life of pi presentation

8/12/2019 life of pi presentation

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A Bot tom less Pit

There are many who have dared,

But no one will find a pattern in Pi


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Geometr ical Defini t ion

(sometimes written pi) isthe ratio of any circle'scircumference to its diameter.

This is the same value as the ratioof a circle's area to the square of

its radius. The ratio C/dis constant,

regardless of a circle's size. Forexample, if a circle has twice thediameter dof another circle it willalso have twice thecircumference C, preserving theratio C/d.


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Ari thmet ical Def in i t ion

is anirrational number.

It cannot be written in the form p/q where p

and q are integers.

Its decimal representation is non- ending &

non- reccuring


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Dec imal Represen tat ion

s Decimal representation is non- terminatingand non- recurring.

Its Decimal Approximation up to 100 digits is3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679.

can be estimated by drawing a large circle,finding its Diameter & Circumference anddividing them.

Now there are soft wares which can find up to a

trillion decimal places of .As of January 2010, the record is almost

2.7 trillion digits


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History o f

The earliest knownusage of was in thePyramids of Egypt.

The history of is as oldas mathematics itself.

It is said that ancientIndians, Babylonians,

Egyptians and Greeksknew that the C/d ratiowas a little more than 3.


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Ancient India and

Ancient India was very advanced in

Mathematics.

India has made many important

contributions in mathematics including 0.

Ancient Indians also knew a lot about .

The Indian text ShatapathaBrahmanagives as 339/1083.139.


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Indian Mathematicians &

Many Indianmathematicians havemade lot of effort on .

Aryabhatta is amathematician from Indiawho has Made a lot ofexperiments on .

Madhava ofSangamagrama has alsomade huge contributions

on . Madhava was able to

estimate as3.14159265359, which iscorrect to 11 decimal

places


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Srinivasa Ramanujan on

In the beginning of the 20th century, the Indian

mathematician Srinivasa Ramanujan found

many new formulas for .

This formula was used to set several computing records in the end of the 1980s,

including the first calculation of over one billion

(1,011,196,691) decimals in 1989. It remains the

formula of choice for calculating software thatruns on personal computers


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Archimedes on

Archimedes (287212BC) was the first toestimate .

For this he inscribedcircles in regularpolygons and calculatedthe outer and innerpolygons' respectiveperimeters.

By using 96-sided

polygons, he proved that310/71<


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Major Mathematicians on

Other Mathematicians including Ptolemy,Liu Hui, Zu Chongzi etc. gave approximatevalues to .

In 1424 by the Persianmathematician,Jamshd al-Ksh, whogave an estimate that is correct to 16decimal digits.

Isaac Newton himself derived a series for and calculated 15 digits.


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Memorizing Digi ts

Well before computers were used in calculating, memorizing arecordnumber of digits hadbecome an obsession for some people.

In 2006, Akira Haraguchi, a retired Japanese

engineer, claimed to have recited 100,000decimal places.

This, however, has yet to be verifiedby Guinness World Records. The Guinness-

recognized record for remembered digits of is67,890 digits, held by Lu Chao, a 24-year-oldgraduate student from China. It took him 24hours and 4 minutes to recite to the 67,890th

decimal place of without an error.


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Use of

In Geometry is used to de operations onCircles, Spheres & Cylinders.

Area of Circle= *r*r

Circumference of a circle= 2**r is also used in Trigonometry, Calculus,

Physics, Probability etc.

is also used in Geomorphology, Under ideal

conditions, the ratio between the actual length ofa river and its straight-line from source to mouthlength tends to approach .


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in popular culture

Day(March 14, from 3.14) is observed inmany schools.

On November 7, 2005, musician Kate

Bush released the albumAerial. The albumcontains the song "" whose lyrics consistprincipally of Bush singing the digits of tomusic, beginning with "3.14.

In Carl Sagan 's novel Contact, played a keyrole in the story. The novel suggested that therewas a message buried deep within the digits of placed there by whoever created the universe.


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in popular culture

ties are also used.

shirts are also out

for sale.

Even plates areused.


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PoemsPoem- 1

Why, ! Stop, ! Weird anomalies do behave badly!You, madly conjured, imperfect, strange, numerical,Why do you maintain this facade?In finite time you are barbaric!You do wonders, mesmerize minds!

O, do elements numerous have a beautiful meaning-A system isolating all mysteries, solutions for puzzles,chaos, aO snafu apparent in O Universal Concept from believinglies?

That there, obstinate in you, O Strange Constant,A Divine Sign O exists is unlikely unlessIs O revealed Something Brilliant, negating belief!In formulas, O, you show yourself in Greek and math asa forever-O hidden wonders absconded, infinite, in atiny constant, O, sneakily, rather?

Never, I say!


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Poem - 2

A Scientific American's Dilemma

Hubble saw the universe expanding , Watson and Crick found life'sstartEinstein sensed relativity , While surgeons transplanted a heart.

Electrons exchange and release energy , So Schrdinger's cat canmeowSimultaneously its life is lost - Quantum mechanics will say how.

Chaos and order are intertwined , Physically, mentally, and more,Maybe matter is vibrating strings , But how could one know for sure?

This philosophy called science , Has plausibly progressedBut after a Grand Theory comes about , Can there be any moresignificant success?

And if a Grand Theory were proposed , Unifying all that exists,Would the end of pi be found as well,Or has math become eclipsed?


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Poem -3

If I gave you a 3and a 1,4,1,5You'd have the startOf the greatest number alive

If Pi were reducedTo a mere 3The circles of the worldWould be hexagonal, you see

What may seem minorJust might be bigSo grab some pie

And do some trig!


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ThankYou

By,

Deepak.P

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life of pi presentation