If it didn’t, it wouldn’t be a circle. Part of the definition of a circle is that *every* point on the line is the same amount of distance from the center, that distance being the radius. With that rigid of a definition, there’s only one way to change its shape which is to make the whole thing bigger or smaller by a specific proportion.
…because that’s what pi is?
Pi is not a special numbers, it is what it is. Pi could have equaled just 3.12345 and ended at just 5 decimals and it would be just as prevalent in math. The fact that it goes on forever without repeating is just additional, there are a ton of other numbers that do it as well (such as *e*). We use the symbol because we can’t right it out in a formula (we probably would also use it even if it equalled 3.12345 because that too is pretty long to do multiple times in a workout).
It’s not equal to pi “for the majority,” it’s flat-out equal to pi.
If you were to take a perfect circle–*any* perfect circle, of any size–and cut it, and then straighten it out into a line, you will find that the length of that line is *always* exactly equal to pi times the diameter of the circle.
If you want to get more technical about it, you can look to calculus. When you have a function, you can take a “derivative” of that function to tell you how it changes with respect to some other variable.
In this case, the function is f(**d**) = π**d**, where d is the diameter of the circle. This gives you the circumference of a circle. If you take the derivative of that function with respect to the diameter (that is, if you want to see how the circumference changes as the diameter does), you get this: d/d**d** πd = π, or f'(d) = π. (“**d**” for diameter is bolded here for ease of reading. The function could also be written f(x) = πx, and d/dx πx = π).
It’s the same reason a square’s perimeter is always 4x its length. It has 4 equal sides, each with the same length, so the total of the sides is 4x its length.
A circle is a consistent shape so its proportions are always the same. A circle has smoothly curved sides instead of straight sides like a square, so the math to calculate that ratio isn’t as simple. But that ratio is pi, and every circle is *exactly* the same as any other circle, just bigger or smaller, so the comparison between its circumference and diameter is always the same.
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