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Proving a2 + b2 = c2 Using Odd Numbers
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Proving a2 + b2 = c2 Using Odd Numbers a2 + b2 = c2 (2n + 1) (2n + 1) + (2n2 + 2n) (2n2 + 2n) = (2n2 + 2n + 1) (2n2 + 2n + 1) 4n2 + 8n3 + 4n2 + 4n + 1 = 4n4 + 4n3 + 2n2 + 4n3 + 4n2 +2n + 2n2 +2n +1 4n4 + 8n3 + 8n2 + 4n + 1 = 4n4 +8n3 + 8n2 +4n + 1 The above proves that a2 + b2 = c2 is correct using odd numbers and is a overall formula for Pythagorean triples. Perimeter Odds Perimeter = a + b + c a= 2n + 1 b= 2n2 + 2n c= 2n2 + 2n + 1 = 4n2 + 6n + 2 Proving that this formula is correct: If I take n=3 = 4x9 + 18 + 2 = 36 + 18 + 2 = 56 So if you look along the odds table on n=3...
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