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What’s irrational and never ends? Pi! Hank explains how we need pi to explain some of the most basic but most important principles of the universe, in honor of Pi Day.

Hosted by: Hank Green
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Inverse square law:

HANK: This week marks a special time of the year, when people of all different backgrounds and beliefs take time to celebrate one of the most powerful figures in the universe, pi. Pi is the ratio between the circumference of a circle and its diameter. This means that no matter how large a circle is, from a coin size to a planet's size, that ratio will always be the same. Pi is also irrational, meaning that it never ends, and it never repeats itself. But it starts with 3.1415, which is why March 14th, 3-14 as Americans write it, is called Pi Day, and this year, Pi Day is March 14th, 2015, so the date will be 3-14-15. A mathematical configuration that only comes around once every hundred years.

But there is so much more to pi than just a holiday when we make math themed baked goods, or however you choose to celebrate it. If you're studying anything that involves circles or spheres, pi is going to come up, and scientists tend to find a lot of uses for circles and spheres in their work, from detecting exoplanets, to measuring electric fields, to describing the very structure of the universe. I'm Hank Green, and here are just 3 examples of how pi can explain practically anything.

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HANK:  Lately astronomers have found loads of exoplanets, or planets outside of our solar system. They can find them because when a planet moves in front of its host star, a portion of that star's light is blocked out. Then as the planet clears, the star's brightness returns to normal. The graph of how we see that light twinkle from Earth is called a light curve, and to figure out how to interpret this light curve, they need to know how big the host star is. So how on Earth do astronomers figure out the area of a star? With the equation for the surface area of a sphere, 4πr², with r being the star's radius. Once they know how big that star is, they can use that, combined with how much its light fluctuated to figure out things like the exoplanet's size and maybe even what's in the atmosphere. Since knowing an exoplanet's size can help scientists guess whether its habitable or not, pi is kind of essential to our search for planets that might support alien life.

So pi is obviously crucial to studying anything that's spherical, like stars, because spheres are just circles swept around in three dimensions.  And as it happens, the way that we calculate the forces of physics has a lot to do with spheres too. Take the electrostatic force, for example, which is the force between two electric charges. It's calculated using a handy equation you may have heard of called Coulomb's Law. So let's say you have two electrons just floating out in the middle of space. Each electron is exerting a force in all directions, so basically, its force forms a sphere, and we call that an electric field. But you only see the effect of these fields when they interact, in this case by repelling each other. If you want to calculate how much electrostatic force is driving those electrons apart, you're going to have to find out how much of each electron's invisible sphere is touching the other. And since we're dealing with spheres again, there's pi. To figure out how much of their electric fields are touching, you need to divide the total force from both electrons by the same formula we used to find the surface area of a star, 4πr².

Now, no discussion of the use of pi in science would be complete without talking about how it was used to describe the universe itself, by one Albert - no middle name - Einstein. Einstein published his theory of general relativity a century ago in 1915, which happens to be the last time that Pi Day was 3-14-15. And do you know what Einstein's birthday is? Just give me a guess. March 14th. Dude was born on Pi Day. And Einstein's theory of general relativity calls on pi to describe how all forms of momentum and energy can curve space-time. Now we often talk around here and on SciShow Space about how huge masses like stars and galaxies can curve space and time with their gravity. But Einstein's theory actually says that just like a ball sitting on a bedsheet, any form of momentum and energy can also curve space-time around it. And the equation that Einstein used to describe that fact uses pi. This equation basically defines the physical universe, so it's got a lot going on in it, but one of its main points is that there's a fixed ratio, a constant, that helps explain the relationship between gravity, momentum, and energy. And pi has to be part of that constant because Einstein was talking about physics in terms of field theory. Just like electrons, each tiny part of an object generates its own gravitational field in every direction, and together, they form a spherical field of force around that object. And where there's a sphere, there's pi.

For such an important number, it seems sad that pi only gets one day a year for official celebrations, and a Pi Day this special won't show up again until 2115. But at practically any moment, you can be sure that somewhere in the world there is a mathematician or scientist using pi for something important.

Thanks for joining us for this special Pi Day edition of SciShow News. If you want to keep getting smarter with us, you can go to and subscribe.

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