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Discovering the Constant π: From Geometry to Exciting Records

Explore the origin, definition, and methods of calculating the mathematical constant π, along with fascinating discoveries and achievements related to its digits. From the principles of Archimedes to modern record-setting feats, unravel the mystique of π.

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Discovering the Constant π: From Geometry to Exciting Records

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  1. The letter π • The constant is named "π" because it is the first letter of the Greek words: • περιφέρεια = periphery • περίμετρος = perimeter

  2. Definition • In Euclidean plane geometry, π is defined as the ratio of a circle's circumference to its diameter. • π = c/d = c/2r

  3. Calculating π • π can be empirically measured by drawing a large circle, then measuring its diameter and circumference, since the circumference of a circle is always π times its diameter. • π can also be calculated using purely mathematical methods

  4. Principle of Archimedes' method to approximate π n=5 n=6 n=8

  5. a few excitements... • In 2002 Kanada and fellow researchers at Japan's Information Technology Center set a new record for finding the number of digits of π 1.24 trillion decimal places. This calculation took about 602 hours. • Chao Lu of China recited π on 67,890 decimal places on 20 November 2005. • Rose Hare is the youngest person to make the Pi World Ranking List (age: 3 years 356 days) • Math lovers celebrate March 14 (or "3-14") as Pi Day. • The theory of elliptic curves and complex multiplication derives the approximation which is valid to about 30 digits.

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