Monthly Archives: June 2016

The route puzzle

Posted on June 17, 2016 by Brent

While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading →

Posted in arithmetic, challenges, number theory, proof, puzzles | Tagged , , , , , , | 7 Comments

The Recamán sequence

Posted on June 12, 2016 by Brent

I recently learned about a really interesting sequence of integers, called the Recamán sequence (it’s sequence A005132 in the Online Encyclopedia of Integer Sequences). It is very simple to define, but the resulting complexity shows how powerful self-reference is (for … Continue reading →

Posted in arithmetic, recursion, sequences | Tagged , , , , | 5 Comments

Apollonian gaskets and Descartes’ Theorem II

Posted on June 10, 2016 by Brent

In a few previous posts I wrote about “kissing sets” of four mutually tangent circles, and the fact that their signed bends satisfy Descartes’ Theorem, (Remember that the signed bend of a circle is like the curvature , except that … Continue reading →

Posted in geometry, pattern, pictures, recursion | Tagged , , , , , , , | 1 Comment

10th anniversary of TMLT!

Posted on June 2, 2016 by Brent

It’s a little hard to believe, but The Math Less Traveled recently had its 10th anniversary! I started it back in March 2006, while I was teaching high school math. Since then I’ve written 333 posts (a bit more than … Continue reading →

Posted in meta | Tagged , | 2 Comments