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The history of pi
Transcript of The history of pi
(c. 287 BC – c. 212 BC)made a huge contribution to the calculation of pi. Archimedes used a different method than Antiphon. Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. Archimedes calculated that
22/7 is still a good approximation. 355/113 is a better one. Anna Vasa School
Poland Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. Zu Chongzhi ( 429 - 501 ) was
a Chinese mathematician and astronomer. He introduced the approximation 355/113 to π which is correct to
6 decimal places. Al'Khwarizmi ( about 790 - about 850) was an Islamic mathematician who wrote on Hindu-Arabic numerals and was among the first to use zero as a place holder in positional base notation. He was the pioneer of the calculation of pi in the East Jamshid al-Kashi (1380 - 1429) was an Islamic mathematician who published some important teaching Works. In 1424 Al-Kashi published a treatise on circumference, in which he calculated "pi", the ratio of a circle's circumference to its diameter, to nine decimal places. Nearly two hundred years would pass before another mathematician surpassed this achievement. Ludolph van Ceulen was born at Hildesheim, Germany, 28 January, 1540. He wrote several books, including one titled "On The Circle", in which he published his geometric findings. Ludolph's most notable accomplishment was the calculation of the circumference/diameter ratio to the 35th decimal place, which he accomplished by using polygons of 2 to the 62nd power sides.(number of sides equals 2 times 2, 62 times). Antiphon of Athens was the first to take a huge leap forward in the mystery of pi. Antiphon drew regular polygons within the circle finding its area and doubling the sides of the polygons again and again. Eventually Antiphon saw that the polygon would have so many sides that it would become a circle. This process would become the first mathematical way of figuring pi but it was very complicated and time-consuming. Millions of people use pi everyday in their personal and professional lives to calculate area, circumference, and volume of circular objects. Objects that are not circular would not use pi.
Pi is connected to every circle
or circular object in our universe, making pi a very important concept, even for
“regular people.” In 1761 Lambert proved that Pi was irrational, that is, that it can't be written as a ratio of integer numbers. In 1882 Lindeman proved that Pi was transcendental, that is, that Pi is not the root of any algebraic equation with rational coefficients.
In the Egyptian Rhind Papyrus (ca.1650 BC), there is evidence that the Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for pi. Four-thousand years ago, people discovered that the ratio of the circumference of a circle to its diameter was about 3. The ancient Babylonians calculated the area ofa circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet
(ca. 1900–1680 BC) indicates a value of 3.125 for pi,
which is a closer approximation.
The Bible (c. 950 BC, 1 Kings 7:23) and the Talmud both (implicitly) give the value simply as 3. One of the greatest achievements of Ptolemy
( about 150 AD) was his approximation of pi as 377/120, which was the closest in his time period. He believed the closest number to pi was the number 3.14166. The beginning of this number, 3.14, tends to be used in early school studies of circumference and diameter of circles, so one can say that Ptolemy was at least partially correct. Some people were “dedicated” enough to actually spend incredible amounts of time and effort continuing the calculation of pi.
1699: Sharp gets 71 correct digits
1701: Machin gets 100 digits
1719: de Lagny gets 112 correct digits
1789: Vega gets 126 places
1794: Vega gets 136 places
1841: Rutherford gets 152 digits
1853: Rutherford gets 440 digits
1873: Shanks calculates 707 places of which 527 were correct
“And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and its height was five cubits: and a line of thirty cubits did compass it about”- (I Kings 7, 23) Pi was calculated to 2000 places with the use of a computer in 1949.
In this calculation, and all calculations following it, the number of 7s does not differ significantly from its expectation.
The record number of decimal places for pi calculated in 1999 was 206,158,430,000. However, this record has already been broken. The Greek letter π was first adopted for the number as an abbreviation of the Greek word for perimeter (π), or as an abbreviation for "perimeter/diameter", by William Jones in 1706.
use of the symbol was popularized by Euler, who adopted it in 1737. In Buffon's Needle experiment you can drop a needle on a lined sheet of paper. If you keep track of how many times the needle lands on a line, it turns out to be directly related to the value of Pi.
Buffon's Needle is a problem first posed by the French naturalist and mathematician, the Comte de Buffon (1707-1788). When the needle lands, it either touches one of the parallel lines, or it doesn’t.
It turns out that the probability of the needle landing on one of the lines is 2/pi. From there, we can get a value of pi, as follows: (2 × the number of drops) (number of line touches) =