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The wonder of Horner’s method

Published online by Cambridge University Press:  01 August 2016

A. A. Collyer  and
Alex Pathan
A. A. Collyer
Affiliation:
Flat 2, 9 Elmhyrst Road, Weston-super-mare BS23 2SJ
Alex Pathan
Affiliation:
45 Hutcliffe Wood Road, Sheffield S8 OEY
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Extract

Apart from false position and double false position, another numerical method for calculating roots of equations was known to the Ancient Chinese. Chia Hsien in the eleventh century is reputed to have given an algorithm for calculating roots as well as describing Pascal’s triangle. The algorithm was mentioned again by the twelfth century scholar Liu I. The Chinese used the method to solve quadratics and cubics as early as 100 BC, but it was not until 1247 that Ch’in Kiu-Shao from South China published its extension to higher order polynomials in his work, Mathematics in nine chapters. A year later in the book, Sea-mirror of circle measurements, Li Yeh, who was from north China, took root-finding for granted. The fact that these quite independent writers published similar work suggests that finding the zeros of polynomials was well known by the middle of the thirteenth century. It was left to one of China’s greatest mathematicians, Chu Shi-kie’ (ca. 1280–1303), to give this algorithm its name fan fa, which means the method of the Celestial Element or sometimes the Celestial Unknown [1,2]. Translations and spellings of these older Chinese words do not always give the same result. This algorithm eventually became known as the Ruffini-Horner Method or more simply Horner’s method.

Type
Articles
Information
The Mathematical Gazette , Volume 87 , Issue 509 , July 2003 , pp. 230 - 242
Copyright
Copyright © The Mathematical Association 2003

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