One of the more difficult constructions to do using unmarked straightedge and compasses is the regular pentagon. There are many ways to do this construction, none particularly easy. Your students might try to develop a construction on their own, realizing that the Golden Section is very much involved here.
For years, engineers have been using a method for drawing what appears to be a regular pentagon; yet careful inspection will show that the construction is a tiny bit irregular.? This method, which we will provide below, was developed in 1525 by the famous German artist, Albrecht Dürer.
We refer to Fig 5.13a on page 162. Beginning with a segment AB, five
circles of radius AB are constructed as follows:
1. Circles with centers at A and B are drawn and intersect at Q and N.
2. Then the circle with center Q is drawn to intersect circles A and B at points R and S, respectively.
3. QN intersects circle Q at P.
4. ??SP and ??RP intersect circles A and B at points E and C, respectively.
5. Draw the circles with centers at E and C with radius AB to intersect at D.
6. The polygon ABCDE is (supposedly) a regular pentagon.
? For a discussion of where the error lies, see A. S. Posamentier and H. A. Hauptman, 101 Great Ideas for Introducing Key Concepts in Mathematics (Thousand Oaks, CA: Corwin Press, 2001), pp. 141–146.
Taken From :Math Wonders to inspire teacher and student
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1 Valuing Stocks That Have a Nonconstant Growth Rate (2) // Sep 11, 2009 at 3:41 am
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