[Verse 1] Ancient Greeks discovered something strange Right triangles with a perfect range Three whole numbers in a special way A squared plus B squared equals C today But not all triples are the same you see Some are primitive, some are family When A and B share no common ground That's when primitive triples can be found [Chorus] M squared minus N squared gives you A Two times M times N shows you the way M squared plus N squared equals C Pythagorean magic, can't you see M is bigger than N, N above zero M and N are coprime, that's our hero M minus N must be odd, don't forget This formula gets every triple set [Verse 2] Let's take M as five and N as two Check our conditions, see what we can do Five is greater than two, that works fine GCD of five and two is one, we're in line Five minus two is three, that's odd indeed Now we calculate what we really need A equals twenty-five minus four B equals twenty, C is twenty-nine for sure [Chorus] M squared minus N squared gives you A Two times M times N shows you the way M squared plus N squared equals C Pythagorean magic, can't you see M is bigger than N, N above zero M and N are coprime, that's our hero M minus N must be odd, don't forget This formula gets every triple set [Bridge] Twenty squared plus twenty-one squared Equals twenty-nine squared, perfectly paired Four hundred plus four-forty-one Equals eight-forty-one when we're done From any M and N that qualify Infinite triples we can multiply Three-four-five and five-twelve-thirteen Generated by this ancient machine [Final Chorus] M squared minus N squared gives you A Two times M times N shows you the way M squared plus N squared equals C Pythagorean triples, wild and free Remember the rules, don't let them go M greater than N, both above zero Coprime together, difference is odd Euclid's gift, mathematically awed [Outro] Every primitive triple you will find Comes from this formula in your mind Pythagorean secrets now revealed Ancient wisdom, forever sealed
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