Question 724661: Consider a circle of radius 1, and corresponding inscribed and circumscribed polygons with the number of sides n = 3, 4, 5, 6, and 8.
As n gets larger, what happens to the ratio of these pairs of perimeters (use the larger perimeter as the numerator, and the smaller perimeter as the denominator)?
Both perimeters tend toward a limiting value as n gets larger and larger. What number would this be?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider a circle of radius 1, and corresponding inscribed and circumscribed polygons with the number of sides n = 3, 4, 5, 6, and 8.
As n gets larger, what happens to the ratio of these pairs of perimeters (use the larger perimeter as the numerator, and the smaller perimeter as the denominator)?
Ans: The 2 perimeters get closer and closer; the ratio approaches "1".
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Both perimeters tend toward a limiting value as n gets larger and larger. What number would this be?
The limit is the circumference of the circle = 2(pi)r = 2pi
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Cheers,
Stan H.
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