perplexus.info :: Shapes : Seven Region Partition

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?

See The Solution Submitted by Brian Smith

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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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