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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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