What is "tangent plane"

Tangent \Tan"gent\, a. [L. tangens, -entis, p. pr.] Touching; touching at a single point; specifically (Geom.) meeting a curve or surface at a point and having at that point the same direction as the curve or surface; -- said of a straight line, curve, or surface; as, a line tangent to a curve; a curve tangent to a surface; tangent surfaces.

Tangent plane (Geom.), a plane which touches a surface in a point or line.

Tangent scale (Gun.), a kind of breech sight for a cannon.

Tangent screw (Mach.), an endless screw; a worm.

n. (context differential geometry English) Given a point ''P'' on a surface ''M'', the tangent plane of ''M'' at point ''P'', denoted by ''T_P(M)'', is the plane passing through P which contains the tangent lines of all the curves on ''M'' passing through ''P''.

n. the plane that contains all the lines tangent to a specific point on a surface