1. MADE BY : SHAHEEN
AFROZ
X-B
KENDRIYA VIDAYALAYA
SEC :30 GNR

2.  Let's look at what Pi really is.
Some declare that Pi is an
edible dessert, usually
circular, consisting of
something sweet enclosed
within a baked crust

3. Pi or π is a mathematical constant and a transcendental (and
therefore irrational) real number, approximately equal to
3.14159, which is the ratio of a circle's circumference to its
diameter in Euclidean geometry, and has many uses in
mathematics, physics, and engineering. It is also known as
Archimedes' constant (not to be confused with an Archimedes
number).

7.  LEIBNITZ (1671) Pi= 4(1/1-1/3+1/5-1/7+1/9-1/11+1/13+...)
 WALLIS Pi= 2(2/1*2/3*4/3*4/5*6/5*6/7*...)
 MACHIN (1706) Pi=16(1/5- 1/(3+5^3) +1/(5+5^5) -1/(7+5^7)+...)
 -4(1/239 -1/(3*239^3) + 1/(5*239^5)-...)
 SHARP (1717) Pi= 2*Sq.Rt(3)(1-1/3*3 + 1/5*3^2 - 1/7*3^5...)
 EULER (1736) Pi= Sq.Rt(6(1+1/1^2+1/2^2+ 1/3^2...))
 BOUNCKER Pi= 4
---
1+1
---
2+9
---
2+25
+...

8.  Pi is one of the longest numbers ever
computed, second only to “e” another
IRRATIONAL number with a value of
2.718281828459045 ….
 It never repeats like the decimal values of
1/3=.33333… or 5/7=.7142857142857…

9.  The early Babylonians and Hebrews used three as a value for Pi.
Later, Ahmes, an Egyptian found the area of a circle . Down through
the ages, countless people have puzzled over this same question,
“What is Pi?"
 From 287 - 212B.C. there
lived Archimedes, who inscribed
in a circle and circumscribed
about a circle, regular polygons.
The Greeks found Pi to be related
to cones, ellipses, cylinders and other
geometric figures.

10. π can be estimated by computing the perimeters of
circumscribed and inscribed polygons.

11. When mathematicians are
faced with quantities which
are hard to compute, they try,
at least, to pin them between
two other quantities which
they can compute. The
Greeks were not able to find
any fraction for Pi. Today we
know that Pi is NOT
a rational number and cannot
be expressed as a fraction.

13. During the 17th century, analytic geometry and calculus were
developed. They had a immediate effect on Pi. Pi was freed from the
circle! An ellipse has a formula for its area which involves Pi (a fact
known by the Greeks); but this is also true of the sphere, cycloid arc,
hypocycloid, the witch, and many other curves.

14. It’s curious how certain topics in mathematics show up over and over. In
the late 1940's two new mathematical streams (electronic computing and
statistics) put Pi on the table again.

15. The development of high speed electronic computing equipment provided
a means for rapid computation. Inquiries regarding the number of Pi’s
digits -- not what the numbers were individually, but how they behave
statistically -- provided the motive for additional research.

16. The computation of Pi to 10,000 places may be of no direct scientific
usefulness. However, its usefulness in training personnel to use computers
and to test such machines appears to be extremely important. Thus the
mysterious and wonderful Pi is reduced to a gargle that helps computing
machines clear their throats.