Difference between revisions of "Pythagorean triple"
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'''Pythagorean triple''' is a triple of [[integer]]s that follow the following formula: | '''Pythagorean triple''' is a triple of [[integer]]s that follow the following formula: | ||
:<math>a^2+b^2=c^2</math> | :<math>a^2+b^2=c^2</math> | ||
| + | Some of the simplest triples are: | ||
| + | :<math>3^2+4^2=5^2</math> and <math>5^2+12^2=13^2</math> | ||
| + | Studying these two triples, the reader may have the [[insight]] that | ||
| + | :<math>3^2=4+5</math> and <math>5^2=12+13</math> | ||
| + | This leads to a trivial sequence that generates some but not all possible triples is based on the positive integers starting with <maht>a=3</math>:<ref>http://web.archive.org/web/20090916034804/http://www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html</ref>: | ||
| + | : If <math>a</math> is odd, then <math>b=a^2/2-1/2</math> and <math>c=b+1</math> | ||
| + | : If <math>a</math> is even, then <math>b=a^2/4-1</math> and <math>c=b+2</math> | ||
==Notes== | ==Notes== | ||
Revision as of 00:25, February 10, 2017
Pythagorean triple is a triple of integers that follow the following formula:
Some of the simplest triples are:
- and
Studying these two triples, the reader may have the insight that
- and
This leads to a trivial sequence that generates some but not all possible triples is based on the positive integers starting with <maht>a=3</math>:[1]:
- If is odd, then and
- If is even, then and
