The blog world is bursting right now. Hundreds of thousands of people are writing about their lives. And a lot of them are quite creative. Just so you know: you may be unique, but each small part of the unique you is probably duplicated in someone else. It’s nigh impossible to do something clever or original when you’re competing with everyone on the Internet. Here are the other names I tried before I got Thales’ Triangles to work:

- Polytropos— from the opening line of the Odyssey, where it is used to describe Odysseus. I’ve seen it translated variously as “many-traveled” and “many-talented,” but most consistently as “many-turnings.”
- Ebenezer— everyone’s favorite 19th century grouch. Which makes people confused the first time they come across it in a hymn, in the second verse of “Come, Thou Fount of Every Blessing.” It’s actually a reference to 1 Samuel 7, and was the name of a stone, raised as a testament to God’s help.
- Joie de vivre— ’cause it’s a good thing to have, and, well, I’m going to France…
- Geometer— no explanation necessary. Although I don’t quite understand why it wasn’t available, since Blogspot doesn’t seem to have a blog by that name right now.
- Horocycle— a kind of curve in hyperbolic geometry. It’s surprisingly useful. And very nifty.

Okay, so where did this name come from? And do I expect anyone to remember it? (Not much of an answer to the second question, I’m afraid.)

Thales was a Greek mathematician, possibly the first mathematician in recorded history. Wikipedia and the MacTutor archive have great long articles on him, so I won’t give a biography here. Instead, I’ll say what connection I have with him and his triangles.

When I was in Peace Corps, teaching math in West Africa, at the end of training we had a 2-week “practice school,” with volunteer students from the neighboring community. One of the weeks I was teaching le théorème de Thalès to the troisième class (essentially the equivalent of 10th grade). As usually stated, it runs something like this: Suppose M, O, and P are colinear, and N, O, and Q are colinear, and MN and PQ are parallel. Then the triangles OMN and OPQ are similar. I didn't actually like teaching this theorem that first time. I taught it again later when I was at my site and had more fun with it. The story is told that Thales used this property to measure the heights of the pyramids in Egypt by measuring the length of their shadows and comparing them to the length of the shadow of a pole stuck in the ground. So on their test I had them compute the (fictional) height of a mosque the same way.

In the U.S., a different theorem is usually known as “Thales’ theorem.” (If you read the MacTutor biography, you’ll see that five theorems are generally attributed to him.) The U.S. prefers the theorem that if one side of a triangle is a diameter of the triangle’s circumcircle, then the opposite angle is a right angle. This is also a good result, although I don’t know of any good stories to go with it.

Triangles are the key to understanding almost any geometry. As a mathematician, I’m following Thales’ footsteps. And, since I’m going to France to work on math, a reference to something mathematical I taught in a former French colony has at least a tenuous connection with my present life. Hopefully the blog’s name is now clear as mud.

As for the pronunciation of Thales’ name, I still hear it in my head as the French “tah-luhs.” But in English I think it’s usually said “thay-leez.”

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Thales could have squared the circle had he been paying closer attention to his Egyptian geometry teachers. A solution has recently been published in Vinculum, an Australian mathematics journal. A proof can be seen at

http://www.jonathancrabtree.com/mathematics/squaring-the-circle-a-practical-approach/

A cartoon showing how to square the circle, which relies on Thales for the proof, can be seen at

https://www.youtube.com/watch?v=lyRbl5zMvKc (And yes it gets around pi being transcendental.)

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