Show, how given a distance r, one can construct a regular pentagon, whose circumradius is r, using only ruler and compass...

Note 1: The ruler doesn't have any marks, so it's no good for measuring. It's only good for joining 2 points by a line.

Note 2: The circle which circumscribes the polygon, such that the polygon lies entirely within the circle and all of whose vertices lie on the circumference of the circle is the circumcircle of the polygon. The radius of this circle is the circumradius of the circle.

It is possible to make a 17-sided polygon using the ruler and compass. If that was too easy, try 257 sides.

Posted by Brian Smith on 2003-05-23 15:13:01