Area of a circle without calculus

[Baluncore]

classic problems in straightedge-and-compass

You are ignoring the requirement that it be done "using only a finite number of steps" with straightedge-and-compass.
Taking an infinite number of steps in one step is what calculus made possible.

 

[Mark44]

You are ignoring the requirement that it be done "using only a finite number of steps" with straightedge-and-compass.
Taking an infinite number of steps in one step is what calculus made possible.

I don't think @PeterDonis's intent was to provide a complete description of "squaring the circle." It was to dispute your claim that finding the area of a circle was "squaring the circle." I agree with Peter -- it isn't.

 

[PeterDonis]

Taking an infinite number of steps in one step is what calculus made possible.

This is perfectly true, and has nothing to do with what I was saying. As @Mark44 has said, I was disputing your claim that the term "squaring the circle" means "finding the area of a circle". It doesn't; the term "squaring the circle" has a much more specific meaning, which I described, and which has nothing whatever to do with using calculus to derive the formula for the area of a circle in terms of its radius.