Subject: isoperimetric quotients

I'm stuck on my GCSE Maths coursework, what do isoperimetric quotients measure?


If you have a simple closed curve with perimeter p units and enclosing an area A square units then the isoperimetric quotient of this curve is

It measures the ratio of the area inclosed by the curve to the area of a circle with the same perimeter. For example the right triangle with sides of length 3, 4 and 5 units has an area of 6 square units. Thus its isoperimetric quotient is

Since pi is approximately 3 this triangle has approximately one-half the area of the circle with the same perimeter.

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