In mathematics, a translation plane is a particular kind of projective plane, as considered as a combinatorial object.
In a projective plane, represents a point, and represents a line. A central collineation with center and axis is a collineation fixing every point on and every line through . It is called an "elation" if is on, otherwise it is called a "homology". The central collineations with centre and axis form a group.
A projective plane is called a translation plane if there exists a line such that the group of elations with axis is transitive on the affine plane Πl (the affine derivative of Π).
Read more about Translation Plane: Relationship To Spreads
Famous quotes containing the words translation and/or plane:
“Whilst Marx turned the Hegelian dialectic outwards, making it an instrument with which he could interpret the facts of history and so arrive at an objective science which insists on the translation of theory into action, Kierkegaard, on the other hand, turned the same instruments inwards, for the examination of his own soul or psychology, arriving at a subjective philosophy which involved him in the deepest pessimism and despair of action.”
—Sir Herbert Read (1893–1968)
“with the plane nowhere and her body taking by the throat
The undying cry of the void falling living beginning to be something
That no one has ever been and lived through screaming without enough air”
—James Dickey (b. 1923)