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Illuminations: Computing Pi - 3 views

    The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. With 100,000 members and 250 affiliates, NCTM is the world's largest organization dedicated to improving math education in preK‑12.

    The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. This activity allows for the investigation and comparison of both methods.

    In this applet, polygons are inscribed and circumscribed around circles. The area of the polygons around a circle of radius 1 are calculated on the left, and the perimeter of the polygons around a circle of diameter 1 are calculated on the right.
    Change the value of n to increase or decrease the number of sides in the polygons, and notice how the calculations of the areas and perimeters begin to approximate pi.
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