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Don’t think I am here to tell you aboutthe character called Pi in the popular

cinema “Life of Pi” but to tell you aboutthe struggle of a constant in mathematicsknown as π. I am sure all of you arefamiliar with it as it is widely used inalmost all branches of mathematics, evenin physics too. That π has to face lots ofproblems now. In fact, it has to strugglefor its existence. Perhaps it is one of themost ill-fated constant in science who hasto face many problems since its birth.Today I am going to tell you that story.

Let us see what is π? How the idea ofPi came? Actually the idea of Pi is verysimple. It is the ratio of the circumferenceto the diameter of a circle and it is aconstant number. That means for anycircle the ratio of the circumference tothe diameter will be the same. Its valueis 3.1415926……… For thousands of years,people were trying to calculate thecorrect value of Pi. Before 2000 AD it wasknown that the value of Pi is constant. Atthat time decimal system was unknown.So people have tried to represent it asthe ratio of two whole numbers; like - 22/7, 333/106, 355/113, 52163/16604,103993/33102 and so on. We usually usethe value of Pi as 22/7 which is very oldand a crude value. The recorded value ofPi was first found in Babylonian andEgyptian civilization. In Babylon we couldfound a clay inscription which was made

LifLifLifLifLife of Pi (e of Pi (e of Pi (e of Pi (e of Pi (πππππ)))))Dhrubajyoti Chattopadhyay

during 1800-1900 AD where the value ofPi is shown as 25/8 which is 3.1250; means1% less than the real value.

The first Scientist who mathematicallycalculated the value of Pi was Archimedes.His calculated value was 3.1410, whichwas much close to the real value3.1415…… But luck betrayed for Pi. Thestory says that while Archimedes wascalculating more accurate value for Pi hewas killed by the Roman soldiers. It was abig setback for Pi. Initially as a decimalsystem was unknown, Pi has to face a lotof problems, secondly the killing ofArchimedes almost stoped the researchfor Pi. Only few Chinees Mathematicianshad tried to calculate the value of Pi butthat was inferior to the value calculatedby Archimedes.

Clay inscription for Pi in Babylon civilization

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In the 18th century, Johann HeinrichLambert proved that π is irrational. Anirrational number is any real number thatcannot be expressed as a fraction a/b,where a is an integer and b is a non-zerointeger. In 1882, German mathematicianFerdinand von Lindemann proved that πis transcendental. Transcendental meansthat if we try to express it in decimals wewill get an infinite series after the pointwhich will be non-repetitive in nature.After that a competition starts to get moreaccurate values for Pi. Again a craze startsin the mathematicians for Pi.Mathematicians started to develop new

equations to get more correct values forPi. In this research, our own Ramanujanwas one of the pioneers. His equationgives us more accurate values for PI.

Archimedes and value of Pi

Today we are using computers to getmore accurate values for Pi. With the helpof super computers we are able to findfew trillion digits after decimal for Pi.Whereas only 40 to 50 digits after decimalcan give us more accurate calculation weneed so far. In this regard Pi is well aheadnow. Not only that the users of a Pi havecovered almost all fields of mathematics,computer and physics. In such a goldenperiod Pi has to face a great threat in thebeginning of the 21st century, even a fewpersons believe that the very existenceof Pi is now under threat. Ramanujan

Ramanujan`s equation

Heinrich Lambert

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In 2001, an American mathematicianBob Palais wrote an article heading as “Piis wrong”. Don’t think, he wanted to saythat the very concept of Pi is wrong -rather his intension was the way we areusing Pi is wrong. According to him- “Acouple of my own observations from thearticle. It seems to me that you can’t haveit both ways on area A= πr2 andcircumference C= πd. If you believediameter is fundamental, then it shouldbe A= πd2/4. I suggest calling the alternateconsultant 2π = 6.283... `1 turn’, so that90 degrees is a quarter turn’, just as wewould say in natural language. The mainpoint is that the historical choice of thevalue of π obscures the benefit of radianmeasure. It is easy to see that 1/4 turn ismore natural than 90°, but π/2 seemsalmost as arbitrary. It is apparent that wecan’t eliminate π but it seems helpful tobe aware of its pitfalls, and introduce analternative for those who might wish touse one.”

He gave a symbol for this new constantturn as -

πIn 2010, momentum has grown in turn.

Another Mathematician Michael Hartlwrote another article “The tau Manifesto.”In his article he suggested the name Tauinstead of turn and simplified the symbolas τ. Not only that, to popularize Tau theystarted a website. After that the Taumovements start. Very next year that isin 2011 the video “Pi is (still) wrong” wasuploaded by MichaelHartl.

Bob Palais

Michael Hartl

The logic of the Tauists

According to them there are a numberof mathematical equations where we haveto use 2π. If we replace 2π with τ thoseequations look good and will be simplifiedtoo. For example, they show:

i) In polar coordinate during integrationwe use the formula -

In this equation if we replace 2 π withτ the equation will look good and well aswill be simplified also. Similar logic alsoholds good for the following equations-

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Gaussian distribution Fouriertransformation Cauchy’s IntegralFormula

Riemann zeta function

ii) In a circle the total angle is 360o or 2πradian. If we replace this 2π with τ wemay get added advantage. We beginby considering the importantelementary functions sinè and cosè.Known as the “circle functions”because they give the coordinates ofa point on the unit circle (i.e., a circlewith radius 1), sine and cosine are thefundamental functions of trigonometry

and both functions are periodic withperiod T. If we replace 2π with τ wecan lucidly correlate τ and T.

Important points of sinè and cosè in theterm of τττττ

iii) Euler’s identity: Euler’s identity is oneof the best equation used inmathematics. It is written as:

If we replace theta with Pi theequation became-

As minus sign in left side looks odd, sothe most used forms of the equation is-

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Now if we replace Pi with Tau theequation will be-

This equation looks more beautiful andalso helps us to think in new ways.

iv) We know that the area of a circle isπr2. If we want to replace Pi with tau inthis equation it will surely be complicated.But the twist has put up another logic.According to them, the equations inPhysics obtained through integral followsa particular pattern and that is 1/2 ax2

where a is constant and x is variable. Forexample - Equation for falling object-1/2gt2d (here g- gravitational Constant abd t-time, variable)

Energy stored in spring-1/2 kx2

(k=Spring constant x=Variable)

Kinetic Energy-1/2 mv2(m=mass,constantandv=Velocity, Variable)

So if we replace this 2π with τ in thearea of circle it will be 1/2 π r2 and followthe pattern.

Like this they have put forwardedmany logics in support of τ

Counter logic of the Pi supporters

On the other hand Pi supporters alsolaunched another website similar to Tausupporters named as ‘Pi manifesto’.According to them Tauist logics are veryweak and not at all scientific. The reasonsare:

1). It is true, where π is used two times ifwe replace Pi with Tau in thoseequations it has advantages, but thereare many equations in Mathematicsand Physics where π is used once. Inthose cases the equation will be morecomplicated. So there is nojustification to replace π with Tau.

2).For Euler’s identity the advantage ofreplacing π with Tau is true only fortwo dimensional geometry, but forhigher dimensional it has noadvantages at all. So the logic in thisconnection are baseless.

3).The Pi supporters claim that theadvantages of using Tau instead of Piare very negligible and only soundsgood. For example:

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Tau supporters are using the abovetype of pictures to show the advantageof using Tau. But it’s a gimmick rather thanhave more advantages. Similar types ofgimmicks can be shown with Pi too.According to them the picture shownbelow is one of such example.

Similarly, artists are observing 28th

June as Tau day as the value of Tau is6.28……. Both sides have opened their blogand websites. Even few journals andacademics are working to give propagandato this. So really it is not easy to say thatthe controversy will dissolve very soon.Very recently we have seen the fate ofPluto, which has been discarded from thelist of planets. So nobody can predict whowill win the race.

Let us think, Tau has won the race. Inthat case whether it will be possible toreplace all the Pi with Tau? If so, whenand how? These are really big questions.Really, it is the biggest struggle for Pi. Inthe cinema Pi won at last; here we areeagerly waiting to see the final result.

Dhrubajyoti Chattopadhyay Education Officer

North Bengal Science Centre P.O. Matigara Siliguri Dist.

Darjeeling – 734 010 E Mail: dckc.sc@gmail.com

If we try to draw a square whose areais equal to the area of a circle having aradius of one unit, it’s side will be rootPi.

In this way the battle between thesetwo groups are now reaching to its climax.Each side puts forward many logics tosupport their agenda, immediatelycounter logics comes from the opponents.Every year we observes 14th March as Piday because the value of Pi is 3.14………

Every year we observes 14th March as Pi day because the

value of Pi is 3.14……… Similarly, artists are observing

28th June as Tau day as the value of Tau is 6.28……. Both

sides have opened their blog and websites. Even few

journals and academics are working to give propaganda

to this. So really it is not easy to say that the controversy

will dissolve very soon.