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Topic: tangrams
Replies: 3   Last Post: Sep 28, 2007 2:55 PM

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Mary Krimmel

Posts: 629
Registered: 12/3/04
Posted: Oct 5, 2004 1:22 PM
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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
middle-sized 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
non-convex pentagon or a non-convex 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 non-convex 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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