A collection of various Mathematica notebooks covering mathematical problems, algorithms, and visualizations.
- 21-digit prime in e - Finding the first 21-digit prime in the digits of e.
- Euler's sum of powers conjecture - Finding counterexamples to Euler's conjecture (a⁴ + b⁴ + c⁴ = d⁴).
- Functional equations - Solving functional equations, including the Quora problem: "If f(x) + 2f(1/x) + 3f(x/(x-1)) == x, what is f(x)?"
- Integer equation solving - Solving Diophantine-style integer equations with constraints.
- Mordell's integral - Computation and analysis of Mordell's integral.
- Ones digit calculation - Computing the ones digit of (√2 + √3)²⁰¹⁴ with high precision.
- Perfect square test - Efficient perfect square detection using Jacobi symbols and modular arithmetic. (Not original work - references StackExchange).
- Period digits - Analysis of the number of decimal digits in the period of 1/n.
- Totient function analysis - Euler totient function analysis with recursive computation and visualization.
- Covid-19 estimation for Spain - An early (and surprisingly accurate) crude estimation of the number of deaths due to Covid-19 in Spain.
- Qubits analysis - Fitting exponential model to historical qubit data (1998-2018).
- Shor's algorithm qubit requirements - Analysis of qubits needed for Shor's algorithm to factor numbers.
- Prime probabilities - Probability analysis of permutations of consecutive numbers being prime.
- Thinking depth game theory - "2/3 of the mean" game theory problem with iterated reasoning.
- Archimedes' method of estimating π - Implementation of Archimedes' geometric approach to approximating π.
- Palindromic number counting - Counting palindromic numbers less than 10ⁿ.
- Pi approximations - Various methods for approximating π, including "Pi instant" calculation.
- Circle-circle intersection points - Algorithm for finding intersection points between two circles.
- Mathematical spirals - Exploration of mathematical spirals (conical, helix, spherical, Seiffert) with 3D graphics.
- Volume of the hypersphere - Evolution of the volume formula for n-dimensional hyperspheres.
- Nearest point to a polygon - Geofence algorithm for finding the nearest point to a polygon.
- Borwein integral formulas - Exploration of the curious Borwein integral formulas.
- Fourier series analysis - Fourier series analysis with coefficient extraction and visualization.
- Interference patterns - Physics visualization of interference patterns using Fourier analysis.
For a more comprehensive listing of notebooks, see NOTEBOOK_CATALOG.md.