In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form q = a + b i + c...

In mathematics, a versor is a quaternion of norm one, also known as a unit quaternion. Each versor has the form u = exp ⁡ ( a r ) = cos ⁡ a + r sin ⁡...

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

theory and hyperbolic geometry, Arithmetic Kleinian groups are a special class of Kleinian groups constructed using orders in quaternion algebras. They...

generates a complex plane with the real line. For split-quaternions there are hyperboloids of hyperbolic and imaginary units that generate split-complex or...

"Circular and hyperbolic quaternions, octonions, and sedenions", Appl. Math. Comput. 28:47–72. K. Carmody, (1997) "Circular and hyperbolic quaternions, octonions...

In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...

Thomas Little Heath Hilbert's problems History of topos theory Hyperbolic quaternion Indian mathematics Islamic mathematics Italian school of algebraic...

was charting this submanifold through his Algebra of Physics and hyperbolic quaternions, though Macfarlane did not use cosmological language as Minkowski...

in the Poincaré ball model, another standard model of hyperbolic geometry. Hyperbolic quaternion Hyperspace Introduction to the mathematics of general...

In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a...

Precursors Galilean relativity Galilean transformation Aether theories Hyperbolic quaternions People Einstein Sommerfeld Michelson Morley FitzGerald Herglotz...

Similar to Homersham Cox (1882/83), Macfarlane uses the hyperbolic versor as the hyperbolic quaternion corresponding to the versor of Hamilton. The presentation...

To uphold causality, Minkowski restricted spacetime to non-Euclidean hyperbolic geometry.[page needed] Because signals and other causal influences cannot...

Precursors Galilean relativity Galilean transformation Aether theories Hyperbolic quaternions People Einstein Sommerfeld Michelson Morley FitzGerald Herglotz...

as in the quaternion group forms a nonassociative loop of order 8. See hyperbolic quaternions for its application. (The hyperbolic quaternions themselves...

The exp, sqrt, and log complex quaternion functions are treated and then applied to obtain the general Lorentz transformation and obtain a simple technique...

Precursors Galilean relativity Galilean transformation Aether theories Hyperbolic quaternions People Einstein Sommerfeld Michelson Morley FitzGerald Herglotz...

the hyperboloid model of hyperbolic space already known in the 19th century, because isometries (or motions) in hyperbolic space can be related to Lorentz...

variants thereof, and the elements of {1, i, j, k} multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions...

cubic extension of Q. The (2,3,7) hyperbolic triangle group is a subgroup of the group of norm 1 elements in the quaternion algebra generated as an associative...

of the nineteenth century, including Quaternions Tessarines Coquaternions Biquaternions Hyperbolic quaternions This disambiguation page lists articles...

dictionary. In mathematics, a versor is a quaternion of norm one (a unit quaternion). Versor may also refer to: Hyperbolic versor, a generalization of quaternionic...

be expressed as a logarithmic function or, equivalently, as an inverse hyperbolic function: τ ( t ) = c g ln ⁡ ( g t c + 1 + ( g t c ) 2 ) = c g arsinh...

term itself.: v  At the time structures such as Lie algebras and hyperbolic quaternions drew attention to the need to expand algebraic structures beyond...

Precursors Galilean relativity Galilean transformation Aether theories Hyperbolic quaternions People Einstein Sommerfeld Michelson Morley FitzGerald Herglotz...

the term itself. At the time, structures such as Lie algebras and hyperbolic quaternions drew attention to the need to expand algebraic structures beyond...

stores hyperbolic manifolds. The construction of arithmetic Kleinian groups from quaternion algebras gives rise to particularly interesting hyperbolic manifolds...

Note however, that non-associative systems like octonions and hyperbolic quaternions represent another type of hypercomplex number. As Thomas Hawkins...

negativity, he has been credited by C. J. Joly with developing hyperbolic quaternions, though in fact that mathematical structure was largely the work...