Tangentilla

Tangentilla is a coined term in differential geometry used to denote a family of loci associated with tangency properties of a base curve. The expression is not part of standard mathematical vocabulary and its exact definition varies with context. In general, tangentilla refers to a set of points derived from selected tangent lines to a given plane curve.

Definition and scope: Let C be a smooth plane curve and let a constraint pick a subset of its tangent lines (for example tangents in a specified direction, or tangents that meet a fixed point). The tangentilla T(C, constraint) is then defined as the locus of points that lie on at least one tangent line satisfying the constraint. The construction emphasizes how tangency conditions shape the resulting locus.

Properties: Tangentilla is not a canonical object; its geometry depends on the base curve and the chosen constraint. In some simple cases, the tangentilla can coincide with the base curve (for instance, when the base curve is a straight line). In other scenarios it can yield multi-component or degenerate loci that illustrate envelope-like behavior.

Notes: Tangentilla loci are mainly used as didactic tools to discuss envelopes, tangency, and parameter dependence. The term remains informal and is not widely adopted in formal literature. Related concepts include tangent lines, envelopes, and evolutes of curves.