Divide a circular disk into seven parts with a straightedge and compass such that each part has the same area and perimeter.

I don't believe this can be done exactly but constructing a regular heptagon in the circle will give approximate divisions. Using the radius, divide the circle into 6 parts and make an equilateral triangle. Find the midpoints of the sides of the 2 top sides of the triangle. Draw 2 lines down from the midpoints to get 2 points on the base of the triangle and bottom of the circle, and then from the top vertex of the triangle use the compass to draw 2 circular arcs through the 4 points on the triangle to get the last 4 points of 7 on the circle. Then, from the center of the circle draw radii to divide the circle into 7 approximately equal parts.

Posted by CeeAnne on 2004-12-09 17:45:03