Who calculates pi to seven decimal places: Zu Chongzhi (429-500). Jiankang (now Nanjing) was an outstanding mathematician and astronomer in the Southern and Northern Dynasties.
Zu Chongzhi studied natural science all his life, mainly contributing to mathematics, astronomical calendar and mechanical manufacturing. On the basis of exploring the accurate method of pi pioneered by Liu Hui, he calculated pi to the seventh place after the decimal point for the first time, that is, between 3. 14 15926 and 3. 14 15927. His ancestral rate has made great contributions to mathematical research. It was not until the 6th century A.D./KLOC-that the Arab mathematician Alkasi broke this record.
The Daming Calendar written by him was the most scientific and progressive calendar at that time, which provided a correct method for future astronomical research. His main works are In the Frontier, Composition, Explaining Words, Li Yi and so on.
Brief introduction of pi
Pi is the ratio of the circumference to the diameter of a circle, which is generally written in Greek letters. Expressions are common mathematical constants in mathematics and physics. ? It is also equal to the ratio of the area of a circle to the square of its radius. Accurate calculation of geometric shapes such as circle perimeter, circle area and sphere volume is the key value. Under analysis? It can be strictly defined as the minimum positive real number x that satisfies sinx=0.
Pi in Greek letters? (pronounced pi) means that it is a constant (approximately equal to 3. 14 1592654), representing the ratio of circumference to diameter. It is an irrational number, that is, an infinite cycle decimal. 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. Even if engineers or physicists want to make more accurate calculations, they only need to take the values to a few hundred decimal places at best.
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.
The experimental period of the historical development of pi
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. Egyptians seem to have known pi earlier. British writer JohnTaylor( 178 1? 1864) In his masterpiece The Pyramid (The Great Pyramid: Why Sibrit and Who Built it? ) It is pointed out that the pyramid of khufu built around 2500 BC is related to pi. 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. SatapathaBrahmana, an ancient Indian religious masterpiece written from 800 to 600 BC, shows that pi is equal to the score of 339/ 108, which is about 3. 139.
Geometric method period
As an ancient geometric kingdom, ancient Greece made great contributions to pi. Archimedes, the great mathematician of ancient Greece (287 BC? 2 12) pioneered the theoretical calculation of the approximate value of pi in human history. 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.
Zu Chongzhi calculated the next 800 years? Value is the most accurate. The secret rate was not obtained by German Otto until the West 1573, and was published in the work of Dutch engineer Antoine in 1625, which was called Metis' number in Europe.
17 At the beginning of the 5th century, the Arabic mathematician Cassie got the exact decimal value of pi17, which broke the record kept by Zu Chongzhi for nearly a thousand years. German mathematician LudolphvanCeulen wrote in 1596? The numerical value is calculated to 20 decimal places and then put into life. In 16 10, calculate to 35 decimal places. This value is called Rudolph number after him.
Analysis period
During this period, people began to use infinite series or infinite continuous product to find? Get rid of the complicated calculation of secant. Infinite product formula, infinite continued fraction, infinite series and so on? Value expressions appear one after another, which makes? The accuracy of numerical calculation is rapidly improved.
The first fast algorithm was proposed by the British mathematician JohnMachin, and Machin was in 1706? The numerical value broke through the decimal mark of 100, and he used the formula: arctanx can be calculated by Taylor series. A similar method is called McKinley formula.
Slovenian mathematician Yuri Vega got it at 1789? The first 140 digits after the decimal point, of which only 137 digits are correct. This world record has been maintained for fifty years. He used the number formula proposed by Mei Qin in 1706.
By 1948, D.F.Ferguson in Britain and Ronchi in the United States have both published? The 808-bit decimal value has become the highest record of manual calculation of pi.
Computer age
The emergence of electronic computers has made? Value calculation has made rapid progress. 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 Mezzopoulos used this computer to calculate? 2037 digits after decimal point. It took the computer only 70 hours to finish the work. Deducting the time of punching in and out is equivalent to calculating single digits in two minutes on average. Five years later, IBMNORC (Naval Weapons Research Computer) only took 13 minutes, even if it counts? 3089 digits after decimal point. With the continuous progress of science and technology, the computing speed of computers is getting faster and faster. In the 1960s and 1970s, computer scientists from America, Britain and France constantly competed on computers. The value of is getting more and more accurate. 1973 JeanGuilloud and MartinBouyer discovered it with the computer CDC7600? Millions of decimal places.
1976 has made a new breakthrough. EugeneSalamin published a new formula, which is a quadratic convergence algorithm, that is, every calculation will be multiplied by the significant number. Gauss had found a similar formula before, but it was so complicated that it was not feasible in the era without computers. This algorithm is called Brent-Salamin (or Salamin-Brent) algorithm, also known as Gauss-Legendre algorithm.
1989, researchers at Columbia University in the United States used Cray-2 and IBM-3090/VF supercomputers to calculate? The value has 480 million digits after the decimal point, and then continues to count to 10 1 100 million digits after the decimal point. 2010 65438+1October 7th French engineer fabrice Bella calculated pi to 2.7 trillion decimal places. On August 30th, 20 10, Japanese computer genius Kondo Mao used the combination of home computer and cloud computing to calculate pi to 5 trillion decimal places.
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.