ABSTRACT
The larger the radius of a circle, the less curved it is. For example, if you look at part of a circle with a very large radius, the line will seem straight. Mathematicians express this property by saying that circles with radius R have curvature 1/R. The notion of the curvature is used to study curves that are different from circles and straight lines. We can say that the curvature of a curve measures the failure of a curve to be a straight line. We know from school geometry that two circles are the same if they have the same radius. Using the notion of the curvature we can now say that two circles are the same if they have the same curvature.
