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 Seven Region Partition (Posted on 2017-05-27)
The diameter of a polygon is defined as the longest distance between any pair of vertices of the polygon.

Partition a unit equilateral triangle into seven regions so that all seven regions have the same polygon diameter.

How small can that diameter be made?

 No Solution Yet Submitted by Brian Smith No Rating

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 re: Solution? | Comment 2 of 3 |
(In reply to Solution? by Steve Herman)

I think you mean similar right trapezoids instead of parallelograms.  Anyways, I come up with a polygon diameter of (-1+sqrt(45))/11 = 0.51893 for your configuration.  But that is still larger than what I have.

My arrangement does use a central triangle like yours, but I don't connect any segments to the midpoints of either triangle.

 Posted by Brian Smith on 2017-05-28 10:31:08
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