You may have seen the joke “Enter any 12-digit prime number to continue.” I’ve seen it floating around as the punchline in several contexts. So what do you do if you need a 12-digit prime? Here’s how to find the…
Blog Archives
Synchronizing cicadas with Python
Suppose you want to know when your great-grandmother was born. You can’t find the year recorded anywhere. But you did discover an undated letter from her father that mentions her birth and one curious detail: the 13-year and 17-year cicadas…
Recognizing numbers
I was playing around with SymPy, a symbolic math package for Python, and ran across nsimplify. It takes a floating point number and tries to simplify it: as a fraction with a small denominator, square root of a small integer,…
Rolling dice for normal samples: Python version
A handful of dice can make a decent normal random number generator, good enough for classroom demonstrations. I wrote about this a while ago. My original post included Mathematica code for calculating how close to normal the distribution of the sum…
Moments of mixtures
I needed to compute the higher moments of a mixture distribution for a project I’m working on. I’m writing up the code here in case anyone else finds this useful. (And in case I’ll find it useful in the future.)…
New introduction to SciPy
The Python stack for scientific computing is more modular than say R or Mathematica. Python is a general-purpose programming language that has libraries for scientific computing. R and Mathematica are statistical and mathematical programming languages that have general-purpose features. The…
Suffix primes
MathUpdate tweeted this afternoon that Any number made by removing the first n digits of 646216567629137 is still prime. and links to sequence A012885 in the Online Encyclopedia of Integer Sequences (OEIS). The OEIS heading for the sequence is Suffixes…
Wallpaper and phase portraits
Suppose you want to create a background image that tiles well. You’d like it to be periodic horizontally and vertically so that there are no obvious jumps when the image repeats. Functions like sine and cosine are period along the…
Exact chaos
Pick a number x between 0 and 1. Then repeatedly replace x with 4x(1-x). For almost all starting values of x, the result exhibits chaos. Two people could play this game with starting values very close together, and eventually their…
Python animation for mechanical vibrations
Stéfan van der Walt wrote some Python code to animate the system described in yesterday’s post on mechanical vibrations. Stéfan posted his code on github. It currently illustrates undamped free vibrations, but could be modified to work with damped or…
Continued fractions with Sage
My previous post looked at continued fractions and rational approximations for e and gave a little Python code. I found out later there’s a more direct way to do this in Python using Sage. At its simplest, the function continued_fraction…
Rational approximations to e
This morning Dave Richeson posted a humorous fake proof that depends on the famous approximation 22/7 for pi. It occurred to me that nearly everyone knows a decent rational approximation to pi. Some people may know more. But hardly anyone,…
Python / Emacs setup
When I got a new computer a few days ago, I installed the latest version of Emacs, 24.2, and broke my Python environment. I decided to re-evaluate my environment and start over. I asked a question on the Python Google+…
Narcissus prime in Python
I’ve been looking back on some of my blog posts that included Mathematica code to see whether I could rewrite them using Python. For example, I rewrote my code for finding sonnet primes in Python a few days ago. Next…
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…
