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Seven Region Partition (Posted on 2017-05-27) Difficulty: 3 of 5
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    
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Solution Probably solution Comment 3 of 3 |
Diameter = 1/(1+sqrt(3)) = .366

A Steve did, place a central equilateral triangle with the same orientation.  

From each corner of this triangle draw two lines to the unit triangle.  These lines are not quite perpendicular, but bent inward slightly to create isosceles trapezoids with 75 and 105 degree angles.  They have two equal diagonals which equal their diameter.

The remaining shapes are kites.  Their symmetry lines show they are composed of two isosceles triangles and so they have three lengths that equal their diameter.

  Posted by Jer on 2017-05-29 08:31:25
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