By Parth Bhide
I am a very augmentative person and, as such, I enjoy the art of the debate. Fortunately for me, many of my friends do as well and this leads to some interesting, but usually useless, arguments. Each week, I will try to present one of our many arguments (or some that I come up with myself). As with all good journalism, I will try to present both sides of the argument, and let the reader decide which stance, if any, he or she prefers.
My second argument is one that I am particularly passionate about, and I realize I will have a difficult time presenting the counter-argument. As an engineer, I love the circle. However, human mathematical convention defines a relationship between two circular dimensions inconveniently:
The implications of this are the following: the relationship between the fraction of π, and the fraction gone around the circle, is not one. In other words, going π radians around a circle does NOT correspond to completing a complete circle.
There does exist an alternate constant that remedies this contradiction:
τ = C/r = 2π
This constant makes mental trigonometric calculations significantly simpler. For example, thinking about the sin(3π/4) , it is not immediately obvious that the angle is in the second quadrant. However, with the sin(3τ/8) , it is obvious that the angle is 3/8th of the way around a circle, and in the second quadrant. This problem recently came up in one of my classes.
There is one obvious hurdle that the incorporation of τ into modern society faces, and it begins with the children. π is revered in the elementary school. There are competitions, challenges, whole days dedicated to reciting, memorizing, and baking π. The concept of pi is indoctrinated into us, and by the time we have the skills to question why it is the standard for a circle, it becomes too late.
I will concede that some equations become more unusual through the incorporation of τ. For example:
A = πr2 = τ(r^2)/2
However, as formulae become more complex, the intuitive meaning of the constant no longer matters; it is simply a number plugged into a calculator. Perhaps it is too late for society, or perhaps the circle can evolve like the number did: convenient base-10 for humans, faster base-2 for computers. Regardless of what the rest of society decides to do, I will be celebrating my circle holiday on June 28th.
If you have any thoughts, or have any arguments you would like featured, please contact me at firstname.lastname@example.org!