How did the Chinese calculate pi?

How did the Chinese calculate pi?

This is precisely what the ancient Chinese mathematicians Liu Hui, and later Zu Chongzhi, were able to do in the third and fifth centuries. They computed the perimeters of polygons with a huge number of sides, getting an excellent approximation for pi in the process.

When Did Chinese discover pi?

Zu Chongzhi, a Chinese mathematician and astronomer from the 5th century, had made a remarkable achievement by determining the Pi value with an accuracy of seven decimal places, between 3.1415926 and 3.1415927. His calculation remained the world’s most accurate for nearly 1,000 years until the 14th century.

Who discovered Pi in China?

Zu Chongzhi
Zu Chongzhi, Wade-Giles Tsu Ch’ung-chih, (born 429, Jiankang [modern Nanjing, Jiangsu province], China—died 500, China), Chinese astronomer, mathematician, and engineer who created the Daming calendar and found several close approximations for π. Like his grandfather and father, Zu Chongzhi was a state functionary.

Who discovered pi for the first time?

pi, in mathematics, the ratio of the circumference of a circle to its diameter. The symbol π was devised by British mathematician William Jones in 1706 to represent the ratio and was later popularized by Swiss mathematician Leonhard Euler.

Did the Chinese know pi?

Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of π to any accuracy. Later he invented an ingenious quick method to improve on it, and obtained π ≈ 3.1416 with only a 96-gon, with an accuracy comparable to that from a 1536-gon.

When was Liu Hui pi calculation?

1 The fact that the ratio of a circle’s circumference to its diameter is a constant has long been known. The ratio first enters human consciousness in Egypt. … In around 263, Hui Liu calculated π to be 3.141024. Zu 3 (429-500) showed that the value of π lies between 3.1415926 and 3.1415927 [1, 2].

How did Archimedes calculate pi?

Archimedes’ method finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle (which is less than the circumference of the circle) and the perimeter of a polygon circumscribed outside a circle (which is greater than the circumference).

How was pi originally calculated?

The first rigorous approach to finding the true value of pi was based on geometrical approximations. Around 250 B.C., the Greek mathematician Archimedes drew polygons both around the outside and within the interior of circles. Measuring the perimeters of those gave upper and lower bounds of the range containing pi.

How did Archimedes find the value of pi?

How much does 355 113 differ from the true value of π?

355113 is the best rational approximation of π with a denominator of four digits or fewer, being accurate to six decimal places. It is within 0.000009% of the value of π, or in terms of common fractions overestimates π by less than 13748629.

How did Zu Chongzhi calculate pi?

Zu took this algorithm and calculated the area out to a shape with 24,576 sides. From this he derived a shockingly accurate approximation of pi: 355/113. This fraction – known today as Zu’s ratio, Zu’s fraction, or just Milü – approximates pi to six decimal places.

What is the value of Pi in ancient China?

The earliest value of pi used in China was 3. In 263 AD, L iu Hui independently discovered the method used by Bryson and Antiphon, and calculated the perimeters of regular inscribed polygons from 12 up to 192 sides, and arrived at the value pi = 3.14159, which is absolutely correct as far as the first five digits go.

How was the value of Pi calculated?

In 263 AD, L iu Hui independently discovered the method used by Bryson and Antiphon, and calculated the perimeters of regular inscribed polygons from 12 up to 192 sides, and arrived at the value pi = 3.14159, which is absolutely correct as far as the first five digits go. Near the end of the 5th century]

What is the value of Pi in Liu Hui’s equation?

Liu Hui’s own calculation with a 96-gon provided an accuracy of five digits: π ≈ 3.1416. Liu Hui remarked in his commentary to The Nine Chapters on the Mathematical Art, that the ratio of the circumference of an inscribed hexagon to the diameter of the circle was three, hence π must be greater than three.

Who invented the π algorithm?

3.14159 26535 89793 23846 26433… Liu Hui’s π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the Cao Wei Kingdom.

https://www.youtube.com/watch?v=Kctu3RWRAs4