Ever-Expanding Circles
Ever-Expanding Circles
Chapter 2 looks at the development of algorithms for estimating the value of Pi and analysing waveforms. Early estimates for Pi – the ratio of a circle’s circumference to its diameter – were produced in Babylonia. The ancient Greek mathematian, Archimedes, produced improved estimates by means of a clever algorithm which used polygons to approximate the dimensions of a circle. Later, the Chinese mathematician Zu Chongzhi and his son used a similar method to produce an estimate that would stand as the most accurate for 900 years. With the decline of ancient Greece, Persia took on the mantel of leadership in mathematics from the 8th to 11th centuries. Al-Khawrzmi’s texts ultimately propagated knowledge of algorithms to the West. In 18th century France, Joseph Fourier proposed that waveforms could be decomposed into their constituent simple harmonics. The resulting algorithm became the key to signal analysis in today’s electronic communication systems.
Keywords: algorithm, enumeration of Pi, Archimedes, Zu Chongzhi, Al-Khawrzmi, House of Wisdom, Joseph Fourier, Fourier transform
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