Retorts

A Regular Pentagon Inside a Circle

Practically everyone knows how to construct a regular hexagon within a circle -- those at least who have been enticed by the title into reading this first sentence. Simply step off the radius around the circumference of the circle and join up the six points.

How about the construction of a regular pentagon within a circle? Can this also be done without the measurement of angles? "Using ruler and compasses only" as school geometry exercises would have it. I have a method which works but it may not be the only way -- I am a chemist and not a mathematician. Any suggestions, please?

Dr Michael Taylor, Chemistry Department, University of Auckland