Tagged: pi

"Ten is doubtless a convenient number of fingers to have, though men have gotten along with less and a few people have been born with more. But as the purely arbitrary unit which determines the form of our numbers, it was a miserable choice." – F. Emerson Andrews

"Do not disturb my circles." – Archimedes

It's that time of year again—time to start thinking about DOZENAL PI DAY.

Overview

Regardless of its radical prejudices, Pi Day has become, in recent years, an annual cultural event of some magnitude, and the occasion for a certain nominal enthusiasm about "math" that people seem to find meaningful. At the very least, it seems to remind us of our own cleverness, which is something I have nothing against in principle.

Yet I am more convinced than ever that, unless we remain firmly mindful of what separates the arbitrary and symbolic in mathematics from the truly meaningful, Pi Day will ultimately remain a rather vacuous and misguided holiday. Thus, I once again propose the observation of DOZENAL PI DAY on 18; March (decimal 20th), to raise awareness of the superior dozenal radix, while also bringing attention to the underlying meaninglessness of our present decimal notation.

An astute reader recently brought to my attention the nascent movement afoot to replace π in common usage with the number now unfortunately known as 2π—viz., 6;349419 (dec. 6.283186):

• Pi Is Wrong! - By Bob Palais
• The Tau Manifesto - By Michael Hartl

(For a reasonably convincing argument on why the letter τ (tau) in particular should be adopted for this value, please read Mr. Hartl's manifesto.)

The fundamental point here is that, in trigonometry and all other manner of angle-measuring endeavors, what we care about is the radius of a circle, not its diameter. The one follows from the other to be sure, but at the end of the day the diameter is more usefully considered twice the radius than the radius is half the diameter. A circle is a circumference around a center—it is the measure of this distance between center and circumference that is elemental to the idea of a circle, not the rather incidental fact that its full width is twice that same distance.

This is a unit circle diagram using both dozenal notation (as with elsewhere on this site, using "A" and "B" for ten and eleven) and the newly proposed circle constant τ (tau), which is equal to 2π. The advantages of τ over π are numerous and obvious—instead of a full circle of arc being two of anything, it is just one τ. Put another way, τ is simply the number of radians in a circle.