Liu Hui's π algorithm: Difference between revisions

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==Significance of Liu Hui's algorithm==

Liu Hui's {{pi}} algorithm was one of his most important contributions to ancient Chinese mathematics. It was based on calculation of {{math|N}}-gon area, in contrast to the Archimedean algorithm based on polygon circumference. With this method Zu Chongzhi obtained the eight-digit result: 3.1415926 < {{pi}} < 3.1415927, which held the world record for the most accurate value of {{pi}} for centuries,<ref>Robert Temple, The Genius of China, a refined value of pi, p144-145, {{isbn|1-85375-292-4}}</ref> until [[Madhava of Sangamagrama]] calculated 11 digits in the 14th century or [[Jamshid al-Kashi]] calculated 16 digits in 1424; even by 1600 in Europe, the Dutch mathematician [[Adriaan Anthonisz]] and hisbest sonapproximations obtainedfor {{pi}} valueknown ofin 3.1415929,Europe accuratewere only accurate to 7 digits.<ref>Robert Temple,until The[[Ludolph Geniusvan ofCeulen]] China,calculated a20 refineddigits valuein of pi, p144-145, {{isbn|1-85375-292-4}}</ref>1596.

== See also ==