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 Π_{l} (the affine derivative of Π).

Read more about Translation Plane: Relationship To Spreads

### Other articles related to "translation plane, translation planes, planes":

**Translation Plane**- Relationship To Spreads

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**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 (1817–1862)

“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 one’s own style and creatively adjust this to one’s author.”

—Paul Goodman (1911–1972)