
Geometry rules! 
. 
The Pythagorean system 
. 
. 
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 
. 
triangle.
In the most general form this is expressed by the Pythagorean theorem, 
. 
a^{2} +
b^{2} = c^{2}, where a and b are the legs and c is the hypotenuse.
What this means 
. 
literally is
that the area of a square with an edge length equal to the hypotenuse of 
. 
a right
triangle is equal to the sum of the areas of two squares whose edge lengths 
. 
are equal to
the length of each leg. The design of the Polymorf panels is based on a 
.. 
special case of
this, the isosceles right triangle, where both legs are equal in length. 
The equation
can then be written a^{2} + a^{2} = c^{2} or simply 2a^{2}
= c^{2}. 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 manmade 
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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