# Projective Planes

### Some articles on projective planes, projective plane, planes, projective:

Bruck–Ryser–Chowla Theorem - Projective Planes
... of a symmetric design with λ = 1, that is, a projective plane, the theorem (which in this case is referred to as the Bruck–Ryser theorem) can be stated as follows If a finite projective plane of order q exists ... Note that for a projective plane, the design parameters are v = b = q2 + q + 1, r = k = q + 1, λ = 1 ... The theorem, for example, rules out the existence of projective planes of orders 6 and 14 but allows the existence of planes of orders 10 and 12 ...
Symmetric Design - Symmetric BIBDs - Projective Planes
... Finite projective planes are symmetric 2-designs with λ = 1 and order n > 1 ... Since k = r we can write the order of a projective plane as n = k − 1 and, from the displayed equation above, we obtain v = (n + 1)n + 1 = n2 + n + 1 points in a ... As a projective plane is a symmetric design, we have b = v, meaning that b = n2 + n + 1 also ...
Projective Planes in Higher Dimensional Projective Spaces
... Projective planes may be thought of as projective geometries of "geometric" dimension two ... Higher dimensional projective geometries can be defined in terms of incidence relations in a manner analogous to the definition of a projective plane ... These turn out to be "tamer" than the projective planes since the extra degrees of freedom permit Desargues' theorem to be proved geometrically in the higher dimensional geometry ...
Freudenthal Magic Square - History - Rosenfeld Projective Planes
... Following the discovery of the Cayley projective plane or "octonionic projective plane" OP2 in 1933, whose symmetry group is the exceptional Lie group F4, and with the knowledge that G2 is the ... in sequel) see classification for details, and the relevant spaces are the octonionic projective plane – FII, dimension 16 = 2×8, F4 symmetry, Cayley projective plane the bioctonionic projective plane – EIII ... the octonions are a division algebra, and thus a projective plane is defined over them, the bioctonions, quateroctonions and octooctonions are not division algebras ...

### Famous quotes containing the word planes:

After the planes unloaded, we fell down
Buried together, unmarried men and women;
Robert Lowell (1917–1977)