At present, pi is defined to mean the ratio of the the circumference of a circle to its diameter. It should have been defined, argues the author, as the ratio of the circumference of a circle to its radius. Because of the wrong choice, 2 pops up everywhere, where a simple pi would be more elegant. As another example, if pi were defined properly, the formula for the area of a circle would be A = (1/2)r^2, which is analagous to the familiar formulas s = (1/2)gt^2 for the distance s fallen under gravitational acceleration g in time t, or E = (1/2)mv^2 for the kinetic energy E of a body of mass m moving at velocity v.

This wrong choice is like the wrong choice made by Benajamin Franklin. He assigned "+" to one kind of static electricity and "-" to the other kind. He could not have known it at the time, but the extra particles, which should have been associated with "+", turned out to have the charge he labeled "-". So now we have to make a distinction between "current" and "electron flow".

The wrong choice for pi has implications for our intergalactic reputation. If we send out "3.141592654..." to S.E.T.I. (S.T.I.) listeners elsewhere in the universe to show how smart we are, they will laugh at us for peculiarly broadcasting only half of the universal constant 6.283185307... .

One fix that has been suggested is to use a three-legged pi for what we now call 2; formulas using the three-legged pi are given in the article.

Update... Spahn continues...

As a follow-up to an earlier note about the misdefinition of pi, and how to fix the problem by using an new consonant defined as equal to 2 and represented by a three-legged version of the lowercase Greek letter pi, we will need a distinctive name for this three-legged pi.

I propose calling this consonant "poi". The allusion is not to the goopy taro-based Hawaiian food, but rather to a form of Maori juggling with balls swung at the end of cords held in the hands. The association of circles with this "poi" is obvious, both because of the shape of the balls, and because of their circular trajectory when juggled.

... Just my little contribution to the progress of mathematics.

In rereading my note on "poi" as a three-legged lowercase Greek letter pi, I notice that I called it a "consonant" when I meant to say "constant". To cover my embarrassment, let's say that "poi" is both a constant and a new Greek consonant which is pronounced like "p", but very vigorously, so as to moisten nearby listeners with spittle sprayed out in a circular arc.