Charles Petzold

The thing we call π is the ratio of the circumference of an ideal circle to its diameter, but the word “ideal” here means “existing only in the mind.” Perfect circles can’t exist in the real world.

You can’t write down all the digits of π, and you can’t even show it on a number line using the traditional construction tools of straightedge and compass. Doing so is equivalent to the unsolvable problem of squaring the circle.

The closest you can come to fully representing π is an algorithm for calculating its digits, but such an algorithm can never finish, and besides, a recipe for a pie is a poor substitute for pie itself.

Hence, π exists only in our minds, but pretty much anything can exist in the mind, such as centaurs and mermaids. We don’t say that these things exist, only that they can be imagined, and imagination is not the same as reality.