How is pi calculated?

Pi is calculated by dividing the circumference of a circle by its diameter. "Pi" is the ratio between the circumference of a circle and its diameter.

1. Pi is a transcendent number, which is not only irrational, but even more irrational than irrational numbers. One of the characteristics of irrational numbers is that the fractional part is infinite and is not cyclical. For example, the circular decimals, although infinite, are repetitive.

Pi, on the other hand, is infinite, and the numbers are not repeated, so pi looks like a very long string of numbers.

2. Archimedes was the first to come up with the approximate equals of pi. Legend has it that when he was dying, he was forced to a beach by Roman soldiers, where he calculated pi and said to the soldiers: "Don't kill me yet, I can't leave an imperfect geometric problem for future generations."

Archimedes calculated pi by two-sided approximation: the circumference of the circle was approximated using the perimeter of the circumference of the circumscribed regular polygon and the circumference of the circumscribed regular polygon. The more sides of a regular polygon, the closer the perimeter of the polygon is to the side length of the circle.

3. In the past, people calculated pi to determine whether pi was a cyclic decimal. The mystery of pi has been unveiled since Lambert proved that pi is an irrational number in 1761 and Lindemann proved that pi is a transcendent number in 1882. Nowadays, people calculate pi, mostly to verify the computing power of computers, and also, for interest.

The circumference of a regular polygon inscribed (or inscribed) can be calculated exactly, and as the number of sides of the regular polygon increases, it will get closer to the circle, and the perimeter of the polygon will get closer and closer to the circumference of the circle. Archimedes gives the lower and upper bounds of pi from the circumference of the circumscribed and inscribed regular polygons of the circle, and the more sides of the regular polygon, the higher the accuracy of the calculated value. Archimedes started from the regular hexagon, doubled the number of sides of the regular polygon one by one, and used the Pythagorean theorem (known as the Pythagorean theorem in the West) to find the side length of the regular polygon after doubling the number of sides.

Thus, as the number of edges is doubled, Archimedes' method can, in principle, calculate arbitrary-precision values. He himself calculated the regular 96 and got 223 71 < < 22 7, i.e. the value is between 845 and 857. In the West, later generations have been using Archimedes' method to calculate pi for almost 19 centuries.

Pi was passed by Liu Xin, a writer in the Western Han Dynasty of China"Turning a circle into a square"According to the known area of the circle of 7 squares, the unknown "ratio of the circumference to the diameter of the circle" is 6 + 2 3 to 3 and the ratio is found to be 6 + 2 3 or 6 + 2 3.

Pi (Pi) is the ratio of the circumference of a circle to its diameter, generally represented by 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, and is the key value for accurately calculating the circumference of the circle, the area of the circle, the volume of the sphere and other geometric shapes. In analytics, it can be strictly defined as the smallest positive real number x satisfying sin x = 0.

Pi is represented by the Greek 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. [1]

In 1965, the British mathematician John Wallis published a mathematical treatise in which he derived a formula that found that pi is equal to the product of the multiplication of infinite fractions. In 2015, scientists at the University of Rochester discovered the same formula for pi in quantum mechanical calculations of the energy levels of hydrogen atoms [2].

On March 14, 2019, Google announced that pi is now in trillions of decimal places. [3]

The Chinese name is Pi.

foreign name ratio of circumference to diameter; pi

Symbolic representation. Approximation.

22 7 (approx. 113 (density).)

Attributes Greek.

Historical development. Experimental period.

An ancient Babylonian stone plaque (circa 1900-1600 BC) clearly states that pi = 25 8 = . [4] An ancient Egyptian artifact from the same period, the Rhind Mathematical Papyrus, also indicates that pi is equal to the square of the fraction 16 9, approximately equal to. [4] The Egyptians seem to have known pi much earlier.

The British writer John Taylor (1781 1864) wrote in his famous book The Greatest Pyramid: Why Was It Built, and Who Built It?It is noted that the pyramid of Khufu, built around 2500 B.C., is related to pi.

For example, the ratio of the circumference and height of a pyramid is equal to twice the ratio of pi and exactly equal to the ratio of the circumference and radius of the circle. The ancient Indian religious magnum opus, the Satapatha Brahmana, written between 800 and 600 B.C., shows that pi is equal to the fraction 339 108, which is approximately equal to. [5]

Geometric period.

Ancient Greece, as an ancient geometric kingdom, made a particularly prominent contribution to pi. The great Greek mathematician Archimedes (287 212 BC) opened.

How did the ancients discover and calculate pi? Is there a hidden pi in the book of Hetuluo?

Zu Chongzhi was an outstanding mathematician during the Northern and Southern Dynasties, how did he calculate pi?

Pi is based on"Turning a circle into a square", it is known that the area of the circle is 7 square and the softened equal area becomes seven-ninths of the area of its inscribed square, and the two-squares are added to the area of its inscribed square with seven-ninths of the area of the inscribed square, and the corresponding diameter is 3 and the circumference of the corresponding circle is 6+2 3. It can be seen that the ratio of the circumference to the diameter of the circle is: 6+2 3 to 3.

Pi = (6+2 3) 3 (or approximately equal to.

In fact, in the past, the so-called pi = the ratio of the circumference of the original regular 6x2 polygon to the diagonal line passing the center point, should be called the positive 6x2 marginal ratio. The value of the positive 6x2 side rate and the value of pi are not the same value at all.

Pi is calculated by dividing the circumference of a circle by its diameter.

"Pi" is the ratio between the circumference of a circle and its diameter. The problem of its calculation has always been of great interest to Chinese and foreign mathematicians. In ancient times, China was ahead of the world level in the calculation of pi for a long time, which should be attributed to the new method created by the mathematician Liu Hui in the Wei and Jin dynasties - "circumcision".

The so-called "circumcision" is a method of using the circumference of a regular polygon within a circle to infinitely approximate the circumference of the circle and obtain pi from this. This method is a brand-new method created by Liu Hui after criticizing and summarizing various old calculation methods in the history of mathematics.

Pi is represented by the Greek letter and is a constant (approximately equal to, which represents the ratio of the circumference and diameter of a circle. It is an irrational number, i.e., an infinite non-cyclic decimal.

The ratio of the circumference to the diameter of the circle is based on"Turning a circle into a square"The area of the known circle is 7 square, and the unknown diameter of 3 and the circumference of 6 + 2 3 are found. Pi is calculated as the ratio of the circumference of a circle 6+2 3 to the diameter of 3.

Steps for HPFYKG:

1. According to the known circle area s=7 square meters, the area of the inscribed square is 9 square meters.

2, then the diameter d = 3 meters corresponding to the curved rise of the circular surface of 7 square meters and the corresponding circumference c = 6 + 2 pins 3 meters.

3, because the circumference of the circle is 6 + 2 3 meters and its corresponding diameter is 3 meters, the ratio of the buried bucket to them is 6 + 2 3 to 3.

4, for this, pi is (6+2 3) 3.

Circumference formula for a circle: circumference of a circle c = x diameter = x radius x 2 (

Pi is calculated by using the ratio of the point diameter to the circumference of the circle and the ratio of their respective numbers to the diameter.

Because the diameter of the circle is the sum of the point diameters of the three points, the circumference c c of the circle corresponding to it is the sum of the six points of the outer points on the circle surface arranged according to the nature of the curve plus the overlapping point diameters 2 3, so when the diameter of the nucleus d is 3, the circumference c of the corresponding circle is 6+2 3.

Because the ratio of the circumference of the circle to the diameter of the smoldering point of the circle is 6+2 3 to 3, the only value of pi is (6+2 3) 3 (or approximately equal to.

40 = to 100.

Values from 1 to 100:

11 =, which 12 =, 13 =, 14 =, 15 =, 16 =, 17 =, 18 =, 19 =, 20 =

21 =, 22 =, 23 =, 24 =, 25 =, 26 =, 27 =, 28 =, 29 =, lead block 30 =

51 =, 52 =, 53 =, 54 =, 55 =, 56 =, 57 =, 58 =, 59 =, 60 =

The Chinese mathematician Liu Hui used the "circumcision" technique 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 a regular 192 side. The so-called "circumcision" is a method of using the area of a regular polygon inside a circle to infinitely approximate the area of a circle and obtain pi from this.

Since "pi, circumference, diameter", where "diameter" is straight, easy to measure; What is difficult to calculate precisely is the "circumference of a circle". Through Liu Hui's "circumcision", the problem of high loss was solved. As long as the circumference of the circle is carefully and patiently calculated, a more accurate "pi" can be obtained.

Characteristics: The value of pi is calculated so accurately that it does not make much practical sense. The pi values used in the field of modern Corson ruler techniques, a dozen digits are sufficient.

If the size of the observable universe is calculated with a 39-bit precision pi value, the error is less than the volume of an atom.

In the past, the empty model man calculated pi to ** whether pi is a cyclic decimal. The mystery of pi has been unveiled since Lambert proved that pi is an irrational number in 1761 and Lindemann in 1882 to prove that pi is a transcendent number. <>