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Unfortunately I am very ignorant when it comes to mathematics. Please understand and forgive me if this question reflects that. Thank you!

I have an observation: Every curve and every circle in the real world is really just a bunch of straight lines and angles. There is no “real” curve that can be seen.

Take any circle. At some point in the circle, however miniscule, is a straight line. Even if to see it you would have to use a microscope that is so powerful it doesn’t exist, in theory the straight line has to be there. If it weren’t, the curvature of the circle would be so sharp that it would converge on itself. Now take it one step further. If you’d take a microscope to any point in a curve, if you take a small enough space, you’ll find a straight line. For the same reason – if it isn’t straight even as you go infinitely small, then at that point it has to keep curving infinitely, which means it should converge on itself. Since it doesn’t, there must be a straight line there. To get to the next point, also a straight line, there must be an angle.

Is this correct?

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    Every curve is a set of points, objects with zero dimension. To study curvature at a point you can consider limits of circles, for example.2012-10-14
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    Maybe you mean circles in the real world. The mathematical circle, is an abstract entity which no one can succeed in drawing on paper. The circles we draw are all approximations to that mathematical circle.2012-10-14
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    @Shahab That is precisely my point. I can accept a circle in the abstract, but I am wondering if in the real world it is ever possible to have a real circle. I shall edit the question accordingly.2012-10-14

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