Category Archives: geometry

Making connections

Posted on April 20, 2013 by

Here’s something fun I was playing around with today. I generated 100 random points and connected some of them with lines. Can you figure out how I chose which lines to draw? How about these? (Same points, different lines.) Or … Continue reading →

Posted in challenges, geometry | Tagged , , , | 10 Comments

Stars of the Mind’s Sky with Diagrams

Posted on April 6, 2013 by

A few weeks ago, Paul Salomon posted a really beautiful work of mathematical art on his blog, Lost In Recursion: Stars of the Mind’s Sky, by Paul Salomon He included a precise mathematical description of the image, and I naturally … Continue reading →

Posted in geometry, group theory, pictures, programming | Tagged , , , , , | 9 Comments

Penrose tiles on my refrigerator!

Posted on March 8, 2013 by

I got some Penrose refrigerator magnets in the mail the other day! They look nice on my fridge, don’t you think? Here’s a close-up: (Unfortunately, since this was just a Kickstarter project there’s no way to order more at this … Continue reading →

Posted in geometry, pattern, pictures | Tagged , , , , | 6 Comments

Book review: Discrete and Computational Geometry

Posted on December 29, 2012 by

Discrete and Computational GeometrySatyan L. Devadoss & Joseph O’Rourke [Full disclosure: Princeton Press kindly sent me a free review copy of this book, and Satyan Devadoss is a (former) teacher and (current) good friend of mine. I was the TA … Continue reading →

Posted in books, computation, geometry, pictures, review

Searchable tiling database

Posted on August 2, 2012 by

Just a link today—check out this awesome tiling database! It’s got tons of beautiful plane tilings (with information and further reading about each one) and many ways to search through the database. It’s a great way to find examples of … Continue reading →

Posted in geometry, group theory, links, pattern, pictures | Tagged , , , , | 2 Comments

Book review: In Pursuit of the Traveling Salesman

Posted on April 7, 2012 by

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 →

Posted in books, computation, geometry, open problems, review | Tagged , , | 6 Comments

Dimensions: go watch! now!

Posted on November 21, 2011 by

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

Posted on November 18, 2011 by

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 →

Posted in books, fractals, geometry, pattern, pictures, review | Tagged , , , , ,

Area paradox unmasked

Posted on May 8, 2011 by

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 →

Posted in geometry, pictures, puzzles, solutions | Tagged , , , | 1 Comment

An area paradox

Posted on May 2, 2011 by

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