Your project, in brief, is to use classical compass and straightedge 
constructions to obtain a regular pentagon inscribed in a circle. 
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More specifically, you should start your project by discussing the 
compass and straightedge construction rules; our work to show that 
we may assume that our compass does not collapse (so we can 
transfer distances with it); the difference between a contructable point
and an arbitrary point in the plane.
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Then explain why if we know the cosine of 72 degrees, then we can construct 
the pentagon. Then from the equation cos (5 theta ) = 1, use trig identities 
to derive a fifth degree polynomial in x= cos (theta) 
whose roots are the cosines of 
0, 72, 144, 216, 288 degrees. Argue that one root is x=1, divid out the 
factor (x-1), obtaining a fourth degree polynomial. Now explain why 
you expect this fourth degree polynomial to be the square of a quadratic, 
find the desired quadratic, then its two roots and identify the root 
that is the cosine of 72 degrees. 
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Now set a unit distance (the radius of the circle that you will construct
the pentagon in) - about 3 inches a good scale for this. Next show how to 
construct the length cos(72). 
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Now construct the regular pentagon.
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As a plus, use your pentagon to construct a regular 10-gon. Remember 
that once you construct your inscribed pentagon you can just 
duplicate it, since our compasses are rigid now.
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Don't for get your reflections page. 
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Here's a set of links to various geometric constructions:
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 <a href=geonotes.html>Discussion of geometry mthods. </a></br>