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Plane tiling proof of …

Simon and Schuster sent me a copy of Alex Bellos' new book: Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math. The book is remarkable. Alex Bellos is a gifted journalist who traveled around the world to interview people who had interesting stories to tell. The stories involve Math but not the kind of Math that one would need college classes nor even much of a high school Math background to enjoy. This is a great book for the mathematically curious layperson.

This blog article is not a review of the book but a sharing of a great experience of joy I had when I saw an amazing tiling in Chapter 2. Rather than scan in the tiling I found one in a paper at Roger Nelsen's site. (Nelsen is the author of "Proofs Without Words" and other books.) The paper, "Paintings, Plane Tilings, & Proofs," is quite a remarkable paper. There are links to a number of interesting papers by Nelsen here.

Here's the tiling:

The tiling is attributed to Annairizi of Arabia. Can you figure out what the tiling illustrates and how it does so?

To say that I was very impressed is a huge understatement.

What do you think?

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  1. This tiling illustrates the Pythagorean Theorem. ‘a’ is the side of the small gray square (one leg of the light gray right triangle) so it’s area is a^2. ‘b’ is the side of the light gray square (the other leg of the light gray right triangle) so it’s area is b^2. The hypotenuse of the light gray triangle is the side, ‘c’, of the blue square outline. The blue square outline covers a^2 +b^2 which equals c^2.

    Nice post!

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