Thread: 4 not so easy pieces? View Single Post
2006-09-27, 21:21   #8
ewmayer
2ω=0

Sep 2002
República de California

100110001111112 Posts

Assume the initial circle is centered at (0,0) and has radius 1. Now draw a pair of circles of half that radius, one centered at (0, 1/2), the other at (-1/2, 0). These intersect (in the sense of touching at a single point) at (0,0), and thus subdivide the large circle into 4 equal-area subsets, two of which are circles, two of which are not.

Quote:
 Originally Posted by Wacky Next divide the remainder into 3 equal parts. The easiest way would be to use radial lines. But this is not allowed. Therefore simply rotate the outer endpoints a uniform distance along the circumference.
"Outer endpoints" of what?

It seems to me a tricky problem might be to subdivide into 4 equal-area pieces, without having any of the resulting piece boundaries intersect the center of the original circle, and without ever placing the point of one's compass or ruler so it touches the center. I need to think about that a bit more...