Intro Question: Farmer John has Four Pieces of 10 foot fencing. (each piece is straight for 10 ft). What is the largest amount of area he can successfully contain? What if it's 5 pieces? 6 pieces?
So the most area appears to be contained in a regular polygon.
Facts about regular polygons:
total degrees on the inside
total degrees on the outside
Where does pi end up coming from?
the relation between the diameter of the object and the circumference
how can we show this?
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And then... 2D shapes--why do they work the way they work? http://people.wku.edu/tom.richmond/rectangle.html