Category Archives: geometry

Book review: In Pursuit of the Traveling Salesman

As mathematical problems go, the “traveling salesman problem” (TSP) is a rare gem: it is simultaneously of great theoretical, historical, and practical interest. On the theoretical front, it is a well-known example of the class of “NP-complete” problems, which lie … Continue reading

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Dimensions: go watch! now!

I finally got around to watching the Dimensions videos, which I mentioned once before. They are super cool and will be sure to blow your mind! They start by explaining some simple tools (stereographic projection) and intuition (with references to … Continue reading

Posted in fractals, geometry, links, video | Tagged , , , , | 2 Comments

Book review: Viewpoints: Mathematical Perspective and Fractal Geometry in Art

This book is certainly quite different from the sort I usually read and review—but I am always interested in new and creative ways to teach mathematics! This is quite a fun book. It’s all about visual art and some of … Continue reading

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Area paradox unmasked

In my last post I presented a paradox, where a set of four pieces forming an 8×8 square could apparently be rearranged to form a 5×13 rectangle, summoning an extra unit of area out of thin air. Quite a few … Continue reading

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An area paradox

Here’s a fun paradox which has been around for quite a while and was apparently a favorite of Lewis Carroll. As you can verify for yourself, the two figures above are composed of two different rearrangements of the same four … Continue reading

Posted in challenges, geometry, paradox, pictures | Tagged , , | 18 Comments

Penn Alexander math club: map coloring

Today in math club I had the students explore map coloring. I tried to leave it as open-ended as possible to start—I just said that we were going to draw maps with countries, and try to give each country a … Continue reading

Posted in geometry, pattern, puzzles, teaching | Tagged , , , | 4 Comments


Just a link today: Mike Croucher over at Walking Randomly has some gorgeous pictures of fractal constructions called “pentaflakes”, made by recursively gluing pentagons together in various ways. He’s also made a Mathematica demonstration for playing around with various sorts … Continue reading

Posted in fractals, geometry, links | Tagged , , , | 1 Comment