Question
I'm a little confused about what a Pythagorean Triple is.
As long as your two legs are both whole numbers, isn't every one a triple?
As long as your two legs are both whole numbers, isn't every one a triple?
Answers
Reiny
A Pythagorean triple consists of 3 whole numbers a, b, and c such that
a^2 + b^2 = c^2 ---> that's the Pythagorean Theorem
e.g. a = 5, b=12, and c=13 is one of them
because 5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
If you randomly pick any such 3 numbers, the vast majority will not fit that pattern.
e.g. a = 4 , b = 7 , c = 9
is 4^2 + 7^2 = 9^2 ? , not very likely
here is a little algorithm that will produce Pythagorean triples.
let m and n be any two whole numbers, where m > n
then
<b>2mn</b>
<b>m^2 - n^2</b> , and
<b>m^2 + n^2</b> will always produce such a triple
e.g. let m = 7, n = 4
2mn = 56
m^2-n^2 = 49-16 = 33
m^2 + n^2 = 49+16 = 65
is 56^2 + 33^2 = 65^2 ? , it sure is !
a^2 + b^2 = c^2 ---> that's the Pythagorean Theorem
e.g. a = 5, b=12, and c=13 is one of them
because 5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
If you randomly pick any such 3 numbers, the vast majority will not fit that pattern.
e.g. a = 4 , b = 7 , c = 9
is 4^2 + 7^2 = 9^2 ? , not very likely
here is a little algorithm that will produce Pythagorean triples.
let m and n be any two whole numbers, where m > n
then
<b>2mn</b>
<b>m^2 - n^2</b> , and
<b>m^2 + n^2</b> will always produce such a triple
e.g. let m = 7, n = 4
2mn = 56
m^2-n^2 = 49-16 = 33
m^2 + n^2 = 49+16 = 65
is 56^2 + 33^2 = 65^2 ? , it sure is !