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It's pi day! Hank explains why this irrational number is important to scientists, and discusses a bit of a controversy that surrounds it.

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Vi Hart's video on τ:


[intro music]

Hank Green: Are you like me? Do you love pie? I don't get it as often as I'd like anymore, but scientists get to have pi day every day.

Pi (π), as you know, is the ratio of a circle's circumference to its diameter. No matter how big or small the circle is or where in the universe the circle might be, this ratio is always the same. You might remember it from 9th grade geometry as 3.14 but of course pi actually goes on forever. Kind of like 9th grade geometry. And like all rational numbers the digits that make up pi never end and never repeat in patterns. The standing record for reciting pi is to sixty seven thousand eight hundred and ninety places, to which I say: challenge accepted! *whispers* No...

 Use of pi

But if you think pi was just high school freshmen and date-less loners with excellent memories, you've got another thing coming, buddy. Because we couldn't do science, any of it, without pi. Name anything in the universe that's round, circular, spherical, globular, even round-ish and we use pi to study or predict the behavior of that thing.

Say you haven an artificial satellite in a circular orbit above Earth, like the International Space Station, and you want to measure the path it travels? Easy peasy. To get the circumference of a circle you just multiply its radius by 2π. Maybe you're observing the night sky and find a planet passing in front of a star. You wanna know what area it covers? pi times the square of its radius is all you need to know. Not only that: you can use those same two numbers, pi and the radius, to figure out the surface area of this new planet that you discovered, as well as its volume! Without having to fly all the way out there.

And of course we're not just talking about astronomy. You can find pi at work in the measurements of anything in Nature that curves. One of your DNA molecules, for example, is 1.5π times shorter when it's a bundle up inside your cells than it would be if it were stretched out. Electromagnetic waves can be measured in terms of pi. The p-word even shows up in Einstein's formula for how energy and mass curve space-time.

 Pi? Or tau?

Now you'll notice that in these awesome applications pi almost always appears in multiples of two: 2πR, 4π, 8πG. Because of that, scientists argue that the real magic number in mathematics is not π but 2π, or about 6.28. Members of this camp point out that the defining feature of a circle is really its radius, not its diameter. And it makes sense when you think about it: every measure of a circle -its circumference, area, volume, or surface area- is expressed as a function of its radius. So the mathematical constant that we should be using is really just twice pi.

Proponents call this number, the ratio of a circle's circumference to its radius, tau. So instead of measuring a space station's orbit as 2πR, it would just be tR. They even propose that, as some people celebrate pi day on March 14, we should observe tau day on June 28. So, I guess I'll see you then.


If you wanna see a really eloquent defense of tau, you can watch Vi Hart's video on this topic. But I wanna know what you think. Are you on the pi team or on the tau team? Let us know on Facebook or Twitter, or of course down in the comments below, and if you want to keep getting smarter with us here at SciShow you can go to and subscribe.