Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei. Before his time, the ratio of the circumference...

mathematics Fangcheng (mathematics) Lists of people of the Three Kingdoms Liu Hui's π algorithm Haidao Suanjing History of geometry Chen, Stephen. "Changing Faces:...

transcendental) List of circle topics List of formulae involving π Liu Hui's π algorithm Mathematical constant (sorted by continued fraction representation)...

of the traditional values of π, that is 3, 3.14, ⁠22/7⁠ and ⁠355/113⁠, the last is the most exact. Liu Hui's π algorithm Yoshio Mikami, Development of...

accurate to two sexagesimal digits. The Chinese mathematician Liu Hui in 263 CE computed π to between 3.141024 and 3.142708 by inscribing a 96-gon and 192-gon;...

mathematician Liu Hui created a polygon-based iterative algorithm, with which he constructed a 3,072-sided polygon to approximate π as 3.1416. Liu later invented...

Spigot algorithm — algorithms that can compute individual digits of a real number Approximations of π: Liu Hui's π algorithm — first algorithm that can...

of the earliest treatises on algebra. 263 – China, Liu Hui computes π using Liu Hui's π algorithm. 300 – the earliest known use of zero as a decimal digit...

by the mathematician Li Shanlan in 1867. Liu Hui's π algorithm: Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of Wei...

describe the lengthy calculations involved. Zu used Liu Hui's π algorithm described earlier by Liu Hui to inscribe a 12,288-gon. Zu's value of pi is precise...

mathematical constant pi (π). For more detailed explanations for some of these calculations, see Approximations of π. As of May 2025, π has been calculated...

In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that π 4 = 1 − 1 3 + 1 5 − 1 7 + 1 9 − ⋯ = ∑ k = 0 ∞ ( − 1 )...

Chongzhi was one of the generations of mathematicians. He used Liu Hui's pi-algorithm applied to a 12288-gon and obtained a value of pi to 7 accurate...

the mathematical constant π. Many of these formulae can be found in the article Pi, or the article Approximations of π. π = C d = C 2 r {\displaystyle...

approximation of π (pi) found by the Chinese mathematician and astronomer Zu Chongzhi during the 5th century. Using Liu Hui's algorithm, which is based...

Springer Verlag, 1994. A full translation and study of the Nine Chapters and Liu Hui's commentary is available in Kangshen Shen, The Nine Chapters on the Mathematical...

roots c. 300 BC – Euclid's algorithm c. 200 BC – the Sieve of Eratosthenes 263 AD – Gaussian elimination described by Liu Hui 628 – Chakravala method described...

Li; Sheng-Kai Liao; Liang Zhang; Ji-Gang Ren; Wen-Qi Cai; Wei-Yue Liu; Bo Li; Hui Dai; Guang-Bing Li; Qi-Ming Lu; Yun-Hong Gong; Yu Xu; Shuang-Lin Li;...

lim t → 0 π 4 2 π t e 2 π t − e 2 π t + 1 π t 2 e 2 π t + t e 2 π t − t = lim t → 0 π 3 t e 2 π t 2 π ( π t 2 e 2 π t + 2 t e 2 π t ) + e 2 π t − 1 = lim...

century CE, Liu Hui found even more accurate approximations using a method similar to that of Archimedes, and in the fifth century Zu Chongzhi found π ≈ 355...

and the divisor must be left in place with one on top of another. In Liu Hui's notes to Jiuzhang suanshu (2nd century BCE), the number on top is called...

∑ i e k i T x + b i ∑ j e k j T x + b j N ( y | μ i , I ) ] = ln ⁡ [ ( 2 π ) − d / 2 ∑ i e k i T x + b i ∑ j e k j T x + b j e − 1 2 ‖ y − μ i ‖ 2 ]...

calculation of π with these "quick methods" involved only multiplication, addition or subtraction, being much faster than classic Liu Hui's π algorithm which involves...

non-negative real number and θ {\displaystyle \theta } lies in the range − π < θ ≤ π {\displaystyle -\pi <\theta \leq \pi } , then the principal complex cube...

Han-era Chinese text The Nine Chapters on the Mathematical Art. Later, Liu Hui of Cao Wei (during the Three Kingdoms period) writes down laws regarding...

structure is not only given by mechanical bonds but also hydrogen bonds and π-π interactions between the rings. On the other hand, the side-chain polycatenanes...

accurate than Liu Hui's contemporary Wang Fan, a mathematician and astronomer from Eastern Wu, would render pi as 3.1555 by using 142⁄45. Liu Hui also wrote...

the value of π and he used the Euclidean algorithm for division. Writing S ( n ) = | 1 − 1 3 + 1 5 − 1 7 + ⋯ + ( − 1 ) n − 1 2 n − 1 − π 4 | {\displaystyle...

method was independently developed in China around the 3rd century AD by Liu Hui, who used it to find the area of the circle. This method was later used...

f ( m ) = 1 / 2 π σ 2 {\displaystyle f(m)=1/{\sqrt {2\pi \sigma ^{2}}}} , thus for large samples the variance of the median equals ( π / 2 ) ⋅ ( σ 2 /...