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Problem of the Week 794:

Straighten These Curves

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Solution:

Here is a six-piece solution, yielding a rectangle of height 3/2 and width 2 Sqrt[3].

I derived the dissection by looking at the unique monorhombic tiling of the plane by "manta rays":


Several different rectangles with area 3 Sqrt [3] "respect" this tiling. Each one results in a different dissection. The one shown here has the fewest pieces of all the dissections that can obtained from this tiling. Other tilings yield even more dissections.

I strongly suspect that the dissection shown here is the only one with six pieces (up to symmetry, of course) and that no dissection with five or fewer pieces is possible.

Solution courtesy Jeff Erickson.

[Back to Problem 794]

©Copyright 1996 Jeff Erickson. Reproduction for profit prohibited. Free reproduction encouraged.

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The Math Forum

6 October 1998