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tangrams
Posted:
Oct 5, 2004 1:22 PM


At 03:44 PM 10/2/04 0400, you wrote: >can anyone help??? > >how do u make a pentagon from 7 tangram pieces??????
Here is one way. Label the two large triangles 1 and 2; label the two small triangles 3 and 5; label the square 4; label the parallelogram 6; label the middlesized triangle 7. Assign an area of 1 for the entire 7 pieces, so that the hypotenuse of 1 or 2 has length 1.
Now make a square of side half the square root of 2, using pieces 3,4,5,6,7. (If you cannot do this, ask here.) On one side of this square place 1. You now have a quadrilateral. On an adjacent side of the square place 2. Depending on which of the adjacent sides you choose and on which side of 2 is "up", you can have either an isosceles right triangle, a nonconvex pentagon or a nonconvex bilaterally symmetric hexagon.
The sides and angles of the pentagon are 1, 225 degrees, 2^2/2, 45 degrees, 1, 135 degrees, 2^2/2, 90 degrees, 2^2, 45 degrees.
If this is not clear, ask.
I expected this problem to be easy. It was not easy for me. I believe that there are other nonconvex pentagons possible and that there is no convex pentagon. Anyone? Google found several tangram sites. Can anyone recommend a site that addresses this problem?
Mary Krimmel
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