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.