The area of a disk (the region inside a circle) is πr2 when the circle has radius r. Here the symbol π (Greek letter pi) denotes, as usual, the constant ratio of the circumference of a circle to its diameter.

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  • The area of a disk (the region inside a circle) is πr2 when the circle has radius r. Here the symbol π (Greek letter pi) denotes, as usual, the constant ratio of the circumference of a circle to its diameter. Modern mathematics can obtain the area using the methods of integral calculus or its more sophisticated offspring, real analysis. However, in Ancient Greece the great mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius. The circumference is 2πr, and the area of a triangle is half the base times the height, yielding the area πr2 for the disk. Beyond these two ancient and modern approaches, we also survey a few alternatives, both exact and approximate, of historical and practical interest. (en)
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  • Laczkovich (en)
  • 1990 (xsd:integer)
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  • Archimedes (en)
  • c. 260 BCE (en)
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  • p. 19 (en)
  • p. 273 (en)
  • pp. 130–132 (en)
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  • The area of a disk (the region inside a circle) is πr2 when the circle has radius r. Here the symbol π (Greek letter pi) denotes, as usual, the constant ratio of the circumference of a circle to its diameter. (en)
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  • Area of a disk (en)
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