The Pythagorean Theorem is famous because it has made almost all upper level math possible, opening up new fields in science. Sine Cosine and Tangent are based on this theorem, and, thereby, all parts of mathematics related directly or indirectly to trigonometry.
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Yes. The square of an odd number is odd. So, if a, b and c are odd then a2, b2 and c2 are also all odd. But the sum of two odd numbers must be even. So for these to be Pythagorean, all three squares cannot be odd. Thus there are no odd triplets.
A "Pythagorean triple" is a set of 3 numbers that fits the Pythagorean Theorem.So your question is: "Do 2, 6, and 8 form a Pythagorean triple ?", and the answeris either 'yes' or 'no'.(2)2 = 4(6)2 = 364 + 36 = 40(8)2 = 6440 is not equal to 64.So the answer is "no".
No. 122 + 162 = 400 = 202 so 12, 16, 20 would be a Pythagorean triple, but 12, 16, 18 would not.
Yes, I have used the Pythagorean system for numerous phrases and words and they all wind up equaling a number between 1 and 9. So go for it.
6, 8, and 10 is simply a scaled up version of a 3,4,5 triangle (simply double each side). Since 3,4,5 is a Pythagorean triple, so is the scaled up triangle. Alternatively, since 6, 8, and 10 are integers (whole numbers) that fulfill the Pythagorean theorem (62 + 82 = 102 ), they are a Pythagorean triple.