Circumference and Pi

Let's explore what the relation is between the circumference and diameter. You may already know the relation,

$$\text{Circumference} = \pi \cdot \text{diameter}$$

$\pi$, or pi, is a constant, meaning it is a fixed value. It is approximately 3.1416. But let's try to get some idea of where this comes from.

Here's a square.

Another way to think about this:

Extending our logic a bit from squares, we maybe can now believe the following general statement:

The ratio between the perimeter and "width" of a geometric shape are constant.

This explanation is about intuition so we won't go into detail about what is a geometric shape and what isn't, and also what width means but...

A circle certainly counts!

Great! So now we say

The ratio between the circumference and diameter of a circle is constant.

And this ratio is of course the number we all love, $\pi$.