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 my solution.
Back to the Fall 1995 PotW Archive.
© Copyright 1996 Stan Wagon. Reproduced with permission.
Jeff Erickson
(jeffe@cs.berkeley.edu)
Last update: 08 Mar 96