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2. Follow Archimedes' ideas to approximate pi, the ratio of the circumference of any circle to its diameter. For the adventurous, see pages 93-98 of the reading "7 Heath The Works of Archimedes Sphere Cylinder Circle Parabola.pdf." Inscribed Polygons (adapted from Katz, A History of Mathematics: An Introduction) You will generate a recursive sequence of sides of a regular inscribed polygon (called s, ) in a circle of radius 1. The number of sides n will follow the pattern n=3-2*. In the diagram, bisect the side of the regular inscribed polygon Sn and construct the segment from the center of the circle to this bisection, making sure to continue to intersect the segment to the circle. This point of intersection generates two new sides of the regular inscribed polygon. 52. doubling its number of sides. 7=1

2. Follow Archimedes' ideas to approximate pi, the ratio of the circumference of any circle to its diameter. For the adventurous, see pages 93-98 of the reading "7 Heath The Works of Archimedes Sphere Cylinder Circle Parabola.pdf." Inscribed Polygons (adapted from Katz, A History of Mathematics: An Introduction) You will generate a recursive sequence of sides of a regular inscribed polygon (called s, ) in a circle of radius 1. The number of sides n will follow the pattern n=3-2*. In the diagram, bisect the side of the regular inscribed polygon Sn and construct the segment from the center of the circle to this bisection, making sure to continue to intersect the segment to the circle. This point of intersection generates two new sides of the regular inscribed polygon. 52. doubling its number of sides. 7=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Follow Archimedes' ideas to approximate pi, the ratio of the circumference of any circle to its diameter. For the adventurous, see pages 93-98 of the reading "7 Heath The Works of Archimedes Sphere Cylinder Circle Parabola.pdf." Inscribed Polygons (adapted from Katz, A History of Mathematics: An Introduction) You will generate a recursive sequence of sides of a regular inscribed polygon (called 5, ) in a circle of radius 1. The number of sides n will follow the pattern n=3-2*. In the diagram, bisect the side of the regular inscribed polygon Sn and construct the segment from the center of the circle to this bisection, making sure to continue to intersect the segment to the circle.. This point of intersection generates two new sides of the regular inscribed polygon, 52, doubling its number of sides. $12 a. Start with s6 = 1. b. Find the perimeter of the n-gon, P. c. Approximate by calculating the perimeter divided by the diameter, 2 d. Use the Pythagorean Theorem to find x in the diagram (x only goes out to the side of the polygon). e. Use the Pythagorean Theorem again to find 52- Repeat. P₁ = ns₂ n sides 6 12 24 48 96 y=1 Sn 2 1 sin S6 Sp Decimals are fine, but keep 7 decimal places. Feel free to use any technology you wish. S₂ X r=1 $12 7=1 P./2 3
Transcribed Image Text:2. Follow Archimedes' ideas to approximate pi, the ratio of the circumference of any circle to its diameter. For the adventurous, see pages 93-98 of the reading "7 Heath The Works of Archimedes Sphere Cylinder Circle Parabola.pdf." Inscribed Polygons (adapted from Katz, A History of Mathematics: An Introduction) You will generate a recursive sequence of sides of a regular inscribed polygon (called 5, ) in a circle of radius 1. The number of sides n will follow the pattern n=3-2*. In the diagram, bisect the side of the regular inscribed polygon Sn and construct the segment from the center of the circle to this bisection, making sure to continue to intersect the segment to the circle.. This point of intersection generates two new sides of the regular inscribed polygon, 52, doubling its number of sides. $12 a. Start with s6 = 1. b. Find the perimeter of the n-gon, P. c. Approximate by calculating the perimeter divided by the diameter, 2 d. Use the Pythagorean Theorem to find x in the diagram (x only goes out to the side of the polygon). e. Use the Pythagorean Theorem again to find 52- Repeat. P₁ = ns₂ n sides 6 12 24 48 96 y=1 Sn 2 1 sin S6 Sp Decimals are fine, but keep 7 decimal places. Feel free to use any technology you wish. S₂ X r=1 $12 7=1 P./2 3
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