Osculating curve

From Wikipedia, the free encyclopedia

In mathematics and geometry, an osculating curve is an extension of the concept of tangent. A tangent line to a curve is the straight line that shares the location and direction of the curve, while an osculating circle to the same curve shares the location, direction, and curvature.

Two curves are said to be osculating at a particular point if they share the same osculating circle but do not cross, just as they are said to be tangent if they share the same tangent line but do not cross. The term derives from the latinate root "osculate", to kiss, because the two curves contact one another in a more gentle way than simple tangency.