If an n-sided regular polygon is inscribed in a circle of radius r find a relationship between θ and n Solve this for n. Keep in mind there are 2π radians in a circle
Some ofthe geometric formulas we take for granted today were
first derived by methods that anticipate some ofthe methods of
calculus. The Greek mathematician Archimedes (ca. 287 212;
BCE) was particularly inventive, using polygons inscribed within
circles to approximate the area ofthe circle as the number of
sides ofthe
a limit, but we can use this idea to see what his geometric
constructions could have predicted about the limit.
We can estimate the area of a circle by computing the area of an
inscribed regular polygon. Think ofthe regular polygon as being
made up of n triangles. By taking the limit as the centex angle of
these mangles goes to zero, you can obtain the area ofthe circle.
To see this, carry out the following steps:
55- If an n-sided regular polygon is inscribed in a circle of radius r find a relationship between θ and n Solve this for n. Keep in mind there are 2π radians in a circle. (Use radians, not degees.)
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