This document provides information about pi (π), including: - Pi is a mathematical constant that is the ratio of a circle's circumference to its diameter. It is an irrational and non-terminating number with a value of approximately 3.14159. - The history of pi discusses how European mathematicians developed formulas to calculate pi more accurately over time. - Pi is used in geometric formulas to calculate areas and volumes of shapes like circles, spheres, and cones. Pi day is celebrated on March 14th in honor of the first three digits of pi.

1. PI (Π)
Name : Shama Singla
Class : X-B
Roll No. : 27

2. INDEX
 Introduction
 Value
 Type of number
 Formula
 History of Pi
 Uses
 Facts
 Pi day

3. INTRODUCTION
 Pi is a mathematical constant that is used to solve
problems generally related to circles.
 Its value is fixed .
 Pi is basically the ratio of a circle's circumference to
its diameter.

4. VALUE
 Its value is fixed universally.
 It is 3.14 or 22/7.
 Actually the value of Pi is endless i.e.
3.141592653589793238462643383279502884197
16939937510582097494459230781640628620899
86280348253421170679821480865132823066470
93844609550582231725359408128

5. TYPE OF NUMBER
 Pi is an irrational number.
 It is non-terminating and repeating.

6. FORMULA
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.

7. HISTORY OF PI
European mathematicians in the early modern period
developed new arithmetical formulae to
approximate the value of pi, such as that of James
Gregory (1638-1675), which was taken up by
Leibniz:
/4 = 1 - 1/3 + 1/5 - 1/7 + . . . . . . . . . . .

8. One problem with using this formula to calculate the
value of pi is that you would have to add 5 million
terms to work out a value of /4 that extends to 6 or
7 decimal places.
In 1706, another mathematician named John Machin
developed a refinement on Gregory's formula,
yielding the formula still used today by computer
programmers to compute pi.
Using this formula, an Englishman named William
Shanks calculated pi to 707 places, a labour of
many years, which he published in 1873.

9. USES
π appears in formulae for areas and volumes of
geometrical shapes based on circles, such
as ellipses, spheres, cones, and tori.
Below are some of the more common formulae that
involve π.
1. The circumference of a circle with radius r is 2πr.
2. The area of a circle with radius r is πr2.
3. The volume of a sphere with radius r is 4/3πr3.
4. The surface area of a sphere with radius r is 4πr2.

10. FACTS
 Pi is the most recognized mathematical constant in
the world. Scholars often consider Pi the most
important and intriguing number in all of
mathematics.
 The symbol for pi (π) has been used regularly in its
mathematical sense only for the past 250 years.
 In the Greek alphabet, π (piwas) is the sixteenth
letter.

11.  Albert Einstein was born on Pi day.
 Hiroyuki Goto of Tokyo, Japan has the world record
for most memorized digits of pie with 42,195 digits
in d4ecimal place.
 Value of pi has been found till 2 trillion decimals.

12. PI DAY
Pi Day is an annual celebration of
the mathematical constant π. Pi
Day is observed on March 14
(3/14 in the month/day date
format) since 3, 1, and 4 are the
first three significant digits of π. In
2009, the United States House of
Representatives supported the
designation of Pi Day.

13. Pi Approximation Day is
observed on July 22 (22/7
in the day/month date
format), since
the fraction 22⁄7 is a common
approximation of π, which is
accurate to two decimal
places and dates
from Archimedes.