You know the name and you know at least some of the number. Pi, a never-ending value a little more than three, is the ratio of a circle’s circumference to its diameter. It’s also *irrational*, meaning that pi — denoted with the Greek symbol **π** since the mid 1700s — cannot be expressed as a common fraction like 1/2 or 3/5. The number never ends, and in the intervening centuries we’ve figured out a few trillion digits behind the 3.

But what *is *π? Maybe the best way to understand this crucial mathematical constant is to see where it comes from.

If π is the ratio between a circle’s circumference — the distance around the circle — and its diameter, then seeing both laid out should show us what π is. Make a circle’s diameter 1 and then lay out the circumference. How many diameters is that? A little over 3, or 3.14159…!

Another way to think of π is to in *radians*, the standard unit of angular measurement. 1 rad is equal to the angle that an arc the same length as the circle’s radius makes. A circle’s radius is one-half its diameter, so you should be able to fit π radians into half a circle. The math works out — you can fit three radians and some change (0.14159…to be precise) in a half-circle!

Another way to think of the ratio of a circle’s circumference and diameter is to imagine the classic “sine wave.” You’ve probably seen these waves blinking and flowing on sci-fi gadgets or in your trigonometry class. A sine wave is the 2D graph of the sine function, which describes the ratio of the length of a side that is opposite a right triangle’s angle to the length of the longest side of that triangle.

The sine wave can be traced out by tracking the coordinates of a point running along a circle with a radius of one. And like the GIF above, when half the circle has been traced, exactly π distance has been covered! See? GIFs are always a bit easier to digest than high school trig.

Remember, it’s OK to be irrational sometimes.

“Three GIFs that make Pi instantly understandable (if GIFs on our site would animate properly on iOS)”

still dont get it, and its not that i can’t see the completion of a circle on a 2d plane.. its just hard for me to see the circle completed on an adjusted 3d plane.. the ends just don’t meet up!

Why would you? A circle is a 2d object. You can’t see it on a 3d plane. Pi or not.

Well now, that clears a few things up!! Thanks “guys!!”

Well now, that clears a few things up!! Thanks “guys!!”