Liu Hui's π algorithm
Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the Cao Wei Kingdom. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, 92/29) or as . Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wang Fan (219–257) provided π ≈ 142/45 ≈ 3.156. All these empirical π values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of π to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of
Approximations of πChinese mathematicsChronology of computation of πHistory of mathematicsList of Chinese discoveriesList of numerical analysis topicsList of topics related to πLiu HuiLiu Hui's Pi algorithmLiu Hui's pi algorithmMilüMing Antu's infinite series expansion of trigonometric functionsPiScience and technology of the Han dynastyTimeline of mathematicsZhang HengZhao Youqin's π algorithmZu ChongzhiΠ algorithmΠ evaluation by Liu Hui
Link from a Wikipage to another Wikipage
primaryTopic
Liu Hui's π algorithm
Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the Cao Wei Kingdom. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, 92/29) or as . Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wang Fan (219–257) provided π ≈ 142/45 ≈ 3.156. All these empirical π values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of π to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of
has abstract
Liu Hui's π algorithm was inve ...... simple iterative π algorithm.
@en
Wikipage page ID
17,829,294
page length (characters) of wiki page
Wikipage revision ID
1,025,151,844
Link from a Wikipage to another Wikipage
wikiPageUsesTemplate
comment
Liu Hui's π algorithm was inve ...... 96-gon provided an accuracy of
@en
label
Liu Hui's π algorithm
@en