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CTK Exchange
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Nick Mitchell
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Dec-17-08, 08:23 AM (EST) |
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2. "RE: Is this a mathematical theorem ?"
In response to message #1
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Alexb, it depends on how you letter the corners of the square. You seem to have assumed that A is diagonally opposite D and B is diagonally opposite C. But if you assume that they are lettered ABCD in order as you go around the square, then the theorem is true and can easily be proved using Pythagoras's Theorem. |
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alexb
Charter Member
2333 posts |
Dec-17-08, 08:32 AM (EST) |
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3. "RE: Is this a mathematical theorem ?"
In response to message #2
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Do not know what it was I assumed. Let the side of the square be 1, the coordinates of P relative to the origin at the left lower corner A, with axes along the sidelines be (a, b). Then AP² = a² + b²
BP² = (1-a)² + b²
CP² = (1-a)² + (1-b)²
DP² = a² + (1-b)² So you are right: it follows by the Pythagorean theorem that AP² + CP² = BP² + DP² Sorry. What a mess! |
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