Divide a Circle into Parts of Equal Area and Perimeter
The problem of dividing a circle - as a curve, which is often referred to as circumference of a circle - into equal parts is sometimes possible and sometimes not. The situation is entirely different if it is required to divided a circle as a 2D shape. Then the problem is solvable for any number of divisions in a particularly pleasant way: the pieces not only have equal areas but also equal perimeters. Check the illustration below.
The derivation is simple and can be found in my blog. A Java illustration is available on a separate page.
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