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The ancient definition of a curve is that it is the path traced by a moving point.



In mathematics the sharp, angular and the straight may all be curves. A closed curve is then the one whose end point is the same as its beginning point. If it does not pass to the same point more than once it is called a simple closed curve.

Circles, triangles, rectangles, polygons, etc. are all simple closed curves. Drawn on a piece of paper they divide it into an inside and outside. This fact is stated by one of the fundamental theorems of topology.