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# Pi

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### Pi

1. 1. 3.1415926535
2. 2. INDEX  Definition of pi  Approximations of pi  Circle and pi  Knowledge of pi in different ancient civilizations i. Great pyramid of Giza ii. Babylonian and Egyptian pi iii. Pi in India  Bibliography
3. 3. Definition of pi  π is commonly defined as the ratio of a circle's circumference C to its diameter d  The ratio C/d is constant, regardless of the circle's size.  This definition of π is not universal, because it is only valid in flat geometry and is not valid in curved geometries. For this reason, some mathematicians prefer definitions of π based on calculus or trigonometry that do not rely on the circle. One such definition is: π is twice the smallest positive x for which cosine(x) equals 0.
4. 4. Approximations of ∏ Some approximations of π include:  Decimal – The first 50 decimal digits are 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 …  Binary – 11.00100100001111 ....  Hexadecimal – The base 16 approximation to 20 digits is 3.243F6A8885A308D31319...  Sexagesimal – A base 60 approximation is 3:8:30.  Fractions – Approximate fractions include (in order of increasing accuracy) 227, 333106, 355113, 5216316604, and 10399333102.
5. 5. Circle and pi  The infinite value pi is usually expressed as 3.14 or sometimes more accurately as 3.1416. It is the ratio of the diameter of a circle and the circumference of a circle. The diameter time’s pi equals the circumference, and the circumference divided by pi gives the diameter. Also, the radius times itself and then multiplied by pi gives the area inside a circle. P x D =∏ , C/∏ = D
6. 6. Knowledge of pi in different ancient civilizations  The Great Pyramid at Giza, constructed c.2589–2566 BC, was built with a perimeter of approximately 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≃ 6.2857 is about equal to 2π ≃ 6.2832. However, mainstream historians believe that ancient Egyptians had no concept of π and that it is merely a coincidence that the ratio of perimeter to height is about 2π.
7. 7. Babylonian and Egyptian pi  The earliest written approximations of π are found in Babylon and Egypt, both within 1 percent of the true value. In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats π as 25/8 ≃ 3.1250. In Egypt, the Rind Papyrus, dated around 1650 BC, has a formula for the area of a circle that treats π as (16/9)2 ≃ 3.1605.
8. 8. Pi in India  In India, around 600 BC, the ancient Indian math texts Shulba Sutras, treat π as (9785/5568)2 ≃ 3.088. In 150 BC, Indian sources treat π as ≃ 3.1622.  The Hebrew Bible (8-3 BC), contains two verses which suggest that π has a value of three. The two verses, 1 Kings 7:23 and 2 Chronicles 4:2, discuss a ceremonial pool in the temple of King Solomon with a diameter of ten cubits and a circumference of thirty cubits.
9. 9. Bibliography  Wikipedia/pi  Google.com  Encyclopedia /DK books  Ask.com/pi