Happy π Day!

A mathematician, a physicist, and an engineer are all given identical rubber balls and told to find the volume. The mathematician pulls out a measuring tape and records the circumference. He then divides by 2π to get the radius, cubes that, multiplies by π again, and multiplies by 4/3 to arrive at the volume. The physicist gets a bucket of water, places 1.00000 liters of water in it, drops in the ball, and measures the displacement to six significant figures. And the engineer? He writes down the serial number of the ball and looks it up.

I had to tell a joke that involves π because it is π Day! Every year on 3/14, nerds around the world get excited because the date resembles the first few digits of π. That is, unless they structure the date in a consistent way, day/month/year, in increasing time increments. Then π day doesn't work because it would be the 31st of April.

π is the ratio between the circumference and the diameter of a circle. That is, a circle that is 1 unit across is π units, or about 3.14 units, around. It may be surprising that π shows up all over the place in mathematics and science, not just in geometry. It might be my favorite number, and not just because I memorized 150 digits of it in middle school. It is kind of the rock star of numbers. Everyone is familiar with π, even if they don't really know how to use it.

So it seems odd that some mathematicians and scientists want to replace π. They propose that we should use τ. That little t is lowercase Greek tau, their letter t. (π is lowercase Greek pi, their letter p.) τ is equal to 2π, or about 6.28. Sometimes supporters of tau use inflationary language like "π is wrong" or things like that, but what they really claim is that since 2π shows up so much, we should just replace 2π with its own symbol and use π less often. Mathematicians don't really use the diameter of a circle much, but they use the radius constantly. τ works nicely in that sense, because it is the ratio between the circumference and the radius.

Another way in which π trumps π is measuring angles. Scientists and mathematicians don't really use degrees much; often they use radians. There are 2π radians in a full circle, so that comes out to exactly τ. So a full revolution is one τ, whereas half of a revolution is one π. A whole corresponding to a whole is better than a half corresponding to a whole. 

There are more reasons that are cited in support of τ, but I don't think the case is strong enough. π has plenty of uses without the 2, and one applies especially to me. You may have noticed that I haven't mentioned engineers in this discussion. That is because I think they generally fall into the π camp. The biggest reason probably is making physical measurements. If I need to know the size of a pipe, I measure across it with some calipers or measuring tape. In the real world, we use diameters much more often because they are natural. How do you measure the radius of a pipe? You would need some kind of specialized tool. 

There are debatable advantages to switching to τ, but the cost of re-education and converting would be much greater. It is claimed that τ is more natural to use, and in the theoretical world it may be. We live in a physical world, however, and we naturally started using π thousands of years ago because it is more natural in a physical world. And that is why I won't be celebrating on June 28th.

For more:
numberphile on π: http://www.youtube.com/watch?v=yJ-HwrOpIps
numberphile on τ vs. π: http://www.youtube.com/watch?v=83ofi_L6eAo
                                    http://www.youtube.com/watch?v=ZPv1UV0rD8U