Monthly Archives: June 2016

The route puzzle

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

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

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!

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