The Alpha Geek Programs Math

judebert@judebert.com (Judebert) — Thu, 11 Jun 2009 15:41:46 -0400

I know I've been neglecting my blogs lately. And my online forums. And FaceBook. I apologize.

I've been working on a neat little puzzle game. Not a "puzzle game" like Bejeweled or those other match-up toys. Something that actually requires a little bit of thought, like Sudoku or Griddlers, but more logic. I've got a prototype, but I'm not ready to release it just yet; I promise to let you know when it's ready.

What's taken me so long is the mathematical whirlwind I've immersed myself in. It's been delightful. (Yes, the Alpha Geek enjoys math.) For a rather minor aspect of the coding, I needed a way to sum any pair of 36 possible numbers and guarantee that the result was unique for that pair. (In mathematical terms, I needed a set such that a_i + a_j is distinct for all i < j.) I searched online for days before finding what I need: weak Sidon sets, also known as "well-spread sets" or S₂ sets.

It turns out that nobody has published any weak Sidon sequences of any appreciable length, though. I needed to write a program to generate them.

My first try turned up a 36-member set and a 100-member set in short order. But I wanted smaller numbers, so I programmed more exhaustive search methods. One of them ran for 36 hours before Kayla decided to log me out, destroying all my progress.

So I modified the program. It now finds all well-spread sequences of a particular length chosen from the set of integers smaller than a specified maximum. And it saves its progress, so if I'm ever interrupted again, I can simply resume. I can even run on multiple computers by generating new start states (although of course I'll have to quit one of the programs manually).

When I've got my first set of sequences, I'll publish my results and my program. I just thought you should know why you haven't heard much from me.

Math Injury

judebert@judebert.com (Judebert) — Mon, 02 Feb 2009 14:35:20 -0500

Tatiana went to another Mu Alpha Theta competition this weekend. She took 9th place in the individual geometry competition! (Read on for one of the interesting problems she couldn't get.)

Unfortunately, she suffered an injury. You don't normally associate injuries with math; it's not a rough sport or anything. But it turns out Tatiana inherited her mother's brittle feet. She severely sprained her ankle on the way to the stage.

She's on crutches and ibuprofen.

Update 2009-02-04: I will no longer take my family to the CentraCare on University Blvd. After 48 hours without a reduction in swelling, we took her to our pediatrician, who discovered that the leg is actually fractured. Tatiana is now in a walking cast for 4 weeks.
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