Write a function for the algorithm for approximating pi. Characterize the performance of the algorithm by plotting the value and the error of the approximation by using the difference or fractional variation from MATLABs pi function and the time spent in the calculation against a range of N values which measures the throughput of the calculation.

1. Archimedes Approximation The idea of Archimedes' method is to notice that a regular N-polygon approac the number of sides, N approaches infinity. Since we can easily calculate the length of the perimeter of the N-polygon, we can approximate t the circumference of the circumscribed circle. IfN 8, then T 3.0614674589207183: Opp B 360/N A = B/2; halfs sind (A) shalfs 2; poly-circ = N*S; pi-approx poly-circ/2; sinA