π(3. 14 15) was calculated by Zu Chongzhi, an ancient mathematician in China. Zu Chongzhi, an ancient mathematician in China, approximated the circumference of a circle with the circumference inscribed by a regular polygon, thus obtaining the value of π accurate to the seventh decimal place. π = perimeter/diameter ≈ inscribed regular polygon/diameter. When the side length of a regular polygon is longer, its circumference is closer to a circle.

Experimental period:

An ancient Babylonian stone tablet, made from BC 1900 to BC 1600, records pi =25/8=3. 125, but the Egyptians seem to know pi earlier. John tyler, British writer (1781–128) For example, the ratio of the circumference to the height of a pyramid is equal to twice the pi, which is exactly equal to the ratio of the circumference to the radius of a circle.

Geometric method period:

Archimedes (287–2 BC12), a great mathematician in ancient Greece, initiated the theoretical calculation of the approximate value of pi in human history. He first calculated π value by exhaustive method in the book Measurement of Circle. The so-called "exhaustive method" is to start from the unit circle, find out that the lower bound of pi is 3 by inscribed regular hexagon, and then find out that the upper bound of pi is less than 4 by circumscribed regular hexagon with the help of Pythagorean theorem.

Then, he doubled the number of sides of inscribed regular hexagon and circumscribed regular hexagon to inscribed regular hexagon 12 and circumscribed regular hexagon 12 respectively, and then improved the upper and lower bounds of pi with the help of Pythagorean theorem. He gradually doubled the number of sides inscribed with regular polygons and circumscribed with regular polygons until inscribed with regular polygons and circumscribed with regular polygons. Finally, he came to the conclusion that 3. 14 185 1 is the approximate value of pi.

Extended data:

π is an irrational number, that is, it cannot be expressed as the ratio of two integers, which was proved by Swiss scientist johann heinrich lambert in 176 1. In 1882, Lin Deman proved that π is a transcendental number, that is, π cannot be the root of any integer coefficient polynomial.

The transcendence of pi denies the possibility of turning a circle into a square, because all rulers can only draw algebraic numbers, and transcendental numbers are not algebraic numbers.

In 65, JohnWallis, a British mathematician, published a mathematical monograph in which he deduced a formula and found that pi is equal to the product of infinite fractions. 20 15 scientists at the university of rochester found a formula with the same pi in the quantum mechanical calculation of hydrogen atomic energy level.