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.

(In reply to A small hint by Fernando)

I would call that a huge hint! Once you have this piece of information, the problem is straight forward, as Charlie's solution demontrates. I spent days on this! Now that I know this trick, I can create angles of three degrees and its multiples. Thanks :P

Is there a list somewhere of integer-based formulae for the trig functions of other angles?

Posted by Bryan on 2003-05-18 17:58:45