Area of a circle without calculus

In summary: Delta r##where ##r_i## is the radius of the ith annulus and ##\Delta r## is the same (small) interval between all of the radii.So, the total area under the curve is the sum of the areas of each of the rectangles (the sum from i = 1 to n) (where n is the number of rectangles).In summary, the value of π can be derived by using circular strips or annuli and applying basic geometric principles. This can be done without using calculus or Archimedes' method, but the accuracy of the result depends on the size of the strips and the number of annuli used.
  • #36
PeterDonis said:
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.
 
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  • #37
Baluncore said:
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.
 
  • #38
Baluncore said:
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.
 
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