Math Playground

I have a passion for numbers and symbolic calculations. Since my teenage years, I have been interested in recreational mathematics, mathematical puzzles, fundamental properties of numbers (number theory), series, polynomials, and integrals. Here is a list of topics that kept me busy for a while. For some of them, the outcome of my calculations is available in XHTML/MathJax or XHTML/MathML format by clicking on the topic (some of these pages are huge and may take a long time to download).

General Topic Especially...
Bernoulli numbers
Carmichael numbers
Chebyshev polynomials
Congruent numbers
Continued fractions Continued fraction expansions of square roots
Diophantine equations Pell's equation
Eight queens puzzle Amazons on NxN chessboard
Euclidean algorithm
Euler's totient function
Feigenbaum constants
Fermat's little theorem
Fractals Mandelbrot set, Julia set
Game of life
Generating functions
Integrals Indefinite integrals, Abelian integrals
Legendre polynomials
Magic squares
Ordinary differential equations Canonical ODEs
Overhanging dominoes
Pi decimals
Polynomial congruences
Polynomial division
Polynomial interpolation Cotesian numbers
Polynomial recurrences
Prime numbers Large primes, Mersenne primes, Prime factors
Primitive roots modulo n
Quadratic residues
Riemann zeta function ζ(s)
Series Power series, Taylor series, Maclaurin series, Laurent series, Formal power series, Closed-form expressions
Sums of powers Faulhaber's formula
Tiling puzzles Squared squares
Trigonometric identities Multiple-angle formulas: sin(2a), sin(3a), sin(4a), etc.