Why the number of Pi is 3.14?

In: Mathematics

If you take a circle and a string, wrap it once around, and measure that string, then you get the circumference of the circle.

If you take a string, stretch out from one end of the circle to the other through its center, and measure that, then you get the diameter of the circle.

Now do that *a lot* more times on circles of all sizes. You’d then notice that when you start dividing the first number by the second one every time, you’d get something around 3.14.

If you measure across the widest part of the circle (diameter), how many of those lenghts do you need to make the circumferance of the circle? Roughly 3.14, or pi, many.

A lot of people are explaining how we get Pi, but not why. The simple fact is, it’s a fact of the universe. Something that is innately a part of any perfect circle. The math we use says it’s 3.14, but if we were to use a different system of mathematics that constant ratio would still show up.

We don’t know why. It’s a part of the universe. Why is the speed of light exactly that number? Same answer.

If you could look from “outside the universe”, maybe you could see exactly what aspect of the universe causes PI to be that number exactly. But you’re part of the universe and can’t “exit” it to “look from the outside”.

So we don’t know.

It’s a property that circles have.

Because the ratio of a circle’s circumference to it’s diameter is **always** 3.141592654… regardless of the actual size of the circle.

As for why that relationship holds…there is no why. It simply is.

You can do a very quick calculation of get some very rough bounds on pi.

We know that if a circle has radius 1 then its area is pi. Now we can completely surround that circle with a square with side length 2 (draw a picture, it will be clear why), and the area of this square is 4. hence pi is less than 4.

Alternatively we can draw a square with diagonal length 2 and fit it inside the circle. A slightly more complex calculation gives the area of that square as 2. So immedaitely we know that pi must be between 2 and 4.

You can use more complex shapes like pentagons, hexagons etc and get even tighter bounds.

It is the ration between the diameter and the circumference of a circle. There is a rigorous math proof to calculate it exactly, but tl;dr is that it’s that rations