Explore: Translation Planes

The familiar Euclidean plane is an affine plane. There are many finite and infinite affine planes. As well as affine planes over fields (and division

Hughes planes and the Figueroa planes, translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast majority of known

smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane E {\displaystyle

projective planes. A systematic study of these planes began in 1954 with a paper by Skornyakov. Earlier, the topological properties of the real plane had been

significant in the theory of translation planes, in that they generate Moufang planes in general, and Desarguesian planes in the finite case when the order

projective planes. The projective planes that can not be constructed in this manner are called non-Desarguesian planes, and the Moulton plane given above

André planes are a class of finite translation planes found by André. The Desarguesian plane and the Hall planes are examples of André planes; the two-dimensional

some infinite Moufang planes are non-Desarguesian planes. In particular, the Cayley plane, an infinite Moufang projective plane over the octonions, is

series of planes of existence.[citation needed] According to Theosophists, after the material plane is the etheric plane and both of these planes are connected

affine plane of order n2 and it, or its projective completion, is called a derived plane. Hall planes are translation planes. All finite Hall planes of the