This document defines pi and provides a brief history of approximations of pi in ancient civilizations. It discusses pi's definition as the ratio of a circle's circumference to its diameter. Approximations of pi are given, including decimal, binary, hexadecimal, and sexagesimal representations. Ancient Egyptians and Babylonians approximated pi around 1900 BC. In India around 600 BC, pi was approximated to (9785/5568)2. The document also notes that the dimensions of structures like the Great Pyramid of Giza and King Solomon's temple suggest approximations of pi in ancient times.

2. 3.1415926535

3. 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

4. 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.

6. 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.

7. 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

8. 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.

9. 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.

10. 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.

11. Bibliography
 Wikipedia/pi
 Google.com
 Encyclopedia /DK books
 Ask.com/pi