Will Pi Go the Way of Pluto?

There is a movement afoot to replace everyone's favorite mathematical constant.

This unassuming little number pervades photometry and geometry. It is an absolute must for those working in the lighting profession. It is the linchpin for calculations relating lumens to candela, lumens to mean spherical candle power (a common metric for some light bulbs and the 5mm series LEDs), and NITS to fL. The constant is central to the geometry associated with lighting and even to the design of the LED's drive electronics. Any circuit operating from AC line voltages will have this factor in its angular frequency, and so will the circuit's EMI filter.

Finally, you can find it in virtually anything circular or spherical. Convention has assigned this constant the moniker and Greek symbol π (pi).

Pi, of course, represents the ratio of the circumference of a circle to its diameter. It is an irrational number; it cannot be expressed exactly in our decimal system with a finite number of decimal places. It shares this characteristic with other lofty constants and values, such as the exponential function e, and common roots such as the square root of two and square root of three. Pi has the approximate value 3.141592654.

Since it is so fundamental and occurs in so many places, some people have developed mnemonics to make memorization easier. Of course, there was the gentlemen in Japan, Akira Haraguchi, who memorized it to 100,000 digits. (Evidence for his feat has not been accepted by Guinness.) Haraguchi made a poem out of π by associating the digits with kana symbols (syllables in the Japanese language).

Other mnemonics are more modest. One can create sentences in which the number of letters in each word represents a digit of π. For example, here is one good to six decimal places:

How3 I1 wish4 I1 could5 calculate9 pi2.

Comparison of relationships based on Pi and Tau

Relationship	Expressions with π	Expressions with τ
Circumference of a circle	2πr = πd	τr = τd / 2
Area of a circle	πr2	τr2 / 2
Surface area of a sphere	4πr2	2τr2
Volume of a sphere	4πr3 / 3	2τr3 / 3

Usurper

Pi has been known for millennia and has survived as a cornerstone of geometry and mathematics.

But beware -- there is now a movement afoot to replace π with a usurper. Pundits are looking to supersize π, à la McDonald's. The new constant tau (Greek Symbol τ) would double the value of π to roughly 6.283. Yes, τ too, is irrational.

Supporters of τ reason that it relates the radius of a circle to its circumference, rather than its diameter, and the radius actually defines the circle as the locus of points a distance r from its center. Most other expressions for circular or spherical relationships involve the radius, as shown in the table above.

I, for one, am not having it. I'll accept τ about the same time they demote Pluto out of the solar system. Oh, wait...