As you may know, I wrote a book on Euler’s polyhedron formula. (Euler’s formula says that every polyhedron with V vertices, E edges, and F faces satisfies V-E+F=2.) I gave a talk recently during which I lamented that kids aren’t taught this beautiful theorem; after all, it relies only on counting, addition, and subtraction.
After the talk one of the professors in the audience told me that there is a kids book that features Euler’s formula: Sir Cumference and the Sword in the Cone (2003), by Cindy Neuschwander. Well, I ordered it through our public library’s interlibrary loan, and it has arrived.
It is an Arthurian legend full of excellently terrible puns (some of the characters are Vertex, Radius, Lady Di of Ameter, and the brothers Geo and Sym of Metry). In the story, five knights are trying to prove themselves worthy of being next in line for the crown. In order to do so, they must find the sword, Edgecalibur. All they have to go on is the following riddle:
Form the solids and find their places.
How many edges, points, and faces?
The shapes that make two will pass the test,
But one that does not must be your quest.
Three times as tall as the base is wide,
The true king’s future lies inside.
After a little puzzling, Vertex figures out that he needs to find a solid for which V-E+F≠2 (as the title betrays, it turns out to be a cone). After he finds Edgecalibur he is dubbed Prince Vertex. The author points out that Vertex eventually becomes king and is known to his people as Vertex the Line-Hearted.
On the last page of the book the author cites Leonhard Euler as the discoverer of the “two’s test.”
It is a cute book. My only wish was that instead of using a cone as the counterexample to the “two’s test,” she had used a polyhedral torus.
By the way, Twitterer (@sumidiot) and blogger Nick Hamblet started a Twitter meme on favorite theorems. He was hoping that everyone would write a blog post about their favorite theorem. Since I wrote a book on mine, I decided not to do so. But hopefully this post counts!