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Pythagorean Triples - Papers

Pythagorean Triples

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
...

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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
y=1 a=24 b=7 c=25

Check: a2+b2=c2

576+49=625
625=625

The five different equations were different ways of generating Pythagoras triples. They were very complicated. I had a very difficult time figuring these out. I am not sure how if anyway these would be useful in my real-world applications.

REFERENCE

Formulas for generating pythagorean triples. Retrieved from http://www.enotes.com/topics/formulas_for_generating_Pythagorean_triples on October 14, ...

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PAPER DETAILS

Added: 4/30/2012 10:35:20 AM
Submitted By: yolinda
Category: Miscellaneous
Type: Free Paper
Words: 239
Pages: 1

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