Problem of the Week 794:

Straighten These Curves

The diagram shows a circle of radius 1, with the boundary of the shaded (gray) portion consisting of three circular arcs of radius 1 whose centers are equally spaced on the ambient circle. Dissect the unshaded (yellow) portion of the circle's interior into pieces that can be reassembled to form a rectangle.

To get the diagram: Start with a unit circle with center O and inscribe an equilateral triangle ABC. Then draw arcs through O centered at A, B, and C, respectively, and consider only the part of the arcs lying inside the circle. The propeller-like region they form is the shaded region referred to.

See Jeff Erickson's solution

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998