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Topic: Pythagorean Primitives
Replies: 4   Last Post: Apr 13, 1993 8:14 PM

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 Paul Stetzer Posts: 9 Registered: 12/4/04
Re: Pythagorean Primitives
Posted: Apr 10, 1993 1:55 PM

>>I got a call from a high school student who said she'd discovered two
>>formulas that generate Pythagorean triples. She wanted to know where to
>>look to find out if they're original. I'm sure I've read of famous

people
>>who've come up with such formulas, but I can't find anything on it. Can
>>anyone suggest where to look? Thanks

In my geometry text, Geometry for Enjoyment & Challenge, McDougal,
Littell, they give four ways to general sets of Pythagorean Triples.

The rule of Pythagoras gives the sides as (n2+1)/2 , (n2-1)/2, and n . [
Can't do exponents, read that as n squared]
The rule of Euclid gives the sides as ( m+n)/2, the root of mn, and
(m-n)/2
The Rule of Plato ( m is any even number)
m2/4 + 1, m2/4 -1, and m.
The Rule of Maseres ( m & n any two integers)
m2 + n2, 2mn, and m2 - n2.

Hope this helps.

Date Subject Author
3/24/93 Dan Bennett
3/25/93 Michael Rogers
3/25/93 Charles Yeomans
4/10/93 Paul Stetzer
4/13/93 Charles Yeomans