April 11, 2007

We got pi wrong

Freedom is under attack, the EPA will be empowered to regulate CO2, single-payer health care is picking up steam. Now I realize that Bob Palais is right: pi is poorly defined. Palais points out that it should have been defined as the ratio of a circle's circumference to its radius, not the diameter.

Palais says "I am not questioning its irrationality, transcendence, or numerical calculation." He's not a commie or anything. But "the proper value, which does deserve all the reverence and adulation" is twice the value that drunken college students used to memorize. Windows calculator goes to 6.283185307179586476925286766559.

Dang it, he's right. Palais's point is that good math gets littered with 2pi (a commenter suggests a three legged pi to represent the "real" pi). Good math guys can handle the twos but it destroys what would be two intuitive demonstrations:

  • Measuring angles in real numbers seems counter-intuitive to young students who are loath to give up the 90-degree, 180-degree names they have used since childhood. Palais points out that using real pi, a quarter-pi angle is a "quarter-turn." Beautiful.

  • Don Luskin reader Mark Spahn (hat-tips all 'round) points out that the area formula would then take the classical integral form A = 1/2 r-squared times the angle through which the radius has moved: just like distance traveled at constant acceleration, kinetic energy, any double integral.

I'd add that it's pretty obvious that the radius of a circle is its interesting mathematical characteristic. If you're a plumber, the diameter counts but a mathematician or engineer will start with the radius. Should have been circumference / radius.

I think it's Bush's fault.

Posted by John Kranz at April 11, 2007 12:15 PM