Question: Archimedes devised a method for computing by approximating a circle of radius 1/2 by successive polygons and computing the perimeter of these polygons. This

Archimedes devised a method for computing by approximating a circle of radius

Archimedes devised a method for computing by approximating a circle of radius 1/2 by successive polygons and computing the perimeter of these polygons. This results in the iteration to 1+-1 tn+1 = tn and an approximation Tin = 6 -2 (a) Write a function that performs this calculation and plot n versus n. On a separate graph, plot | | vs. n using a log scale on the y-axis. The command to do this is semilogy. How large can you take n before improvements are limited by roundoff error? How accurately can you compute ? (b) What is the main source of error when n is large? (c) Rewrite the iteration in a way that will reduce this source of error. Repeat the calculation and plot the error in both results on one graph. How large can you take n this time before improvements are limited by roundoff error? How accurately can you compute now?

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