## Pythagorean Triples

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PYTHAGOREAN TRIPLES

YOLINDA RATLIFF

MAT 126: SURVEY OF MATHEMATICAL METHODS

LAURA CELLA

OCTOBER 15, 2011

RUNNING TITLE: PYTHAGOREAN

There are many different ways of generating triples. Many of which have no specific origin. In this assignment several of these different formulas were used. There are also versions that have been designated to one person such as Euclid's formula, and the parent/child relation- ship.

a=2n+1 b=2n(n+1) c=2n(n+1)+1
a=2(2)+1 b=2(2)(2+1) c=2(2)(2+1)+1
a=4+1 b=4(3) c=4(3)+1
a=5 b=12 c=13

Check: a2+b2=c2

25+144=169
169=169

a=u2+2uv b=2v2+2uv c=u2+2v2+2uv
a=9+2(3(5)) b=2(25)+2(3(5)) c=9+2(25)+2(3(5))
a=9+30 b=50+30 c=9+50+30
a=39 b=80 c=89

Check: a2+b2=c2

1521+6400=7921
7921=7921

a=2m b=m2-1 c=m2+1
a=2(4) b=16-1 c=16+1
a=8 b=15 c=17

Check: a2+b2=c2
8,2+15,2=17,2
64+225=289
289=289

new side a new side b new side c
a-2b+2c 2a-b+2c 2a-2b+3C
a=3 3-2(4)+2(5) 2(3)-4+2(5) 2(3)-2(4)+3(5)
b=4 3-8+10 6-4+10 6-8+15
c=5 -5+10=5 -2+10=12 -2+15=13

Check: a2+b2=c2

25+144=169
169=169

z=6 5. a=x+z b=y+z c=x+y+z
x=18 a=18+6 b=1+6 c=18+1+6<...

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