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SOLVED:GEOMETRY The area of a regular n -sided polygon circumscribed about a circle of radius 1 is given by A=n tan(180^∘)/(n) (A) Find A for n=8, n=100, n=1,000, and n=10,000 Compute each to five decimal places. (B) What number does A seem to approach as n →∞? (What is the area of a circle with radius 1 ? ) (GRAPH CANT COPY)
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The formula for the area of a circle, pi r^2, is traditionally attributed to ancient Greek mathematicians. The method for calculating the area of a circle was likely known in some form by earlier cultures, such as the Egyptians and Babylonians, but it was the Greeks who provided a more rigorous mathematical treatment. One of the key figures in this development was Archimedes of Syracuse (c. 287–212 BCE). Archimedes used a method involving the approximation of the circle by inscribed and circumsc
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