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Pythagoras Theorem applied to triangles with whole-number sides such as the 3-4-5 triangle. Here are online calculators, generators and finders with methods to generate the triples, to investigate the patterns and properties of these integer sided right angled triangles.
Suppose that we are asked to find the area enclosed by a circle of given radius. A simple way to go about this is to draw such a circle on graph paper and count the number of small squares within it. Then area contained ≈ number of small squares within circle × area of a small square.