Exercise 1.20. One approximation for consists of inscribing polygons in a circle of radius 0.5, starting...

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Exercise 1.20. One approximation for consists of inscribing polygons in a circle of radius 0.5, starting with hexagons, and successively doubling the number of sides. The recurrence formula for the perimeters of such polygons is Pn+1 6-2. In+1 where +1-1 In+1 In+1 = (1.12) In Observe that we can rewrite the expression above in the mathematically equivalent form In /x+1+1' x1 = 1 √3 x1 = 1 ig n = 1,2,... (1.13) Write a MATLAB function that calculates the first 26 approximations for based on both (1.12) and (1.13) and compare the results. Explain the differences in terms of rounding errors for floating-point operations. = n=1,2,... Exercise 1.20. One approximation for consists of inscribing polygons in a circle of radius 0.5, starting with hexagons, and successively doubling the number of sides. The recurrence formula for the perimeters of such polygons is Pn+1 6-2. In+1 where +1-1 In+1 In+1 = (1.12) In Observe that we can rewrite the expression above in the mathematically equivalent form In /x+1+1' x1 = 1 √3 x1 = 1 ig n = 1,2,... (1.13) Write a MATLAB function that calculates the first 26 approximations for based on both (1.12) and (1.13) and compare the results. Explain the differences in terms of rounding errors for floating-point operations. = n=1,2,...

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Solution Second scheme converges to the value of pi whi... View the full answer