Geometry rules |
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The Pythagorean system |
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| The great diversity of models that can be constructed with Polymorf panels is | |||||||||
due in large part to the relationship of the legs to the hypotenuse of the right |
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triangle. In the most general form this is expressed by the Pythagorean theorem, |
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a2 + b2 = c2, where a and b are the legs and c is the hypotenuse. What this means |
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literally is that the area of a square with an edge length equal to the hypotenuse of |
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a right triangle is equal to the sum of the areas of two squares whose edge lengths |
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are equal to the length of each leg. The design of the Polymorf panels is based on a |
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special case of this, the isosceles right triangle, where both legs are equal in length. |
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The equation can then be written a2 + a2 = c2 or simply 2a2 = c2. Further simplifying |
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the equation gives c = 1.414 X a. The Polymorf system uses these two edge lengths |
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for its panels where the long edge is 1.414 times longer than the short edge length. |
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The seven different panel shapes come from combinations of the two edge lengths. |
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Exercise: Prove the Pythagorean theorem using Polymorf panels only. |
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No math is permitted. |
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Geometry rules! - Introduction - Pythagorean system |
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