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- 1. 3.1415926535
- 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. 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. 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. 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. 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. 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. 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. Bibliography Wikipedia/pi Google.com Encyclopedia /DK books Ask.com/pi

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