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:
“Any translation which intends to perform a transmitting function cannot transmit anything but information—hence, something inessential. This is the hallmark of bad translations.”
—Walter Benjamin (1892–1940)
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)