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Topic: Tangram and Pythagoras

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Tangram and Pythagoras
Posted: Jun 2, 1994 4:21 PM

Han: where did you find that Pythagoras proof? I've seen a lot
of proofs in my time (and have read systematically through books
that contain more than 50 of them), but don't recall anything
like that one.

Here's what I consider one of the simplest proofs:

A---B-------C A---B-------C
| | | | |
| D H---I-------D
| | | | |
H | | | |
| | | | |
G-------F---E G---F-------E

4 triangles + 4 triangles +
square on hypotenuse sum of squares
on other two sides

I mentioned another one on geometry forum recently: Plainly
the truth-value of the theorem would be unaltered if we place
d any similar figures (eg., semicircles) on the edges, instead
of squares. But look:

/| \
/ | \
/ | \

The triangles ADC, CDB, and ACB ARE similar figures,
and plainly ADC + CDB = ACB.

John Conway


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