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How Archimedes Helped Students to Unravel the Mystery of the Magical Number Pi

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Abstract

This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes’s method of exhaustion in order to compute the number π. Working in a computer environment, students inscribe and circumscribe regular polygons inside and around a circle in order to find the approximate area of the circle. They then compute the ratio of that approximation to the area of a square with side-length equal to the radius of the circle. This ratio indicates how many times larger the area of the circle is than the area of the square. Mirroring Archimedes’s findings, students discover that as they increase the number of sides in their polygons, the numerical results they obtain convince them that this number is almost equal to 3.14.

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Notes

  1. In December 2002, computer scientists Kanada, Ushio and Kuroda, University of Tokyo, Japan, computed π to a world record 1.2411 × 1012 (more than one trillion) decimal digits. The computation consumed more than 600 h of time of a Hitachi SR8000 super computer (www.super-computing.org/pi_current.html. Accessed 23 October 2012).

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  1. Aristotle University of Thessaloniki, Thessaloníki, Greece

    Ioannis Papadopoulos

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  1. Ioannis Papadopoulos
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Papadopoulos, I. How Archimedes Helped Students to Unravel the Mystery of the Magical Number Pi. Sci & Educ 23, 61–77 (2014). https://doi.org/10.1007/s11191-013-9643-0

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