Constructing the Golden Ratio Using a CompassDate: 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/ |
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