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Pythagorean Triples

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OCTOBER 15, 2011


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


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


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

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


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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