thumb|right|214px|A tacnode at the origin of the curve defined by (x^2+y^2-3x)^2 - 4x^2(2-x) = 0.
thumb|right|214px|A tacnode at the origin of the curve defined by (x^2+y^2-3x)^2 - 4x^2(2-x) = 0.
In classical algebraic geometry, a tacnode (also called a point of osculation or double cusp) 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.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).