2011-06-28

Happy Tau Day

Three months and fourteen days ago, I wrote an article in celebration of "Half Tau Day" (better known to many as "Pi Day"). In that article I began to point out the benefits of using Tau (τ) or 2*pi (2π) in Mathematics.

Today, in full celebration of Tau Day, I would like to present more about the benefits of adjusting our established norms for a more comfortable digestion of Math. (A great deal of the information I will present here is processed from "The Tau Manifesto" website. I encourage you to take a more detailed look at the information there, if what I present here intrigues you.)

The constant of 2π is wide-spread in use throughout Mathematics, especially in Trigonometry and Calculus. This commonality occurs simply because of the relationship between circles and their radii.

Pi (π) exists because it is the ratio between a circle's diameter and its circumference. It has been stated (and sometimes argued) that "it is easier to measure a circle by its diameter than its radius". That may be so, but most formulas involving circles use its radius (e.g. area, angles, fractions, etc.); some charts and real world applications use radius as well, such as "pie graphs" and even slice the real-world application of slicing a piece of pie. Which means that the diameter would have to be divided after measurement anyway, especially if you want to measure more than circumference.

So, why not use a variable based on the ratio between a circle's radius and its circumference in the first place?

Circumference:
C = τ r
Area:
A = (τ/2) r²
Volume (of a sphere):
V = 2/3 τ r³

There may be some formulas which may seem more useful with π. Personally, I have no objection. Afterall, a meter is just 100 centimeters, yet we choose to use both "m" and "cm" everyday. I think π and τ should coexist in Mathematics in the common goal of providing a consistently easy and logical understanding of the concepts. (Meaning, let's make Math easy and fun for students.)

Keeping the students as the priority, certain "weird math" gets discarded. For example, did you know that a full pi radian angle is only 180°. If I were to use only pi to cut you a slice of pie that means you would only get half of what you asked for because a circle is really 2π. Using τ you would have access to the full 360°.

All-in-all, I want the focus in learning to be on the learner not the establishment. I encourage you to challenge yourself, question your logic, and most of all keep your eyes open and focused on new horizons.

Happy Tau Day! Now, go enjoy TWO pies!
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