Constructing the Golden Ratio Using a Compass

Date: 12/30/2003 at 11:09:38
From: Sam
Subject: Constructions of the Golden Ratio

I am writing a paper on the Golden Ratio and want to include a section
on how to construct the ratio on a line using a compass.  Could you
please explain the construction?

Date: 12/30/2003 at 14:16:00
From: Doctor Rob
Subject: Re: Constructions of the Golden Ratio

Thanks for writing to Ask Dr. Math, Sam!

Start with a line segment OS.  Draw a circle with center O and radius
OS.  Then follow the construction of the regular pentagon as described
on this page:

  Construction of a Regular Pentagon
    http://www.mathforum.org/dr.math/faq/formulas/faq.regpoly.html#floor

Then the ratio of OE' to E'S is (1+sqrt[5])/2 = 1.61803..., the Golden
Ratio, and the ratio of OS to OE' is also the Golden Ratio.

Feel free to write again if I can help further.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/