Difference between revisions of "Construct a pentagon/proof"
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Revision as of 13:48, 12 April 2007
I say the figure ABCDE is a regular pentagon.
Proof: Inscribed Pentagon
P 01
Consider a regular decagon AD'BE'CA'DB'EC' inscribed in a circle O with radius AO. Set AO = r = 1.
• We may consider the inscribed decagon given without having a construction.
P 02
A decagon has 10 vertices and a pentagon has 5 vertices, so if we can construct the first then we can construct the second.
P 03
Connect every vertex of the decagon to every other vertex.
• This is called a complete graph.
P 04
Remove most of the lines from the last figure, for simplicity. Find the intersection of DD' and A'E; call this N.
P 05
Since the complete circle has an angle of 2π, the angle connecting adjacent vertices (such as