A game for budding knot theorists

Thanks to Sam Shah for introducing me to this fascinating online game: Entanglement. The rules are simple. You are given hexagonal tiles, one at a time, each adorned with six short segments of rope. Use them to construct the longest possible knot (measured in segments) before running into a wall.  Entanglement is fun and addicting!…

Mathematical surprises

I’m interested in compiling a list of “mathematical surprises.” The best possible example would be a mathematical discovery that no mathematician saw coming, but after it was discovered it changed mathematics in some fundamental way—Cantor’s discovery of the nondenumerability of the continuum is such an example. But I’ll settle for any surprise—Andrew Wiles surprised everyone…

Goodstein’s unprovable theorem

Recently I learned about a family of sequences of nonnegative integers (called Goodstein sequences) and two remarkable theorems about these sequences. Begin with any positive integer . This is the first term in the sequence. For example, suppose we begin with . The first step in computing the second term of the sequence, , is…

An island on an island on an island

A few weeks ago I wrote about an island on an island on a landmass. Today I found this website which shows an island on an island on an island. Pretty cool! Zoom out on the map below to see the nested islands. There is a puddle… …on an island… …in a lake (Crater Lake)……

The left-handed boy problem

A few months ago Gary Foshee was scheduled to speak at the Gathering for Gardner. He got up and gave a presentation that was all of three sentences. He said: I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? This deceptively simple problem quickly made…

Mathematical magic tricks for kids

My six-year-old son loves the website ActivityTV.com, especially their science, origami, cooking, and magic videos. I watched a few of the magic how-to videos with him and was pleasantly surprised to see that some of them had a distinctly mathematical feel to them. For example: Jumping rubber bands: topological properties of circles and linked circles…