Methods of Solving Complex Geometry Problems by Ellina Grigorieva

Author:Ellina Grigorieva
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Solution.

Let us assume that the square has side a and the circle has radius R. Using the condition of the problem, we can write the equation: and . Let us express the circumference and perimeter in terms of R and then compare the expressions:

In order to compare the formulas, we can the divide the perimeter of the circle by that of the square giving . Now compare to 1. Pretending that we don’t have a calculator, let us do it mentally. What is ? It is some irrational number. But how big is it? , then , and . Because the ratio is less than 1, the circumference is less than the perimeter of the square.

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