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:
“...it is better to marry than to be aflame with passion.”
—Bible: New Testament, 1 Corinthians 7:9.
King James translation reads, “It is better to marry than to burn.”
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)