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June 28 is Tau Day! Join SciShow as we celebrate circles by exploring the many uses of twice pi.

Hosted by: Caitlin Hofmeister
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Sources:
http://www.math.utah.edu/~palais/pi.pdf
http://tauday.com/tau-manifesto
http://www.thepimanifesto.com/
http://www.youtube.com/watch?v=FtxmFlMLYRI
(SciShow Intro plays)

Caitlin: It's time for another science holiday.  I'm Caitlin Hofmeister from SciShow Space, filling in while Hank and Aranda are out of town, and I want to talk to you about Tau.  On June 28th, we're celebrating Tau Day because, at least according to the American system, the date is written as 6-28, which is 2 times pi, otherwise known as Tau.  We've mentioned Tau before as a proposed alternative to Pi.  Like Pi, Tau is irrational and goes on forever, but most of the formulas that we use involving pi, like calculating the circumference of a circle or the surface of a sphere actually require using two Pi, so using Tau instead of Pi seems, to some mathematicians and scientists, to make a lot more sense. 

However, Pi has been around for a long time, and there are plenty of people who have very strong feelings about which constant we should be using.  We here at SciShow are mostly curious about why Tau shows up so much in the first place and how it can help us understand the world.  It all comes from the way we define Pi, which is the circumference of a circle divided by its diameter.  That's really handy, because it's easy to measure the diameter of a circle: you just find the distance across.  Problem is, most things in math use the radius, which is half the diameter.  That's why 2 Pi shows up in formulas so often.  But if you replace Pi with Tau, bam, no more messy formulas.  For example, the circumference of a circle is just Tau times the radius, and if you wanna know the angle that's covered by, say, 3/4 of a circle, it's just 3/4 of Tau expressed in units called radians, half of a circle, half of Tau. 

If there's anything that mathematicians really like, it's elegance, and Tau adds that to a lot of our most useful calculations.  That's why Utah mathematician Robert Palais got the whole Tau movement started when he wrote a paper in 2001 with the inflammatory title, "Pi is wrong!"  Then, in 2010, physicist Michael Hartl upped the ante with his Tau Manifesto, an exhaustive treatise on how, if we all acted like Pi never even existed and we used Tau instead, everyone's life would be easier.  Now to be clear, we are not taking sides here, at least I'm not personally, but still, it's useful to understand how Tau can help clarify science, especially physics, because when you're studying the physical laws of the universe, angles show up a lot.

Let's say you wanna know how fast a satellite is moving through its orbit.  Well, you might use something called Mean Motion.  One way to calculate mean motion is to take two Pi and divide it by the period of time it takes the satellite to complete one orbit.  Now, Tau-ists, which is what Tau advocates call themselves, point out the quicker, easier way to make that calculation is just Tau/P, Tau divided by the period of the orbit.  It makes sense if you think about it.  For each orbit, the satellite's moving through a full circle's worth of angles, which is exactly Tau radians.  Divide that by the amount of time it takes, and you get a measure of angular frequency, or how fast the satellite's angle is changing as it moves through its orbit. 

And Tau tends to show up in other cases where angular frequency is important.  Take a simple pendulum for example.  The weight on the string does its thing, moving back and forth in a consistent pattern, with a set amount of time between each swing, as long as you ignore complications like the air slowing it down, which physicists tend to do because it's just a lot simpler that way.  So let's say you want to know the angular frequency of your pendulum.  If you know that it completes a full swing in one second, to get the angular frequency, all you have to do is multiply it by 2 Pi.  Tau again! 

But 2 Pi shows up in a less Newtonian world, too.  You've probably heard of Max Planck, the theoretical physicist involved in quantum mechanics.  Basically, he said that energy is measured in tiny packets, and the amount of each packet can be calculated using a number called Planck's constant, represented by an h.  And one of the most important constants in quantum mechanics is actually h/2Pi.  It's what you use to figure out the energy of something like a photon, using its angular frequency or how it vibrates, and this super important quantum constant is just h/Tau. 

So it didn't seem right to celebrate Super Pi Day this year without also giving Tau its due.  Whether you're on Team Pi or Team Tau, the important thing to remember is that Pi is delicious and 2 Pis?  More delicious.  Thanks for watching this episode of SciShow, which we couldn't make without the support of our Patrons on Patreon.  If you wanna help us make this content and receive rewards like access to early videos and blooper reels, go to Patreon.com/SciShow, and don't forget to go to YouTube.com/SciShow and subscribe.