## A nice proof without words

Here's a very cool proof without words by Burkard and Marty.

Can you figure out what this proof without words illustrates?

## 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?

## A beautiful proof without words

While surfing the Web for Math-related stuff I happened upon this wonderful "proof" without words:

Can you figure out what the image illustrates? Can you figure out what two facts you need to know to do the "proof?" Yes, I realize that visual demonstrations are not proofs.

If you need a hint, check out the original document by Professor Osler.

## A picture is worth …

How many of you remember doing geometry proofs in High School? How many of you enjoyed writing them? I don’t know about you but I’ve always preferred pictures to words when it comes to understanding how something works.

“Proofs Without Words: Exercises in Visual Thinking” by Roger B. Nelsen is a wonderful book that provides visual insights into how one might go about proving mathematical theorems. The Pythagorean Theorem has always been a mystery to me. How are the squares of the sides of a right triangle related to its hypotenuse? “Proof Without Words” has five clever illustrations that guide readers in writing their own proofs.

If you ever doubted that algebra and geometry were related, the diagrams demonstrating how to compute sums of series will produce aha! experiences.

Writing proofs when one is guided by visual cues is a much more fulfilling endeavor than stringing together dry facts from memory. This book delivers much fulfillment in exploring theorems in geometry, algebra, trigonometry, sequences, and other aspects of Math.