Definition:Generatrix
Definition
A generatrix is an element of a set of straight lines which constitute a given surface.
Generatrix of Right Circular Cone
Let $K$ be a right circular cone.
Let $A$ be the apex of $K$.
Let $B$ be the base of $K$.
Then a line joining the apex of $K$ to its directrix is a generatrix of $K$.
Generatrix of Cylinder
Each of the parallel straight lines forming a cylindrical surface $S$ which pass through the directrix of $S$ is called a generatrix of $S$.
Also known as
A generatrix of a surface can also be referred to as a generator or generator element.
Some sources just use the term element, but this word has uses in a number of different contexts.
Linguistic Note
The word generatrix is the feminine form of the word generator.
As such, the form is archaic, and is rarely (if ever) found outside the context of mathematics.
Its plural is generatrices.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generator: 1. (element)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generatrix
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generator: 1. (element)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generatrix