Tau versus Pi

Beyond Tech, Features — By on April 22, 2014 11:03 pm

Most people have heard of pi , the mathematical constant that is defined as the ratio of a circle’s circumference to its diameter. However, most of you probably don’t know what tau  is. There is debate over whether to use tau  instead of  pi. The problem with this is that the argument is superficial and matters not to the practicing mathematician – it would be nothing more than an aesthetic change that would only make an equation look a bit prettier. However, there is a benefit that most students as well as teachers would appreciate: when teaching, it makes things easier to understand.

We can begin with radians. If we go around a full circle, we have  radians; ergo half of the circle is  radians, a quarter is  radians, and so forth. Using , going around a circle is simply one . Arguments made by those in opposition to this include the fact that with , the unit is not the whole thing, nor should it be. It can be said that going around a circle with  gets you nowhere. Euler’s (pronounced “oiler’s”) identity is another case in which  is more beneficial; the original statement is . This gives us a value equal to a negative number. However, what does this mean? We can now work with a simple 1 instead of having the bother of working with a negative number.

It isn’t just in pure mathematics that the debate between  and  exists – quantum mechanics also has its share of argument over this. For example, take the variable  (omega). It is defined by  (where F is frequency). Certainly  is both a cleaner and easier way of expressing it. Then we have Planck’s constant, denoted by h. Although an important term in the field, even those who use it express it as h  (h-bar), which is equivalent to h/2pi . And, of course, we have the Fourier transform: F(w)= (1/2pi) times the integral of f(t)e^(iwt) from negative infinity to positive infinity. Of course, this complex equation conjured up using the magic like genius of long-gone physicists and mathematicians probably means nothing to you now, but just looking at it, you see three instances of 2pi : two omega’s and in the denominator before the integral. If the terms were expanded, tau  would be an undoubtedly better alternative to  when it comes to having things looking clean and simpler.

The purpose of using  is not to replace  pi entirely; that was never the intention nor was it the basis of the argument. Simply put, teaching tau  as an alternative to  2pi is advantageous for both the student and teacher as it allows the student to understand the material more easily and leaves the teacher with fewer troubled students. The entire replacement of  pi is stupid and impossible – not only would it take an immensely long amount of time, but in cases where pi is not used with a multiple of 2,  becomes impractical and actually makes things worse. Besides, pi  has been used historically and so far its job has been very well done (although, historically, we also used to sacrifice goats and consider it bad luck to pee towards the sun, and I think that both of those are great ideas).