High Quality Content by WIKIPEDIA articles! In geometry, a tacnode is a kind of singular point of a curve. It is defined as a point where two (or more) osculating circles to the curve at that point are tangent. This means that two branches of the curve have ordinary tangency at the double point. The canonical example is (y – x2)(y + x2) = 0. A tacnode is then a point of self tangency locally diffeomorphic to the origin in the case of (y – x2)(y + x2) = 0. Another example of a tacnode is given by the links curve with equation (x2 + y2 – 3x)2 – 4x2(2 – x) = 0. See the figure.

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