styczny

Styczny is a Polish adjective meaning tangent. In mathematics, it describes a line, plane, or surface that touches a curve or another surface at a point without crossing it in a neighborhood. The tangent line to a differentiable function y=f(x) at x=a has the same slope as the function's derivative there; its equation is y=f(a)+f′(a)(x−a). For a circle, the tangent line at a point is perpendicular to the radius drawn to that point. More generally, a line is tangent to a curve if it has first-order contact with the curve at the point of contact; a tangent plane serves a similar role for surfaces.

In geometry and differential geometry, the concept extends to tangent spaces, where the tangent space at a point on a surface abstracts the directions in which one can move along the surface from that point. The noun form "styczność" denotes tangency, and the phrase "prosta styczna" is used for the tangent line.

Beyond pure math, "styczny" appears in descriptions of contact between bodies in mechanics, where surfaces meet with a common tangent direction at the contact point; "kontakt styczny" indicates such a point contact.

The term derives from styk, meaning contact. In Polish mathematical writing, "styczny" thus governs the language of touching objects—lines, curves, and surfaces—that share a common tangent at a point.