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1900 BCE
Babylonian Tablet Approximation for π
During approximately 1900-1600 BCE the Babylonians created a tablet which historians believe they used as an approximation for π. They believed 3 was the approximation for π. On this tablet contains a circle with the numbers 3,9, and 45. The 3 measures the circle's circumference and the 45 indicates the area. The 9 is believed to be the circumference squared.
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1900 BCE
Babylonian Polygon Approximation Tablets (Susa Tables)
The Babylonian's created tablets TMS 2 and TMS 3 in which contain different polygons. TMS 3 contain geometric constraints, complicated geometric shapes, and 68 constants over 71 lines. Line 30 shows the perimeter at 24 and circumcircle circumference at 25, which represents π to be 3.125 (3+1/8). interactive content -
1650 BCE
Rhind Mathematical Papyrus
Egyptians created the Rhind Mathematical Papyrus which includes 87 problems. Using this they estimated pi as 256/81. This is found in RMP 41, 42, 43, and 44. video and descriptions -
200 BCE
Archimedes
Archimedes used the perimeter of regular polygons. He used one polygon inscribed and one circumscribed to approximate pi.
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300
Exhaustion Method
Chinese mathematician Liu Hui used the Pythagorean Theorem to find the area of a disk which brought him to approximate pi. Liu inscribed regular polygons and found their areas by the recursive method. The recursive method used the areas of kites constructed by pairs of triangles. Through his results he found outthat 3.14103 < π < 3.14271 and accurately estimated the value at 3.1416.
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Ludolph van Ceulen
Ludolph van Ceulen was a Dutch professor of mathematical sciences and calculated 35 digits of π. tombstone -
The Symbol π
William Oughtred was the first to use the symbol π which stood for the Greek work for "periphery" and the Greek letter delta to find a circle's dimensions. Oughtred used the sign to represent the ratio of circumference (π) to diameter (delta) in 1647. It was used on it's own to represent 3.14 in 1706 by William Jones. Controversy occurred between whether it should represent 3.14 or 6.28 until 1761. comp. explanation -
Buffon's Needle
French philosopher Georges-Louis Leclerc, Comte de Buffon, discovered a theorem of approximating pi. Buffon stated if you drop needles on grids of parallel lines then the probability of it crossing a line is connected with pi.
pi= (2x stick lenth x # sticks tossed) / (distance between lines x # sticks crossing a line)
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Ramanujan's Formula for Pi
Ramanujan proved the formula on the following link proof
in which William Gosper used in 1985 to accurately find the first 17 million digits of pi. -
Woman Calculates 31 Trillion Digits of Pi
Emma Haruka Iwao set the Guinness World Record for correct digits of pi at 31,415,926,535,897 digits. Iwao and her team used a super computer and beat the previous record by trillions. video