The origin of the mathematical symbol pai

The ancient Greek Euclid "Geometry Original" (c. early 3rd century BC) mentions pi as a constant, and the ancient Chinese arithmetic book "Zhou Ji Suanjing" (

c. 2nd century B.C.) has a record of "one and three days", and it is also believed that pi is constant. Various approximations of pi have been used throughout history, and most of the early ones were obtained through experiments, such as =(4 3) 4 in the ancient Egyptian papyrus (c. 1700 BC).

The first person to scientifically find the value of pi was Archimedes, who, in The Measurement of a Circle (3rd century BCE), determined the upper and lower bounds of the circumference of a circle by using the circumference of the circumference of the circle and the circumscribed regular polygon, starting with the regular hexagon and doubling it to the regular 96 sides, giving (3+(10 71))<3+(1 7)).

He pioneered the geometric method of calculating pi (also known as the classical method, or the Archimedes' method), which yielded values accurate to two decimal places.

Pi, generally speaking, is a mathematical constant that is prevalent in mathematics and physics. It is defined as the ratio of the circumference to the diameter of a circle. It is also equal to the ratio of the area of the circle to the square of the radius.

It is the key value of accurately calculating the circumference of the circle, the area of the circle, the volume of the ball and other geometric shapes.

Analytically, it can be strictly defined as satisfying sin(x).

The smallest positive real number x of 0, where sin is a sinusoidal function (as defined in analytical).

The origin of pi "".

Long ago, it was recognized that the ratio of the circumference of a circle to the diameter of a circle was a constant independent of the size of the circle, and called it pi. William of England, 1600. Ottolante was first used to denote pi because it was Greek"Ashwagandha early circumference"The first letter, and the δ is"Diameter"When δ=1, pi is

Jones in England was first used in 1706In 1737 Euler used the term in his writingsLater, it was widely accepted by mathematicians and has not been used to this day.

is a very important constant. A German mathematician commented:"The accuracy of pi calculated by a country in history can be used as an important indicator of the level of development of mathematics at that time.

Many mathematicians, both ancient and modern, have worked tirelessly to find ways to calculate excess values.

In 200 B.C., the ancient Greek mathematician Archimedes was the first to theoretically give the correct way to find values. He used the circumference of the circumsection of the circle and the circumference of the inscribed polygon to gradually approach the circumference of the circle from the large and small directions at the same time, and skillfully obtained it

About 150 years ago, another ancient Greek mathematician, Ptolemy, gave an approximation by using the string table method (multiplying the length of the chord at the central angle of 1 by 360 and dividing it by the diameter of the circle).

In 200 AD, the Chinese mathematician Liu Hui provided a scientific method for finding pi --- circumcision, which embodied the limit view. Liu Hui differed from Archimedes in his approach, he only took"Internal"Do not take"Extrophic".Using the circular area inequality to launch the results has the effect of doing more with less.

Then, Zu Chongzhi achieved a world leader in the calculation of pi and obtained"Approximate rate"with"Density rate"(also known as the ancestral rate) has to be keyed to.

1. is an irrational number, and its value is between and .

2. Pi is the ratio of the circumference of a circle to its diameter, which is generally expressed in Greek letters, and is a mathematical constant that is common in mathematics and physics. It is also equal to the ratio of the area of the circle to the square of the radius. It is the key value to accurately calculate the geometric shape of the circumference, area of the circle, and the volume of the sphere.

In analytics, it can be strictly defined as the smallest positive real number x satisfying sin x = 0. Pi is represented by a letter (pronounced pài) and is a constant (approximately equal to, representing the ratio of the circumference to the diameter of a circle. It is an irrational number, i.e., an infinite non-cyclic decimal.

In daily life, it is common to approximate the approximate rate of pi. Ten decimal places is sufficient for general calculations. Even the most sophisticated calculations for engineers or physicists can be taken to a few hundred decimal places.

3. In 263 AD, the Chinese mathematician Liu Hui used the "circumcision" to calculate pi, he first connected the regular hexagon from the circle, and then divided it one by one until the circle was connected with the regular 192 sides. He said, "If you cut it finely, you will lose it, and if you cut it again, you will not be able to cut it, but it will be combined with the circumference and there will be nothing lost." It contains the idea of finding the limit.

Liu Hui gave an approximate value of pi of =, and after obtaining pi =, Liu Hui tested this value with the diameter and volume of the copper volume measurement standard Jia Lianghu made in the Han Dynasty in the Jin arsenal, and found that this value was still on the small side. So I continued to cut the circle to the 1536 polygon, and found the area of the 3072 polygon, and obtained the pi that was satisfactory to me.

4. Around 480 A.D., Zu Chongzhi, a mathematician in the Northern and Southern Dynasties, further obtained the result accurate to 7 decimal places, gave the insufficient approximation and excess approximation, and also obtained two approximate fractional values, the density rate and the approximate rate. The density ratio is a good approximation of fractions, and it needs to be taken to get a slightly more accurate approximation.

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