A while back, someone asked me for a good way to plot a Klein Bottle in Maple. I didn't have a good answer at the time, but I recently stumbled upon the following, which does a pretty good job if you don't mind the use of Heaviside in the parameterization.

plot3d(
   [4*(1-1/2*cos(u))*sin(v),
    6*cos(u)*(1+sin(u))+4*(1-1/2*cos(u))*(cos(u)*(1-Heaviside(u-Pi))+Heaviside(u-Pi))*cos(v+Pi*Heaviside(u-Pi)),

In a previous post, I promised to write about testing the quality of pseudo-random number sequences.  I'll post later about some of the statistical tests often used, but I first wanted to mention a sort of practical test one can do. One of the many things you might want to do with pseudorandomly generated numbers is Monte Carlo integration/simulatation/etc.  As mentioned by acer in this comment, Monte Carlo integration can be shown to work better with some of the pseudorandom number generators (PRNGs) which are considered inferior in a statistical sense.  In this post, we will play with a simple Monte Carlo approximation of π.

It always makes me happy to see people using Maple for interesting things.  So I was pleased to see this blog post on Technology Review about this paper on arXiv on quantum randomness.  In this case, they are just comparing random numbers generated from lasers (this is why physicists get better press than mathematicians: LASERS!) with pseudo-random numbers generated using Meresenne Twister implemented in Maple, pseudo-random numbers generated using a Celluar Automata method implemented in another computer algebra system, and then binary digits of π treated as a pseudo-random sequence.  (Spoiler: the lasers win)

While not a particularly interesting use of computer algebra systems, it did inspire me to revisit my old blog post on pseudo-random numbers in Maple and now I am working on a follow up that talks about some of the mathematical and statitical tests used to test the quality of pseudo-random number sequences which I hope to post soon.

A long while ago, I wrote a couple posts (part1 and part2) about mining data from the US SSA website.  I subsequently adapted the code from those blog posts into a visual application with sliders and interactive plots.  If you have played with the new ?MapleCloud functionality in Maple 14, you may have seen it posted already.

Every year my extended family does a "secret santa" gift exchange. Each person draws another person at random and then gets a gift for them. At first, none of my siblings were married, and so the draw was completely random. Then, as people got married, we added the restriction that spouses should not draw each others names. This restriction meant that we moved from using slips of paper on a hat to using a simple computer program to choose names. Then people began to complain when they would get the same person two years in a row, so the program was modified to keep some history and avoid giving anyone a name in their recent history. This year, not everyone was participating, and so after removing names, and limiting the number of exclusions to four per person, I had data something like this: