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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. |
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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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Exercise: Prove the
Pythagorean theorem using Polymorf panels only. |
No math is permitted. |
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Geometry rules!
- Introduction - Pythagorean system |