There has been this constant debate among mathematicians in choosing which is the better constant among tau and pi to be used in the mathematical equations. Let me give you some background information about both tau and pi. There are two approaches to this, and I will explain both of them. First arithmetically, pi is an irrational number that can be approximately considered to have a value of 3.14. While tau is twice of pi. Geometrically speaking, pi is the ratio circumference over diameter while tau is the ratio of circumference over radius. This again tells us that pi is half of tau.
To be really honest there is not a paradigm shift happening when we replace tau with pi. There real crunch seems to happen when we use tau in place of pi in measurement of angles. Let me explain that to you fellas here when we use pi, we say that the angle represented by a circle is 2pi, while we could say that the angle described by a circle is tau when using tau. This seems rather easy for someone who is newly introduced to the arena of geometry and trigonometry.
The argument to replace pi began as a certain faction of mathematicians and physicists saw that there is more usage of radius in mathematics and science, than the usage of diameter. So, it is only justified that we use a ratio that is based on radius than diameter, which as we all know by this point as tau. Robert Palais, (Ph.D. in Mathematics UC Berkley.) a professor at the University of Utah discussed how tau trumps pi in an article named “pi is wrong” in the year 2001[pdf]. Robert starts the paper with,
I know it will be called blasphemy by some, but I believe that pi is wrong. For centuries pi has received unlimited praise; mathematicians have waxed rhapsodic about its mysteries, used it as a symbol for mathematical societies and mathematics in general, and built it into calculators and programming language. Even a movie has been named after it. I am not questioning its irrationality, transcendence, or numerical calculation but the choice of the number on which we bestowed a symbol conveying deep geometric significance. The proper value, which does deserve all of the reverence and adulation bestowed upon the current imposter, is the number now unfortunately known as 2pi.
Palais,R., Pi is Wrong, 2001.
This paper can be cited as the start of a mere struggle for the ultimate constant in mathematics.
Clearly tau is better than pi while measuring angles in radians but what about their arithmetic use in equations. Such as the formula for finding area of a circle is A=(pi)r2. Now it seems pi is clearly the logical choice in this case because if we would have used tau the formula would have been A=(tau/2)r2. While this example is often cited by tauians (yes, they call themselves that), that this area formula suggests an integration. But the counter argument can be that as the students learn area of a circle much prior to learning calculus it would be unnatural for them to use this formula. Now similar arguments and counter arguments can be produced from both sides. So, which constant should we use it then? For me it is more intuitive using pi than tau, because my equations feel pretty neat when I am using only pi which would been tau/2, if I would have used tau.
So, this was pretty interesting to me, so I thought of giving you all an introduction to this power struggle between two constants in mathematics. Hope You all enjoy it.