {Arrowheads[{{0.011025574780078054`, 1.}}], 
      ArrowBox[{{1.7592669720949596`, 0.6259891711786754}, {
       1.6693044564764674`, 0.6597251145356099}}]}, 
     {Arrowheads[{{0.015389465600533827`, 1.}}], 
      ArrowBox[{{1.7742607246980417`, 0.8271553519366929}, {
       1.6543107038733855`, 0.887130362349021}}]}, 
     {Arrowheads[{{0.020290070780602517`, 1.}}], 
      ArrowBox[{{1.7892544773011236`, 1.0245730945439397`}, {
       1.6393169512703034`, 1.1182840483132024`}}]}, 
     {Arrowheads[{{0.025808918415141213`, 1.}}], 
      ArrowBox[{{1.8042482299042057`, 1.2182423990004163`}, {
       1.6243231986672213`, 1.3531861724281546`}}]}, 
     {Arrowheads[{{0.032007799369224404`, 1.}}], 
      ArrowBox[{{1.8192419825072876`, 1.4081632653061222`}, {
       1.6093294460641392`, 1.591836734693877}}]}, 
     {Arrowheads[{{0.04098360655737703, 1.}}], 
      ArrowBox[{{1.8571428571428563`, -1.607142857142857}, {
       2.142857142857142, -1.3928571428571428`}}]}, 
     {Arrowheads[{{0.03340913411259935, 1.}}], 
      ArrowBox[{{1.8775510204081625`, -1.3644314868804666`}, {
       2.122448979591836, -1.206997084548105}}]}, 
     {Arrowheads[{{0.026568049806404453`, 1.}}], 
      ArrowBox[{{1.8979591836734686`, -1.1260932944606417`}, {
       2.1020408163265296`, -1.0167638483965016`}}]}, 
     {Arrowheads[{{0.02038346766373741, 1.}}], 
      ArrowBox[{{1.9183673469387748`, -0.8921282798833821}, {
       2.0816326530612232`, -0.8221574344023325}}]}, 
     {Arrowheads[{{0.014759559554887298`, 1.}}], 
      ArrowBox[{{1.938775510204081, -0.6625364431486882}, {
       2.0612244897959173`, -0.6231778425655978}}]}, 
     {Arrowheads[{{0.009580341962714197, 1.}}], 
      ArrowBox[{{1.9591836734693868`, -0.4373177842565599}, {
       2.0408163265306114`, -0.41982507288629756`}}]}, 
     {Arrowheads[{{0.004710648323964141, 1.}}], 
      ArrowBox[{{1.979591836734693, -0.21647230320699723`}, {
       2.0204081632653055`, -0.21209912536443162`}}]}, 
     {Arrowheads[{{0.004710648323964064, 1.}}], 
      ArrowBox[{{2.020408163265305, 0.21209912536443132`}, {
       1.9795918367346932`, 0.2164723032069969}}]}, 
     {Arrowheads[{{0.009580341962714173, 1.}}], 
      ArrowBox[{{2.0408163265306114`, 0.4198250728862972}, {1.959183673469387,
        0.4373177842565596}}]}, 
     {Arrowheads[{{0.01475955955488732, 1.}}], 
      ArrowBox[{{2.0612244897959173`, 0.6231778425655975}, {
       1.9387755102040807`, 0.6625364431486879}}]}, 
     {Arrowheads[{{0.020383467663737453`, 1.}}], 
      ArrowBox[{{2.0816326530612237`, 0.8221574344023322}, {
       1.9183673469387748`, 0.8921282798833817}}]}, 
     {Arrowheads[{{0.026568049806404447`, 1.}}], 
      ArrowBox[{{2.1020408163265296`, 1.0167638483965014`}, {
       1.8979591836734686`, 1.1260932944606412`}}]}, 
     {Arrowheads[{{0.033409134112599284`, 1.}}], 
      ArrowBox[{{2.1224489795918355`, 1.2069970845481046`}, {
       1.8775510204081625`, 1.364431486880466}}]}, 
     {Arrowheads[{{0.04098360655737702, 1.}}], 
      ArrowBox[{{2.142857142857142, 1.3928571428571426`}, {
       1.8571428571428563`, 
       1.6071428571428565`}}]}}}, {{{{}, {}}, {}, {{}, {}, 
      TagBox[
       {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
        LineBox[CompressedData["
1:eJw0m3c81f/7/62yikhCRikULVTeUi4lJUVC0yiR2SCKzMomGSkjMpJkZK+M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         "]]},
       Annotation[#, 
        "Charting`Private`Tag$869749#1"]& ]}, {}, {{{}, {}, {}, {}}, {}}}, \
{}}},
  AspectRatio->1,
  DisplayFunction->Identity,
  Frame->True,
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
    "TransparentPolygonMesh" -> True},
  PlotRange->{{-2.1785714285714284`, 
   2.1785714285714284`}, {-1.6785714285714286`, 1.6785714285714286`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{None, None}, {None, None}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.8163105347436953`*^9, {3.8163105694612722`*^9, 3.816310616030424*^9}, 
   3.8163152896440163`*^9, 3.816315492212942*^9, 3.816318448802443*^9},
 CellLabel->
  "Out[138]=",ExpressionUUID->"c83a179a-522e-4b5b-92ba-329520d4a010"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{
    "The", " ", "circulation", " ", "of", " ", "the", " ", "vector", " ", 
     "field", " ", "can", " ", "be", " ", "computed", " ", "using", " ", 
     TemplateBox[{Cell[
        TextData["Curl"]],"paclet:ref/Curl"},
      "RefLink",
      BaseStyle->{"InlineFormula"}]}], ":"}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"circ", " ", "=", " ", 
   RowBox[{"Curl", "[", 
    RowBox[{
     RowBox[{"v", "[", 
      RowBox[{"x", ",", "y"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "y"}], "}"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.816310738679386*^9, 3.816310773783422*^9}, {
  3.816315506761738*^9, 3.816315531706539*^9}},
 CellLabel->
  "In[139]:=",ExpressionUUID->"89667f8a-fc5d-4818-afdb-96ebaecd969f"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["x", "2"], "+", 
  SuperscriptBox["y", "2"]}]], "Output",
 CellChangeTimes->{3.8163107755028963`*^9, 3.816315294310151*^9, 
  3.816315516165724*^9, 3.8163184620920258`*^9},
 CellLabel->
  "Out[139]=",ExpressionUUID->"d1be26f0-f9cd-4c47-a04c-6c9f578e382f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Now", ",", " ", 
    RowBox[{
    "integrate", " ", "over", " ", "the", " ", "interior", " ", "of", " ", 
     "the", " ", 
     RowBox[{"Cardioid", ":"}]}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{" ", "1", ")"}], " ", "Convert", " ", "to", " ", "Polar", " ", 
    RowBox[{"Coordinates", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"circPolar", "=", " ", 
   RowBox[{
    RowBox[{"TransformedField", "[", 
     RowBox[{
      RowBox[{"\"\<Cartesian\>\"", "\[Rule]", " ", "\"\<Polar\>\""}], ",", 
      "circ", ",", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"x", ",", " ", "y"}], "}"}], "\[Rule]", " ", 
       RowBox[{"{", 
        RowBox[{"r", ",", " ", "\[Theta]"}], "}"}]}]}], "]"}], "//", 
    "FullSimplify"}]}]}]], "Input",
 CellChangeTimes->{{3.816310791752042*^9, 3.8163108352777863`*^9}, {
  3.816310867332529*^9, 3.816310938646831*^9}, {3.816311566804701*^9, 
  3.816311573324272*^9}, {3.816311635663135*^9, 3.816311770591168*^9}, {
  3.8163118034241447`*^9, 3.8163118138739557`*^9}, {3.8163118672802773`*^9, 
  3.816311946898035*^9}, {3.816311982562213*^9, 3.816312001748397*^9}, {
  3.8163148628961163`*^9, 3.816314866387727*^9}, {3.816315070345092*^9, 
  3.816315102226461*^9}, {3.816315305242552*^9, 3.816315306749558*^9}, {
  3.816318468745668*^9, 3.816318470934555*^9}},
 CellLabel->
  "In[140]:=",ExpressionUUID->"5898e81b-98eb-49da-97ea-55b105309fd6"],

Cell[BoxData[
 SuperscriptBox["r", "2"]], "Output",
 CellChangeTimes->{
  3.816314869164064*^9, 3.81631510438553*^9, {3.816315301221942*^9, 
   3.816315307701939*^9}, 3.8163155444794817`*^9, 3.8163184720197906`*^9},
 CellLabel->
  "Out[140]=",ExpressionUUID->"1d667318-18fb-4fb4-9bed-397cc381eda2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{" ", "2", ")"}], " ", "Area", " ", 
    RowBox[{"element", ":", " ", 
     RowBox[{
     "Use", " ", "Jacobian", " ", "determinant", " ", "of", " ", "the", " ", 
      "coordinate", " ", "conversion", " ", "formula"}]}]}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"(", "Inverse", ")"}], " ", "coordinate", " ", "conversion", " ", 
    
    RowBox[{"formula", ":"}]}], " ", "*)"}], " ", 
  RowBox[{"transf", " ", "=", " ", 
   RowBox[{"FromPolarCoordinates", "[", 
    RowBox[{"{", 
     RowBox[{"r", ",", " ", "\[Theta]"}], "}"}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.816314872670815*^9, 3.8163149078943233`*^9}, {
  3.8163149414021177`*^9, 3.8163149478262053`*^9}, {3.816315110893346*^9, 
  3.816315200760178*^9}, {3.816315309912304*^9, 3.816315310358348*^9}, {
  3.816318493691877*^9, 3.816318494295416*^9}},
 CellLabel->
  "In[142]:=",ExpressionUUID->"415d3fe6-0cc1-43ff-8dcb-9e0efb127951"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"r", " ", 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ",", 
   RowBox[{"r", " ", 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.816314948578909*^9, 3.816315127897647*^9, {3.816315190700178*^9, 
   3.816315201411191*^9}, 3.816315312546166*^9, 3.816315551762903*^9, {
   3.8163184862113943`*^9, 3.816318494843745*^9}},
 CellLabel->
  "Out[142]=",ExpressionUUID->"abb7d5d2-7f54-4d99-970e-dd22b3cc7376"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", 
    RowBox[{"matrix", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"J", "=", " ", 
   RowBox[{"Grad", "[", 
    RowBox[{"transf", ",", " ", 
     RowBox[{"{", 
      RowBox[{"r", ",", " ", "\[Theta]"}], "}"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.81631538997197*^9, 3.8163153932596283`*^9}, {
  3.816315560563181*^9, 3.816315567013771*^9}},
 CellLabel->
  "In[143]:=",ExpressionUUID->"623ae2fb-127b-44d1-b8e5-90196d347476"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", 
     RowBox[{
      RowBox[{"-", "r"}], " ", 
      RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Sin", "[", "\[Theta]", "]"}], ",", 
     RowBox[{"r", " ", 
      RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.816315393728365*^9, 3.816315406818012*^9}, 
   3.816315567359387*^9, 3.816318496103951*^9},
 CellLabel->
  "Out[143]=",ExpressionUUID->"520d28e1-a98a-4621-8959-f3d2ac5db91f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", "matrix", " ", 
    RowBox[{"determinant", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"detJ", " ", "=", " ", 
   RowBox[{
    RowBox[{"Det", "[", "J", "]"}], "//", "FullSimplify"}]}]}]], "Input",
 CellChangeTimes->{{3.816315028453423*^9, 3.8163150434377003`*^9}, {
  3.816315222396887*^9, 3.816315223904204*^9}, {3.816315571189762*^9, 
  3.816315579539771*^9}},
 CellLabel->
  "In[144]:=",ExpressionUUID->"20b347c3-1b61-4e6f-beab-d6b8d7bdfc7a"],

Cell[BoxData["r"], "Output",
 CellChangeTimes->{{3.8163150311485023`*^9, 3.816315044580998*^9}, {
   3.8163152242736273`*^9, 3.816315245854583*^9}, 3.816315332524596*^9, {
   3.8163153984500217`*^9, 3.816315407600917*^9}, 3.8163155798289413`*^9, 
   3.816318498303776*^9},
 CellLabel->
  "Out[144]=",ExpressionUUID->"abfa4537-9788-4370-9b5f-356ce2a2ef35"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SubsuperscriptBox["\[Integral]", "0", 
   RowBox[{"2", "\[Pi]"}]], 
  RowBox[{
   SubsuperscriptBox["\[Integral]", "0", 
    RowBox[{"r", "/.", 
     RowBox[{"r", "\[Rule]", " ", 
      RowBox[{"a", 
       RowBox[{"(", 
        RowBox[{"1", "+", 
         RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ")"}]}]}]}]], 
   RowBox[{"circPolar", " ", "detJ", " ", 
    RowBox[{"\[DifferentialD]", "r"}], 
    RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]}]], "Input",
 CellChangeTimes->{{3.816310791752042*^9, 3.8163108352777863`*^9}, {
  3.816310867332529*^9, 3.816310938646831*^9}, {3.816311566804701*^9, 
  3.816311573324272*^9}, {3.816311635663135*^9, 3.816311770591168*^9}, {
  3.8163118034241447`*^9, 3.8163118138739557`*^9}, {3.8163118672802773`*^9, 
  3.816311946898035*^9}, {3.816311982562213*^9, 3.816312001748397*^9}, {
  3.8163148628961163`*^9, 3.816314866387727*^9}, {3.816315229250332*^9, 
  3.8163152356188593`*^9}, {3.8163153611061897`*^9, 3.816315372223165*^9}},
 CellLabel->
  "In[145]:=",ExpressionUUID->"3a0094b1-1188-4132-bda5-18e66024d5c4"],

Cell[BoxData[
 FractionBox[
  RowBox[{"35", " ", 
   SuperscriptBox["a", "4"], " ", "\[Pi]"}], "16"]], "Output",
 CellChangeTimes->{{3.816311956362567*^9, 3.816312003702928*^9}, 
   3.816315238355794*^9, 3.816315334623827*^9, 3.816315373653*^9, 
   3.816315409095196*^9, 3.816315582187272*^9, 3.81631850158743*^9},
 CellLabel->
  "Out[145]=",ExpressionUUID->"4bdc5577-7707-424e-a154-35711a3219db"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", " ", 
  RowBox[{
   RowBox[{"That", "'"}], "s", " ", 
   RowBox[{"it", "!"}]}], " ", "*)"}]], "Input",
 CellChangeTimes->{{3.816315599983572*^9, 3.816315603196588*^9}, {
  3.8163185060180817`*^9, 3.8163185062979918`*^9}},
 CellLabel->
  "In[146]:=",ExpressionUUID->"3383dc85-779f-4d4d-86cc-ae57b7e75229"],

Cell[BoxData[
 RowBox[{"(*", " ", 
  RowBox[{
   RowBox[{
   "Another", " ", "example", " ", "of", " ", "Jacobian", " ", "determinant", 
    " ", 
    RowBox[{"(", 
     RowBox[{"spherical", " ", "coordinates"}], ")"}]}], ":"}], " ", 
  "*)"}]], "Input",
 CellChangeTimes->{{3.81631853032943*^9, 
  3.816318554267198*^9}},ExpressionUUID->"745eb0a7-202f-4577-9085-\
82de73e161d7"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"transf", " ", "=", " ", 
  RowBox[{"FromSphericalCoordinates", "[", 
   RowBox[{"{", 
    RowBox[{"r", ",", " ", "\[Theta]", ",", " ", "\[Phi]"}], "}"}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.816318563716234*^9, 3.816318579502755*^9}},
 CellLabel->
  "In[147]:=",ExpressionUUID->"f14310e3-dcd1-405e-880b-c765f3b4dfe6"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"r", " ", 
    RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ",", 
   RowBox[{"r", " ", 
    RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
    RowBox[{"Sin", "[", "\[Phi]", "]"}]}], ",", 
   RowBox[{"r", " ", 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], "}"}]], "Output",
 CellChangeTimes->{3.8163185805365667`*^9},
 CellLabel->
  "Out[147]=",ExpressionUUID->"0d717d2d-541f-48eb-a0fa-a8847609e1b7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", 
    RowBox[{"matrix", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"J", "=", " ", 
     RowBox[{"Grad", "[", 
      RowBox[{"transf", ",", " ", 
       RowBox[{"{", 
        RowBox[{"r", ",", " ", "\[Theta]", ",", " ", "\[Phi]"}], "}"}]}], 
      "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"J", "//", "MatrixForm"}]}]}]], "Input",
 CellChangeTimes->{{3.8163185979572783`*^9, 3.816318626039452*^9}},
 CellLabel->
  "In[153]:=",ExpressionUUID->"e517a54d-a736-477c-a9f4-4c67e6b960c3"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}]}], 
      RowBox[{"r", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Cos", "[", "\[Phi]", "]"}]}], 
      RowBox[{
       RowBox[{"-", "r"}], " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}]},
     {
      RowBox[{
       RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], 
      RowBox[{"r", " ", 
       RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Phi]", "]"}]}], 
      RowBox[{"r", " ", 
       RowBox[{"Cos", "[", "\[Phi]", "]"}], " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}]}]},
     {
      RowBox[{"Cos", "[", "\[Theta]", "]"}], 
      RowBox[{
       RowBox[{"-", "r"}], " ", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.816318599574214*^9, 3.816318626527117*^9}},
 CellLabel->
  "Out[154]//MatrixForm=",ExpressionUUID->"c2231e8b-3e0e-4911-a873-\
5ca4f16b25f5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", "matrix", " ", 
    RowBox[{"determinant", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"detJ", " ", "=", " ", 
   RowBox[{
    RowBox[{"Det", "[", "J", "]"}], "//", "FullSimplify"}]}]}]], "Input",
 CellLabel->
  "In[155]:=",ExpressionUUID->"2dc3d3ab-e138-4c30-a0b0-2c5dbd2ec677"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["r", "2"], " ", 
  RowBox[{"Sin", "[", "\[Theta]", "]"}]}]], "Output",
 CellChangeTimes->{3.816318641265304*^9},
 CellLabel->
  "Out[155]=",ExpressionUUID->"a8f6a72b-5ff8-4746-ab40-417268b71f5a"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", 
  RowBox[{" ", 
   RowBox[{":", "-"}], ")"}], " ", "*)"}]], "Input",
 CellChangeTimes->{{3.816318645058762*^9, 
  3.816318648104053*^9}},ExpressionUUID->"a1638960-d2d3-410b-99ad-\
9e69be359904"],

Cell[BoxData[
 RowBox[{"(*", " ", 
  RowBox[{"Another", ",", " ", 
   RowBox[{"from", " ", "polar", " ", "to", " ", 
    RowBox[{"cartesian", ":"}]}]}], " ", "*)"}]], "Input",
 CellChangeTimes->{{3.816322383805523*^9, 
  3.8163223947980213`*^9}},ExpressionUUID->"dfb81485-847e-4050-8d3c-\
6ffa7e05f6dd"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"transf", " ", "=", " ", 
  RowBox[{"ToPolarCoordinates", "[", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.816322409782222*^9, 3.816322416358968*^9}},
 CellLabel->
  "In[159]:=",ExpressionUUID->"eca8e341-d39f-4fd6-af32-b519665beaf4"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   SqrtBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"]}]], ",", 
   RowBox[{"ArcTan", "[", 
    RowBox[{"x", ",", "y"}], "]"}]}], "}"}]], "Output",
 CellChangeTimes->{3.81632241675746*^9},
 CellLabel->
  "Out[159]=",ExpressionUUID->"10af8f20-1ea0-40e4-981f-8348b2be03ac"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", 
    RowBox[{"matrix", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"J", "=", " ", 
     RowBox[{"Grad", "[", 
      RowBox[{"transf", ",", " ", 
       RowBox[{"{", 
        RowBox[{"x", ",", " ", "y"}], "}"}]}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"J", "//", "MatrixForm"}]}]}]], "Input",
 CellChangeTimes->{{3.816322431863669*^9, 3.8163224324092503`*^9}},
 CellLabel->
  "In[160]:=",ExpressionUUID->"ccab8048-76a8-4418-884c-ea15f130ed42"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      FractionBox["x", 
       SqrtBox[
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"]}]]], 
      FractionBox["y", 
       SqrtBox[
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"]}]]]},
     {
      RowBox[{"-", 
       FractionBox["y", 
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"]}]]}], 
      FractionBox["x", 
       RowBox[{
        SuperscriptBox["x", "2"], "+", 
        SuperscriptBox["y", "2"]}]]}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.8163224336999617`*^9},
 CellLabel->
  "Out[161]//MatrixForm=",ExpressionUUID->"b3d22ffc-83a0-40fc-85e7-\
fd0932440dd2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", "matrix", " ", 
    RowBox[{"determinant", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"detJ", " ", "=", " ", 
   RowBox[{
    RowBox[{"Det", "[", "J", "]"}], "//", "FullSimplify"}]}]}]], "Input",
 CellLabel->
  "In[162]:=",ExpressionUUID->"ca63f3b6-8e83-4d16-ad7c-df997c25fbaa"],

Cell[BoxData[
 FractionBox["1", 
  SqrtBox[
   RowBox[{
    SuperscriptBox["x", "2"], "+", 
    SuperscriptBox["y", "2"]}]]]], "Output",
 CellChangeTimes->{3.816322454052668*^9},
 CellLabel->
  "Out[162]=",ExpressionUUID->"f5e948f3-0ac7-4ca9-b1d7-cbdf5bc7bb19"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", " ", 
  RowBox[{"Another", ",", " ", 
   RowBox[{"from", " ", "spherical", " ", "to", " ", 
    RowBox[{"cartesian", ":"}]}]}], " ", "*)"}]], "Input",
 CellChangeTimes->{{3.8163224815323668`*^9, 
  3.816322487114018*^9}},ExpressionUUID->"3b10f521-bc03-429e-9de0-\
b59246a3bbb2"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"transf", " ", "=", " ", 
  RowBox[{"ToSphericalCoordinates", "[", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y", ",", " ", "z"}], "}"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.816322497121811*^9, 3.816322507195179*^9}},
 CellLabel->
  "In[163]:=",ExpressionUUID->"af2c492c-a98b-46e1-aec3-663553886f73"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   SqrtBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"], "+", 
     SuperscriptBox["z", "2"]}]], ",", 
   RowBox[{"ArcTan", "[", 
    RowBox[{"z", ",", 
     SqrtBox[
      RowBox[{
       SuperscriptBox["x", "2"], "+", 
       SuperscriptBox["y", "2"]}]]}], "]"}], ",", 
   RowBox[{"ArcTan", "[", 
    RowBox[{"x", ",", "y"}], "]"}]}], "}"}]], "Output",
 CellChangeTimes->{3.8163225075467167`*^9},
 CellLabel->
  "Out[163]=",ExpressionUUID->"263d57cf-2a07-43d5-84da-5f99ee230653"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", 
    RowBox[{"matrix", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"J", "=", " ", 
     RowBox[{"Grad", "[", 
      RowBox[{"transf", ",", " ", 
       RowBox[{"{", 
        RowBox[{"x", ",", " ", "y", ",", "z"}], "}"}]}], "]"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{"J", "//", "MatrixForm"}]}]}]], "Input",
 CellChangeTimes->{{3.816322533813401*^9, 3.81632253417319*^9}},
 CellLabel->
  "In[164]:=",ExpressionUUID->"62acff55-da66-4e67-868a-7e4df43881bb"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      FractionBox["x", 
       SqrtBox[
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"], "+", 
         SuperscriptBox["z", "2"]}]]], 
      FractionBox["y", 
       SqrtBox[
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"], "+", 
         SuperscriptBox["z", "2"]}]]], 
      FractionBox["z", 
       SqrtBox[
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"], "+", 
         SuperscriptBox["z", "2"]}]]]},
     {
      FractionBox[
       RowBox[{"x", " ", "z"}], 
       RowBox[{
        SqrtBox[
         RowBox[{
          SuperscriptBox["x", "2"], "+", 
          SuperscriptBox["y", "2"]}]], " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["x", "2"], "+", 
          SuperscriptBox["y", "2"], "+", 
          SuperscriptBox["z", "2"]}], ")"}]}]], 
      FractionBox[
       RowBox[{"y", " ", "z"}], 
       RowBox[{
        SqrtBox[
         RowBox[{
          SuperscriptBox["x", "2"], "+", 
          SuperscriptBox["y", "2"]}]], " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["x", "2"], "+", 
          SuperscriptBox["y", "2"], "+", 
          SuperscriptBox["z", "2"]}], ")"}]}]], 
      RowBox[{"-", 
       FractionBox[
        SqrtBox[
         RowBox[{
          SuperscriptBox["x", "2"], "+", 
          SuperscriptBox["y", "2"]}]], 
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"], "+", 
         SuperscriptBox["z", "2"]}]]}]},
     {
      RowBox[{"-", 
       FractionBox["y", 
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox["y", "2"]}]]}], 
      FractionBox["x", 
       RowBox[{
        SuperscriptBox["x", "2"], "+", 
        SuperscriptBox["y", "2"]}]], "0"}
    },
    GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.81632253472744*^9},
 CellLabel->
  "Out[165]//MatrixForm=",ExpressionUUID->"721c4a99-5a8a-4881-8055-\
5ea988008476"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{"Jacobian", " ", "matrix", " ", 
    RowBox[{"determinant", ":"}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{"detJ", " ", "=", " ", 
   RowBox[{
    RowBox[{"Det", "[", "J", "]"}], "//", "FullSimplify"}]}]}]], "Input",
 CellLabel->
  "In[166]:=",ExpressionUUID->"c853cb5b-6b90-4a93-adb1-65e894a6cb61"],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{
   SqrtBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"]}]], " ", 
   SqrtBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"], "+", 
     SuperscriptBox["z", "2"]}]]}]]], "Output",
 CellChangeTimes->{3.8163225545587587`*^9},
 CellLabel->
  "Out[166]=",ExpressionUUID->"c4f04016-417f-49f2-afab-2ab90cffef72"]
}, Open  ]]
},
WindowSize->{785, 646},
WindowMargins->{{Automatic, 6}, {6, Automatic}},
FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 1873, 47, 133, "Input",ExpressionUUID->"d9a963c7-af47-4c7b-be6d-ef7222b8b9f9"],
Cell[2434, 69, 550, 13, 55, "Input",ExpressionUUID->"9dac9486-7675-4d75-9f41-1f3228cf0215"],
Cell[2987, 84, 1273, 37, 88, "Input",ExpressionUUID->"6b5d85f4-dd9b-4ff4-ba7d-177082207cd1"],
Cell[CellGroupData[{
Cell[4285, 125, 1108, 25, 55, "Input",ExpressionUUID->"98adb345-ac70-4a54-8b92-4c4c3f3a637c"],
Cell[5396, 152, 32858, 618, 370, "Output",ExpressionUUID->"1c56aa61-0239-499e-a0c3-603bfa293c05"]
}, Open  ]],
Cell[CellGroupData[{
Cell[38291, 775, 563, 14, 31, "Input",ExpressionUUID->"b3a56e8f-4120-4267-a7c3-fef7772e4aa9"],
Cell[38857, 791, 55683, 991, 370, "Output",ExpressionUUID->"c83a179a-522e-4b5b-92ba-329520d4a010"]
}, Open  ]],
Cell[CellGroupData[{
Cell[94577, 1787, 810, 22, 58, "Input",ExpressionUUID->"89667f8a-fc5d-4818-afdb-96ebaecd969f"],
Cell[95390, 1811, 296, 7, 37, "Output",ExpressionUUID->"d1be26f0-f9cd-4c47-a04c-6c9f578e382f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[95723, 1823, 1491, 33, 101, "Input",ExpressionUUID->"5898e81b-98eb-49da-97ea-55b105309fd6"],
Cell[97217, 1858, 298, 6, 37, "Output",ExpressionUUID->"1d667318-18fb-4fb4-9bed-397cc381eda2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[97552, 1869, 1009, 24, 101, "Input",ExpressionUUID->"415d3fe6-0cc1-43ff-8dcb-9e0efb127951"],
Cell[98564, 1895, 495, 12, 35, "Output",ExpressionUUID->"abb7d5d2-7f54-4d99-970e-dd22b3cc7376"]
}, Open  ]],
Cell[CellGroupData[{
Cell[99096, 1912, 517, 13, 55, "Input",ExpressionUUID->"623ae2fb-127b-44d1-b8e5-90196d347476"],
Cell[99616, 1927, 604, 17, 35, "Output",ExpressionUUID->"520d28e1-a98a-4621-8959-f3d2ac5db91f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[100257, 1949, 531, 12, 55, "Input",ExpressionUUID->"20b347c3-1b61-4e6f-beab-d6b8d7bdfc7a"],
Cell[100791, 1963, 355, 6, 35, "Output",ExpressionUUID->"abfa4537-9788-4370-9b5f-356ce2a2ef35"]
}, Open  ]],
Cell[CellGroupData[{
Cell[101183, 1974, 1078, 23, 49, "Input",ExpressionUUID->"3a0094b1-1188-4132-bda5-18e66024d5c4"],
Cell[102264, 1999, 397, 8, 58, "Output",ExpressionUUID->"4bdc5577-7707-424e-a154-35711a3219db"]
}, Open  ]],
Cell[102676, 2010, 333, 8, 31, "Input",ExpressionUUID->"3383dc85-779f-4d4d-86cc-ae57b7e75229"],
Cell[103012, 2020, 379, 11, 31, "Input",ExpressionUUID->"745eb0a7-202f-4577-9085-82de73e161d7"],
Cell[CellGroupData[{
Cell[103416, 2035, 349, 8, 31, "Input",ExpressionUUID->"f14310e3-dcd1-405e-880b-c765f3b4dfe6"],
Cell[103768, 2045, 493, 13, 35, "Output",ExpressionUUID->"0d717d2d-541f-48eb-a0fa-a8847609e1b7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[104298, 2063, 600, 16, 78, "Input",ExpressionUUID->"e517a54d-a736-477c-a9f4-4c67e6b960c3"],
Cell[104901, 2081, 1527, 43, 83, "Output",ExpressionUUID->"c2231e8b-3e0e-4911-a873-5ca4f16b25f5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[106465, 2129, 365, 9, 55, "Input",ExpressionUUID->"2dc3d3ab-e138-4c30-a0b0-2c5dbd2ec677"],
Cell[106833, 2140, 236, 6, 37, "Output",ExpressionUUID->"a8f6a72b-5ff8-4746-ab40-417268b71f5a"]
}, Open  ]],
Cell[107084, 2149, 224, 6, 31, "Input",ExpressionUUID->"a1638960-d2d3-410b-99ad-9e69be359904"],
Cell[107311, 2157, 303, 7, 31, "Input",ExpressionUUID->"dfb81485-847e-4050-8d3c-6ffa7e05f6dd"],
Cell[CellGroupData[{
Cell[107639, 2168, 307, 7, 31, "Input",ExpressionUUID->"eca8e341-d39f-4fd6-af32-b519665beaf4"],
Cell[107949, 2177, 348, 11, 50, "Output",ExpressionUUID->"10af8f20-1ea0-40e4-981f-8348b2be03ac"]
}, Open  ]],
Cell[CellGroupData[{
Cell[108334, 2193, 570, 16, 78, "Input",ExpressionUUID->"ccab8048-76a8-4418-884c-ea15f130ed42"],
Cell[108907, 2211, 1141, 38, 95, "Output",ExpressionUUID->"b3d22ffc-83a0-40fc-85e7-fd0932440dd2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[110085, 2254, 365, 9, 55, "Input",ExpressionUUID->"ca63f3b6-8e83-4d16-ad7c-df997c25fbaa"],
Cell[110453, 2265, 261, 8, 64, "Output",ExpressionUUID->"f5e948f3-0ac7-4ca9-b1d7-cbdf5bc7bb19"]
}, Open  ]],
Cell[110729, 2276, 307, 7, 31, "Input",ExpressionUUID->"3b10f521-bc03-429e-9de0-b59246a3bbb2"],
Cell[CellGroupData[{
Cell[111061, 2287, 326, 7, 31, "Input",ExpressionUUID->"af2c492c-a98b-46e1-aec3-663553886f73"],
Cell[111390, 2296, 557, 18, 50, "Output",ExpressionUUID->"263d57cf-2a07-43d5-84da-5f99ee230653"]
}, Open  ]],
Cell[CellGroupData[{
Cell[111984, 2319, 577, 16, 78, "Input",ExpressionUUID->"62acff55-da66-4e67-868a-7e4df43881bb"],
Cell[112564, 2337, 2434, 81, 148, "Output",ExpressionUUID->"721c4a99-5a8a-4881-8055-5ea988008476"]
}, Open  ]],
Cell[CellGroupData[{
Cell[115035, 2423, 365, 9, 55, "Input",ExpressionUUID->"c853cb5b-6b90-4a93-adb1-65e894a6cb61"],
Cell[115403, 2434, 419, 14, 64, "Output",ExpressionUUID->"c4f04016-417f-49f2-afab-2ab90cffef72"]
}, Open  ]]
}
]
*)