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In this quest You should perform 7. (a) On the (b) and th Assum that T (c) Using and b) (d) Archim over 20 method approxi

In this quest You should perform 7. (a) On the (b) and th Assum that T (c) Using and b) (d) Archim over 20 method approxi

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In this question we are going to find approximate values of T using geometrical constructions. You should perform the constructions using computer software and include them with your solution. 7. (a) On the same circle, inscribe and circumscribe squares. (b) Assuming the circle has a radius of 1, find the areas of the circle and the two squares, and then compare them to create an inequality for r: that is, you should be able to show that is between two numbers. Comment on how good this approximation is. (c) Using the fact that tan = v2-1 (but don't bother proving that fact), repeat parts a) and b) for inscribed/circumscribed octagons. Archimedes (of bathtub fame) used polygons inside and outside circles to approximate TT (d) over 2000 years ago, although he compared perimeters instead of areas. Research his method to find out what size polygon he used (that is, how many sides) and his final approximation for 7.
Transcribed Image Text:In this question we are going to find approximate values of T using geometrical constructions. You should perform the constructions using computer software and include them with your solution. 7. (a) On the same circle, inscribe and circumscribe squares. (b) Assuming the circle has a radius of 1, find the areas of the circle and the two squares, and then compare them to create an inequality for r: that is, you should be able to show that is between two numbers. Comment on how good this approximation is. (c) Using the fact that tan = v2-1 (but don't bother proving that fact), repeat parts a) and b) for inscribed/circumscribed octagons. Archimedes (of bathtub fame) used polygons inside and outside circles to approximate TT (d) over 2000 years ago, although he compared perimeters instead of areas. Research his method to find out what size polygon he used (that is, how many sides) and his final approximation for 7.
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