Connection With Projective Planes
Given a planar ternary ring, one can construct a projective plane in this way ( is an extra symbol not in ):
- We define the incidence relation in this way :
One can prove that every projective plane is constructed in this way starting with a certain planar ternary ring. However, two nonisomorphic planar ternary rings can lead to the construction of isomorphic projective planes.
Read more about this topic: Planar Ternary Ring
Famous quotes containing the words connection with, connection and/or planes:
“We should always remember that the work of art is invariably the creation of a new world, so that the first thing we should do is to study that new world as closely as possible, approaching it as something brand new, having no obvious connection with the worlds we already know. When this new world has been closely studied, then and only then let us examine its links with other worlds, other branches of knowledge.”
—Vladimir Nabokov (18991977)
“Self-expression is not enough; experiment is not enough; the recording of special moments or cases is not enough. All of the arts have broken faith or lost connection with their origin and function. They have ceased to be concerned with the legitimate and permanent material of art.”
—Jane Heap (c. 18801964)
“After the planes unloaded, we fell down
Buried together, unmarried men and women;”
—Robert Lowell (19171977)