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.

The equation can then be written a2 + a2 = c2 or simply 2a2 = c2.  Further simplifying

the equation gives c = 1.414 X a.  The Polymorf system uses these two edge lengths

for its panels where the long edge is 1.414 times longer than the short edge length.

The seven different panel shapes come from combinations of the two edge lengths. It just so happens that this particular family of shapes can used to model some important structural types that constantly recur in natural and man-made systems.   This will be demonstrated in the following lessons. It's serendipitous!  Exercise:  Prove the Pythagorean theorem using Polymorf panels only.

No math is permitted.

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