- #1

- 125

- 1

Here is what I know and what I think about calculus. Please let me if my knowledge or conception is wrong.

A friend of mine gave me ( I can't remember exactly, so there are chances that my memory may also be erroneous ) an example of using calculus. If I recall what he said correctly, he said to me, ''Suppose, you have a circle. Now you want to measure the circumference of this circle using calculus. What calculus does is breaking this circle in so many pieces that each piece can be considered a straight line. Now if you can measure the length of each individual straight line, you can multiply that length with the number of straight lines you got. And there you get the circumference of the circle.''

Now my conception on calculus is based on what he said ( or in case I remembered it wrong, what I think he said. ) So the rest of this post is based on what I remember him to say.

If you do that trick, how can you get a correct answer? For example, you break the circumference in 1,000,000 tiny equal pieces, and you might think each of them has become close to a straight line. Now, since those pieces are NOT actually straight lines, no matter how hard you try, you'll never get the exact length of that ( imagined ) straight lines. So, maybe you get the length of one of this broken down straight line as 1 mm, but in reality the length of that line ( which is in fact, still a curved line ) may be a little more: say, 1.000001 mm. While the difference is not much in case of a single straight line, the difference will be magnified when you get the total length of the circumference. If you multiply 1 mm with 1,000,000 the circumference is 1,000,000 mm ( or 1 km. ) However, if you multiply 1.000001 with 1,000,000 it is 1,000,001 mm ( or 1,000.001 m or 1.000001 km ).

Oops. The difference is not much. I thought the difference would be much more than. It's only by 1 mm. And 1 mm is negligible indeed when the actual length is above 1 km.

So, if that is how calculus is done, I assume calculus can give you pretty close answer indeed.

So, the question is, is it really how calculus works? Or my knowledge or conception is not correct?