Mystery curve
This afternoon I got a review copy of the book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. Here’s a striking curves from near the beginning of the book, one that the author calls the “mystery curve.” The curve is the plot of exp(it) − exp(6it)/2 + i exp(−14it)/3 with t running from 0 to 2π. Here’s Python code to draw the curve. import matplotlib.pyplot as plt from numpy import
Sonnet primes in Python
A while back I wrote about sonnet primes, primes of the form ababcdcdefefgg where the letters a through g represent digits and a is not zero. The name comes from the rhyme scheme of an English (Shakespearean) sonnet. In the original post I gave Mathematica code to find all sonnet primes. This post shows how to do it in Python. from sympy.ntheory import isprime from itertools import permutations de
Introduction to Sweave and Pweave
Sweave is a tool for embedding R code in a LaTeX file. Pweave is an analogous tool for Python. By putting your code in your document rather than the results of running your code somewhere else, results are automatically recomputed when inputs change. This is especially useful with graphs: rather than including an image into your document, you include the code to create the image. To use either Swe
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Ellipsoid surface area
Log semiring
Number theoretical determinant & SymPy
Prime generating formula & SymPy
Ramanujan's nested radical
Visualizing category theory concept dependencies
Airy functions and Bessel functions
Iterating sines
Golden strings & rabbit constant
Synchronization of cicadas
Ramanujan approximation ellipse circumference
Suffix primes
Moments of mixture distributions
Exact chaos
Undamped forced vibrations: beats and resonance
Animation for mechanical vibrations
Finding 2013 in the digits of pi