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.

7panelswhitebkgrndclradjorig180x146res72gif128.gif (7494 bytes)

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!

 

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introduction - symmetry elements defined

Exercise:  Prove the Pythagorean theorem using Polymorf panels only.

No math is permitted.

 

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Geometry rules! -  Introduction - Pythagorean system

 

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