‘HIISTORY’ AND ‘JOURNEY OF PI’

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 .

The circumference of every circle bears a constant ratio to its diameter and this constant

ratio is defined as no.

Its decimal expansion is 3.145926535897932384626433832795028…………………………………………………………..…. It is non terminating non-recurring .

’

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

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

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<

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

ZU CHONGHZIIn 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

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

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

it took 70 hours and number of digit was 2,037 .

JOHN VON NEUMANN

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 .

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.

• nl/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. based on the counts .

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

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

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

UNIVERSAL RELATION OF PI

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 , = /2 & some

people use a different transcendental number for TAU’s

value = 6.28

HAPPY PI DAY TO ALL OF YOU