Posted by: Dave Richeson | December 13, 2008

## Is π the right constant?

In the November 3, 2001 issue of the Mathematical Intelligencer Bob Palais wrote an article called $\pi$ is wrong!” In it Palais does not assert that we have miscalculated the value of $\pi$, just that many mathematical formulas would be more elegant if we had chosen a different value for our named constant—he thinks that $2\pi$ is a better constant than $\pi$.

Essentially, Palais’ objection boils down to the question: why did we chose our constant to be half the circumference of the unit circle? If we had chosen it to be the circumference, students would be less confused when they learn about radians and formulas would be more elegant (our formulas have a lot of extra 2’s hanging around). He writes:

An enlightening analogy is to leave clocks the way they are, but define an hour to be 30 minutes. In that case, 15 minutes or a quarter of a clock would indeed be called half an hour, just as a quarter of a circle is half of $\pi$ in mathematics!

It was Archimedes who first noticed the importance of the constant that we call $\pi$—the ratio of the circumference of a circle to its diameter. But mathematicians didn’t settle on $\pi$ as the important constant until Euler adopted it in 1737.

In the February 1, 2008 issue of Physics World Robert Crease wrote a similar article called “Constant failure.”

Crease wrote:

I posed this question to the Princeton University mathematician John Conway, one of the most creative mathematicians working today. Conway, it turned out, had strong feelings on the subject. “$2\pi$ is obviously the correct constant!” he told me immediately — although he also told me of arguments, which he did not find persuasive, for a third option, $\pi/2$.

Crease goes on to ask whether we’ve chosen the right value for Planck’s constant, the gravitational constant, and others.

Now, in the December 1, 2008 issue he wrote a follow-up piece called “Shifty constants” in which he shares the thoughts of some of his readers. They ask, for example, if the base 10 system should be discarded in place of a friendlier one.

## Responses

1. “They ask, for example, if the base 10 system should be discarded in place of a friendlier one.”

I’ve been arguing for a move to a base 12 system ever since my evening job in college at a doughnut shop.

• Mmmm…. doughnuts…..