In geometry, a generatrix (/dʒɛnəˈreɪtrɪks/) or describent is a point, curve or surface that, when moved along a given path, generates a new shape. The path directing the motion of the generatrix motion is called a directrix or dirigent.
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👉 Generatrix in the context of Solid of revolution
In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary). The surface created by this revolution and which bounds the solid is the surface of revolution.
Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area (Pappus's second centroid theorem).
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Generatrix in the context of Surface of revolution
A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).The volume bounded by the surface created by this revolution is the solid of revolution.
Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on whether or not the line is parallel to the axis. A circle that is rotated around any diameter generates a sphere of which it is then a great circle, and if the circle is rotated around an axis that does not intersect the interior of a circle, then it generates a torus which does not intersect itself (a ring torus).
Generatrix in the context of Right circular cylinder
A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides and around one of its sides. Fixing as the side on which the revolution takes place, we obtain that the side , perpendicular to , will be the measure of the radius of the cylinder.
In addition to the right circular cylinder, within the study of spatial geometry there is also the oblique circular cylinder, characterized by not having the generatrices perpendicular to the bases.