Cayley plane information

In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions. The Cayley plane was discovered in 1933...

mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by Cayley (1846), the Cayley transform...

Sir George Cayley, 6th Baronet (27 December 1773 – 15 December 1857) was an English engineer, inventor, and aviator. He is one of the most important people...

controlled heavier-than-air powered flight". They built on the works of George Cayley dating from 1799, when he set forth the concept of the modern airplane (and...

engineering Cayley graph Cayley numbers Cayley plane Cayley table Cayley transform Cayleyan Cayley–Bacharach theorem Cayley–Dickson construction Cayley–Hamilton...

protocol based on the OBEX protocol Octonionic projective plane, or Cayley plane, a projective plane over the octonions Oriented Polypropylene, and specifically...

called non-Desarguesian projective planes and are an active area of research. The Cayley plane (OP2), a projective plane over the octonions, is one of these...

In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract...

Arthur Cayley's article. The octonions were discovered independently by Cayley and are sometimes referred to as "Cayley numbers" or the "Cayley algebra"...

complex plane. These distinct faces of the complex plane as a quadratic space arise in the construction of algebras over a field with the Cayley–Dickson...

complex projective space, the quaternionic projective space, or else the Cayley plane F4/Spin(9); see (Brendle & Schoen 2008). The odd-dimensional projective...

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

octonionic projective plane – FII, dimension 16 = 2 × 8, F4 symmetry, Cayley projective plane P2(O), the bioctonionic projective plane – EIII, dimension 32...

spaces, classification to which must be added one exceptional space, the Cayley plane. Let ⟨ u , v ⟩ := − u 1 v 1 ¯ + u 2 v 2 ¯ + ⋯ + u n + 1 v n + 1 ¯ {\displaystyle...

showed that if the Cayley absolute is a real curve then the part of the projective plane in its interior is isometric to the hyperbolic plane..." For more history...

upper half-plane is the Möbius transformation g ( z ) = i 1 + z 1 − z {\displaystyle g(z)=i{\frac {1+z}{1-z}}}   which is the inverse of the Cayley transform...

to be necessarily locally symmetric, i.e., locally isometric to the Cayley plane F4/Spin(9) or locally flat. See below.) It is now known that all of these...

model and the Klein disk model. The real line forms the Cayley absolute of the Poincaré half-plane model. Pasch's axiom and the exterior angle theorem still...

1933, Moufang showed Desargues's theorem does not hold in the Cayley plane. The Cayley plane uses octonion coordinates which do not satisfy the associative...

founders of modern aeronautics, Leonardo da Vinci in the Renaissance and Cayley in 1799, both began their investigations with studies of bird flight. Man-carrying...

bold S {\displaystyle \mathbb {S} } . They are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic...

named after American mathematician Hassler Whitney, and sometimes called a Cayley umbrella, is a specific self-intersecting ruled surface placed in three...