An ancient Babylonian stone tablet (about BC 1900 to BC 1600) clearly recorded that pi =25/8=3. 125. At the same time, the ancient Egyptian cultural relic RhindMathematicalPapyrus also showed that pi was equal to the square of score 16/9, which was about 3. 1605.
Second, the geometric method period
Starting from the unit circle, Archimedes first found that the lower bound of pi was 3 by inscribed regular hexagon, and then found that the upper bound of pi was less than 4 by 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 found that the upper and lower bounds of pi were 223/7 1 and 22/7, respectively, and took their average value of 3. 14 185 1 as the approximate value of pi. Archimedes used the concepts of iterative algorithm and bilateral numerical approximation, which is the originator of computational mathematics.
Third, the analysis period
During this period, people began to use infinite series or infinite continuous product to find π and get rid of the complicated calculation of secant. Various expressions of π value, such as infinite product, infinite continued fraction and infinite series, appear one after another, which makes the calculation accuracy of π value improve rapidly.
1789, Slovenian mathematician Yuri Vega got the first 140 digits after π decimal point, of which only 137 digits were correct. This world record has been maintained for fifty years. He used the number formula proposed by Mei Qin in 1706.
By 1948, both D.F.Ferguson in Britain and Ronchi * * in the United States had published the 808-bit decimal value of π, which became the highest record for manually calculating pi.
Fourth, the computer age.
The appearance of electronic computer makes the calculation of π value develop by leaps and bounds. 1949, ENIAC (Electronic Digital Integrated Computer), the world's first American-made computer, was put into use at Aberdeen proving ground. The following year, Ritter wiesner, Von Newman and Mezopolis used this computer to calculate the 2037 decimal places of π.
20 1 1, 10, the staff of Iida City, Nagano Prefecture, Japan used their home computers to calculate pi to 10 trillion digits after the decimal point, setting a Guinness World Record of 5 trillion digits created by themselves in August of 20 10. 56-year-old Mau Kondo used his own computer to calculate from June+10 in 5438, which took about 1 year, setting a new record.
Extended data:
Pi is expressed by the Greek letter π (pronounced pài) and is a constant (approximately equal to 3. 14 1592654), which represents the ratio of the length to the diameter of a circle. It is an irrational number, that is, an infinite cycle decimal.
1965, the British mathematician JohnWallis 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.
In daily life, pi is usually expressed as 3. 14, which is used for approximate calculation. The fractional part 3. 14 1592654 is enough for general calculation.
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