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The math of pi explained, as simply as possible

Pi day is March 14. Here’s the famous irrational number, explained in one GIF.

Brian Resnick is Vox’s science and health editor, and is the co-creator of Unexplainable, Vox's podcast about unanswered questions in science. Previously, Brian was a reporter at Vox and at National Journal.

March 14 is a date that coincidentally spells out the first three digits of pi (represented by the symbol π). Thirty-one years ago, physicist Larry Shaw decided to celebrate 3/14 at a San Francisco science museum. Since then, Pi Day has grown into a worldwide celebration of math and pastry.

But the math is cool! And much more useful than a pie recipe.

The simplest explanation of pi, in one GIF

If you were paying attention in grade school, you’ll remember pi is the number that describes how the circumference of a circle relates to its diameter (how wide a circle is if you draw a line straight across the middle). If a circle’s diameter is 1, then its circumference is π. If a circle’s diameter is 2, then its circumference is 2π. And so on. Here’s a helpful demonstration of that in GIF form:

This simple relationship has proved enormously useful for math and engineering throughout the course of human history. NASA uses π to calculate the trajectory of spacecraft orbits. It’s essential for engineering anything that involves the motion of circles (like wheels on a car), the area of a circle, or the volume of a sphere. Pi is also extremely useful for describing the motion and shape of waves.

And you can use pi to describe the size of angles. Sure, you may know that a circle contains 360 degrees. But that number, 360, is arbitrary. We could say a circle has 500 degrees, or 1,000, and it’d be equally random. It’s more precise to describe the size of angles in terms of pi. These units are called radians (apologies if this term provokes a violent and sickening flashback to high school math), and there are 2π of them in a circle.

Pi, you may also remember from grade school, is not an ordinary number. It’s irrational, meaning it has an endless number of decimals that never repeat. Though even cutting off pi at 15 digits allows for extremely precise measurements.

If you were to draw a circle with a diameter of 25 billion miles, using 15 digits of pi, you’d only arrive at a measurement of the circumference that’s off by 1.5 inches, NASA’s Marc Rayman explained in a post on NASA’s JPL website. And that’s good enough. If you wanted to calculate the circumference of the known universe, he explained, you’d only need 40 decimal places to be accurate within a range the size of a single atom of hydrogen (the smallest element).

Of course, that hasn’t stopped people from looking for more and more digits of pi. Currently, there are 31 trillion known digits, which show no hint of ending or repeating.

Further reading: pi and pie

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