The ultimate answer to the question 42

[motorollin]

A square is flat digital representation of 2 dimensions, a circle is the infinity end of 2 dimensions.

Why is a circle infinite? It has measurable dimensions and a boundary separating it from whatever surrounds it. It is no different in these respects to a square.

[motorollin]

How much area exactly does it occupy?  Or how long exactly is its edge?

It is easy to estimate the area or circumference of a circle using simple equations. These can only be estimates since pi is imprecise, but that doesn't mean that a circle has infinite area or circumference.

If I walk around the edge of a circle, have I travelled an infinite distance? Of course not. And if I take a piece of string and wrap it around the edge of a circle, then lay it out straight and measure it, will my measurement reveal that the string is of infinite length? Of course not.

[motorollin]

infinite in the sense that it will take an infinitely long number to determine exactly what its length and area is.

No it won't. We just don't know how many decimal points of pi to go to to get the precise area. If we knew exactly what factor to use in the equation (i.e. how long to make pi) then we could calculate the area of the circle.

perhaps a better term is indeterminate?

Perhaps the best way to put it is that we are unable to calculate the precise area of a circle because our mathematics are not sufficient to do so.

[motorollin]

Well, whatever word you use to describe it, and whichever method you use to calculate it, I think to consider the area or circumference of a circle to be infinite is just ridiculous.