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### How Many Proofs of the Pythagorean Theorem?

```Date: 03/27/2003 at 19:11:14
From: Coco
Subject: The Pythagorean Theorem

I was wondering if you know the exact number of proofs of the
Pythagorean Theorem in existence.
```

```
Date: 03/27/2003 at 23:20:16
From: Doctor Peterson
Subject: Re: The Pythagorean Theorem

Hi, Coco.

Even if I had every single proof anyone had ever written, I couldn't
count them, because I couldn't decide how different two proofs have
to be in order to be counted.

But someone wrote a book in which he showed 367 proofs that were
41 of them:

Pythagorean Theorem and its Many Proofs - Bogomolny
http://www.cut-the-knot.org/pythagoras/index.shtml

and has a footnote:

W.Dunham [Mathematical Universe] cites a book The Pythagorean
Proposition by an early 20th century professor Elisha Scott
Loomis. The book is a collection of 367 proofs of the

Pythagoras' Theorem
http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/java/html/
pythagoras.html

describes the book just a little differently:

Elisha Loomis, The Pythagorean Proposition, National Council of
Teachers of Mathematics, 1968. This eccentric book was first
compiled in 1907, first published in 1928 (at a price of \$2.00!),
and reissued in this edition. It contains 365 more or less
distinct proofs of Pythagoras' Theorem. The total effect is
perhaps a bit overwhelming, and the quality of the figures is
very poor, but nonetheless there are a few gems distributed
throughout.

The following page

The Pythagorean Theorem - Jim Loy
http://www.jimloy.com/geometry/pythag.htm

says

The book The Pythagorean Proposition, By Elisha Scott Loomis,
is a fairly amazing book. It contains 256 proofs of the
Pythagorean Theorem. It shows that you can devise an infinite
number of algebraic proofs, like the first proof above. It
shows that you can devise an infinite number of geometric
proofs, like Euclid's proof. And it shows that there can be
no proof using trigonometry, analytic geometry, or calculus.
The book is out of print, by the way.

I'm not sure which number is right, but it appears that you can't
count the number of distinct proofs, in any case.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

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