Pi is the ratio of a circle's circumference to its diameter. It was first discovered around 250 BC by Archimedes, who calculated upper and lower bounds for pi. Over centuries, many mathematicians have calculated pi to increasing levels of accuracy using polygon approximations of circles. In the modern era, computers have been used to calculate pi to trillions of digits. Pi is an irrational and transcendental number that is ubiquitous in formulas relating to circles, spheres, and trigonometry.

1. ‘HIISTORY’
AND
‘JOURNEY OF PI’

2. Q-1 => WHAT IS PI ?
ANS->The number
is a mathematical constant that is the
ratio of a circle’s circumference to its
diameter & is approx. equal to 3.1459
It has been represented by the Greek
letter since the mid-18th
centaury being
an irrational no. Can’t be expressed
exactly as a common fraction .
Consequently, its decimal representation
never ends and never settle into a
permanent repeating pattern .

3. The circumference of every circle
bears a constant ratio to its
diameter and this constant ratio is
defined as no. π

4. Its decimal
expansion is
3.1459265358979
32384626433832
795028…………………
…………………………………
……..….
It is non
terminating non-
recurring .
’

5. Is a transcendental no.- a no.
that is not the root of any non
zero polynomial having rational
coefficients .Fraction such as
22/7 & other rational no. are not
the exact but approx. value of

6. Q-2=>How pi is Discovered ?
Who discovered it ? How its value is
calculated ?
ANS=> It was in 250 BC mathematician
‘ARCHIMEDES’ discovered pi so pi is
named as ‘ARCHIMEDIAN CONSTANT’ .
The other mathematicians who worked on
pi are :-
‘LIU HUI’ , ‘ZU CHONGHZI ‘ ,
‘ARYABHATTA’ , ‘FRANCOIS VIETE’ ,
‘ADRIAN VAAN ROOOMEN’ ,
‘LUDOLPHVAN CEULAM’ , ‘WILLEBROD’ ,
‘CHRISTOPH GRIENBERGER’ , ‘JOHN VON
NEUMANN’ , ‘NIKANTHA SOMAYAJI’ , ‘
MADHAVA’ , ‘JAMSHID-AL-KASHI’ ,
‘GREGORY’ , ‘JOHN MACHIN’S ‘ ,
‘WILLIAM JONES’ , ‘EULER’ , ‘’ ,
‘ALBERT EAGLE ‘ …….etc

7. Archimedes computed lower and upper
bound of pi by drawing a regular hexagon
inscribing and circumscribing a circle &
successively doubling the no. of sides till he
reached a 96 SIDED POLYGON
By calculating parameters of these
Polygons , he proved that 223/71<π<22/7

8. LIU HUI created a polygon based
on iterative algorithms & used it
with a 3072-sided polygon to
obtain a value of π 3.14

9. ZU CHONGHZI
In 480 AD it was a great
achievement of the time
,the value of PI which was
more than 100 times
accurate then Liu hui’s .
Zu got 2 values for the
ratio the ‘approximation
values of PI which is 22/7
& Precise value of 355/113

10. Aryabhata used the value of 3.14 in his ‘Aryabhatiya’ .
Fibnacei computed 3.1418 using a polygon method,
independent of Archimedes.
Jamshid-al-kashi produced 16 digits in 1424 using a polygon
method with 3X2^28 sides of polygon which stood as a
world record for 180 years.
Franco-is-viete in 1579 archived 9 digits with a polygon of
3X2^17 sides.
Adriaan vaan roomen arrived at 15 decimal place.
Ludilphvan ceulen in 1596 calculate 20digits, a record he
later increased to 35 digits .
Dutch scientist Willebroad Snellius reached 34 digits in 1621
.
Austrian astronomer Christoph Grienberger arrived at 38
digits in 1630, which remains the most accurate approx.
Manually achieved using polygon algorithms

11. INTERESTING FACT that british
mathematician WILLIAM SHANKS
FAMOUSTY took 15 years to calculate the
value of pi to 707 digits , but made a mistake
in the 528th
digit , rendering all subsequent
digits incorrect .
John von Neumann was part of the team that
first used digital computer ENIAC, to compute
π it took 70 hours and number of digit was
2,037 .
JOHN VON NEUMANN

12. ADOPTION OF SYMBOL OF PI
• The earliest known use of the Greek letter
pi to represent the ratio of a circle’s
circumference to its diameter was by
Mathematician WILLIAM JONES .

13. BUFFON’S NEEDLE
• In figure 1st
needle a & b are dropped
randomly .
• In figure 2nd
random dots are place on the
quadrant of a square with a circle inscribed in
it.
• π ∼ 2nl/xt
•If a needle of length ‘l’ is
dropped ‘n’ times on a surface on
which parallel lines are drawn ‘t’
units apart, and if X of those
times it comes to rest crossing a
line (x>0) , then one may
approx.π based on the counts .

14. By this graph we can see that
As mathematicians discovered new logarithmic &
computer became available the no. of decimal digits of pi
increased dramatically . In 2011 the value of pi reached
to 2.7x10^13 by ALEXANDER YEE & SHIGER KONDO

15. INTERESTING FACT OF PI
•FRACTION:- Approximate fractions include 22/7 ,
333/100, 355/113 ……etc
•DECIMAL:-
3.14592653589793238462643383279……………………………………
•BINARY:-
11.001001000011111011…………………………………………………………………
…
In India around 600BC the
Shulba Sutras treat pi as
(9785/5568)~3.088 . In 150BC or
perhaps earlier, Indian sources treats
pi as √10 ~ 3.1622

16. USES OF PI
Pi is used in a ellipse , sphere, trigonometry, cones .
Special cases of the surface area Sn(r) and volumje
Vn(r) of an N-dimensional sphere

17. UNIVERSAL RELATION OF
PI
π appears frequently in equations
describing fundamentals principles of
the universe, often because of pi’s
relationship to the circle and to
spherical coordinate systems .
For example :- In classical mechanics
approx. time period or simple pendulum
INTERESTINFG FACT
In 1957 Albert eagle proposed
replacing π ,τ = π/2 & some people
use a different transcendental
number for TAU’s value τ = 6.28

18. HAPPY PI DAY TO ALL OF YOU