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Pythagorean Perimeters
Posted:
Sep 28, 2005 1:01 AM


It is not often that a new theorem of exquisite simplicity arrives  least of all in the context of Pythagoras.
The world is vast, and time has aeons  so perhaps some other has made the same discovery.
However, to me, and everyone I know this is a new discovery.
It begins with the 3 4 5 triangle.
You know  you create a square on side 3, add the square on side 4 and get the square on side 5. This is all to do with AREAS.
However, what if you examine the PERIMETER of the square on side 3, and compare it with the perimeter of the triangle?
What of the 5 12 13 triangle?
Create a 2:1 rectangle on side 5. That is a 10:5 rectangle. How do the perimeters compare?
What of the 7 24 25 triangle?
Try a 3:1 rectangle  21:7.
And so on.
These are the base triangles  the smallest.
Of course, for the square you can scale up the 3 4 5 to 6 8 10, to 9 12 15 and onward.
There are also 3:2 rectangles that convert to triangles. Indeed all wholenumber ratios relate to base triangles.
It is the kind of thing that can be taught even to children. Yet it is new.
Go to http://wehner.org/pythag for the introduction, and follow the link, or directly to http://wehner.org/pythag/ratios.htm for more examples of this perimeterclassification of right triangles.
Charles Douglas Wehner
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