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Why is pi between three and four?

Why is pi between three and four?

Author: Steve Anastasi
Description:

To show why pi must be less than 4 but greater than 3.

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Tutorial

Demonstration of why pi must be less than four but more than three

This video shows how to verify that the value of pi must be less than four by illustrating how a circle inscribed in a square must have a circumference of less than 4 times the diameter of the circle. It goes on to show that pi must be more than 3 but using facts about equilateral triangles.