Calculation of the area of a circle

Author Topic: Calculation of the area of a circle  (Read 860 times)

Offline Kishwar-E Hasin

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Calculation of the area of a circle
« on: July 19, 2017, 05:56:41 PM »
Rearrangement proof:

We can use inscribed regular polygons in a different way. Suppose we inscribe a hexagon. Cut the hexagon into six triangles by splitting it from the center. Two opposite triangles both touch two common diameters; slide them along one so the radial edges are adjacent. They now form a parallelogram, with the hexagon sides making two opposite edges, one of which is the base, s. Two radial edges form slanted sides, and the height is h (as in the Archimedes proof). In fact, we can assemble all the triangles into one big parallelogram by putting successive pairs next to each other. The same is true if we increase to eight sides and so on. For a polygon with 2n sides, the parallelogram will have a base of length ns, and a height h. As the number of sides increases, the length of the parallelogram base approaches half the circle circumference, and its height approaches the circle radius. In the limit, the parallelogram becomes a rectangle with width πr and height r.
« Last Edit: July 19, 2017, 06:04:03 PM by Kishwar-E Hasin »
Kishwar-E Hasin
Lecturer in Physics,
Department of General Educational Development,
Daffodil International University.

Offline Mosammat Arifa Akter

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Re: Calculation of the area of a circle
« Reply #1 on: February 26, 2020, 11:17:36 AM »
Thanks for sharing
Mosammat Arifa Akter
Senior Lecturer(Mathematics)
General Educational Development
Daffodil International University