eli5 Why is the circumference of a circle divided by its diameter always (for the majority) equal to pi?
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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).
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