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).
Other articles related to "translation plane, translation planes, planes":
... Translation planes are related to spreads in finite projective spaces by the André/Bruck-Bose construction ... of, the André/Bruck-Bose construction1 produces a translation plane of order q2 as follows Embed as a hyperplane of ... "points," the points of not on and "lines" the planes of meeting in a line of ...
Famous quotes containing the words plane and/or translation:
“As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the plane at the base of a mountain, instead of climbing steadily to its top.”
—Henry David Thoreau (18171862)
“To translate, one must have a style of his own, for otherwise the translation will have no rhythm or nuance, which come from the process of artistically thinking through and molding the sentences; they cannot be reconstituted by piecemeal imitation. The problem of translation is to retreat to a simpler tenor of ones own style and creatively adjust this to ones author.”
—Paul Goodman (19111972)