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Use Cases
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Resources
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Pricing
1650 B.C.
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Egypt: The Rhind Papyrus formulated for the area of a circle that makes pi equal to (16/9)2 ≈ 3.1605.
1600 B.C.
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Babylon: Clay tablet that has inscribed a geometrical statement stating that pi is equal to 25/8 = 3.1250.
600 B.C.
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Found in India, the text enriched in mathematical equations just like a textbook, makes pi equal (9785/5568)2 ≈ 3.088.
400 B.C.
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Describe the construction of The Temple of Solomon, saying that the ceremonial pool's dimensions include a diameter of 10 cubits and circumference of 30 cubits. This would leave to assumption that pi would equal around 3, if the pool is circular.
250 B.C.
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First recorded algorithm for calculating pi's value by using the help of polygons. Essentially, he computed upper and lower bounds of pi, by drawing a hexagon inside and outside of a circle. Then doubled the number until reaching a 96-sided polygon. By doing this, he proved that pi equaled 223/71 < π < 22/7 and/or (3.1408 < π < 3.1429).
150 B.C.
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Gave pi the value of 3.1416, which he obtained from Archimedes polygonal algorithms.
150 A.D.
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Explained his version of pi to be valued around 3 and 1 seventh.
265 A.D.
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Created a polygon based algorithm and used to calculate a 3,072 sided polygon to figure out the value of pi 3.1416.
Later invented a faster way of calculating pi and the rounded value of 3.14 by using a 96 sided polygon. Knowing that the differences in area of the two polygons, he figured out the polygons made a geometric factor with the number 4.
480 A.D.
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Calculated pi equaled around 355/133 by using Hui's algorithm, applying it to a 12,288 sided polygon. With a correct assumption of the first 7 digits of pi in the form of "3.141592920" remained the most accurate approximation of pi for the next 800 plus/minus years to come.
499 A.D.
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Indian astronomer, used the value of pi in 3.1416 form in his "Aryabhatiya"
1220 A.D.
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Computed 3.1418 by using polygonal method, separate from Archimedes' method.
1424 A.D.
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Persian astronomer produced 16 digits using a polygon with 3×2 (to the 28th power) sides, which stood as the world record for the next 180 years.
1500 A.D.
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Used by Indian Astronomer Nilakantha Somayaji in his "Tantrasamgraha".
1530 A.D.
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Yuktibhasa was one of the firsts to show the written use of proofs.
1579 A.D.
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French mathematician achieved 9 digits with a polygon of 3x2 (to the seventeenth power) sides.
1593 A.D.
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Flemish mathematician valued pi around 15 places.
1593 A.D.
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First discovered in Europe. This is the form of an infinite product, rather than a sum, which in present day used in more pi calculations. Founded by French mathematician Francois Viete.
1596 A.D.
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Dutch mathematician reached 20 digits in the value of pi. Later on went to break his record further 35 digits. (Now having the nickname Ludolphian Number)
1621 A.D.
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Dutch scientist who reached pi valued pi back down to 34 places.
1630 A.D.
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Brought pi back up to 38 digits, which at this time, remained the most accurate approximation achieved without a computer using the polygonal algorithms.
1655 A.D.
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Second founded of Infinite Sequence. (Also with the use of product.)
1706
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Used the Gregory-Leibniz series to form an algorithm that was much faster. With the new formula, pi over 4 equals four arctan one fifth minus arctan one over two hundred thirty-nine, his version of pi reached to 100 places. Used as the most accurate method for calculating, well even into the computer era.
1761
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Proved that pi was irrational.
1794
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French mathematician proved that pi squared is also irrational.
1844
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Used the Machin-like formula to calculate 200 decimals of pi in his head.
1882
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German mathematician that proved pi is transcendental, or not a non-constant polynomial.
1949
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American mathematicians reached the value of pi to 1,120 places with using a desk calculator.
1951
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Leaders of a mathematical team, was able to prove pi's value to 2,037 places with a calculation that took about 70 hours of computer time on the ENIAC computer.
1960
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The study and re-calculation of Pi continues on well into the early 2000s. Constantly changing and expanding. Challenging the boundaries of the mathematical world.