Analytic Hyperbolic Geometry: Mathematical Foundations and Applications

Notation and Special Symbols

?

Gyroaddition, Gyrogroup operation.

?

Gyrosubtraction, Inverse gyrogroup operation.

?

Cogyroaddition, Gyrogroup cooperation.

?

Cogyrosubtraction, Inverse gyrogroup cooperation .

? E

Einstein addition (of relativistically admissible coordinate velocities, and generalizations).

? E

Einstein subtraction.

? E

Einstein coaddition.

? E

Einstein cosubtraction.

? M

M bius addition.

? M

M bius subtraction.

? M

M bius coaddition.

? M

M bius cosubtraction.

? U

PV addition (of relativistically admissible proper velocities, and generalizations).

? U

PV subtraction.

? U

PV coaddition.

? U

PV cosubtraction.

?

Scalar multiplication (scalar gyromultiplication) in a gyrovector space.

? E

Einstein scalar multiplication.

? M

M bius scalar multiplication.

? U

PV scalar multiplication.

Gyropolygonal gyroaddition, Definition 2.13.

ab

A segment with distinct endpoints a and b of (i) a gyroline (gyrosegment), or (ii) a cogyroline (cogyrosegment). A gyroline (cogyroline) containing the distinct points a and b.

ab

Length of (i) a gyrosegment (gyrolength), or (ii) a cogyrosegment (cogyrolength).

abc

A gyrotriangle with vertices a, b and c.

a

a = ? a ? is the gyrolength of gyrovector a.

a s

a s = a/s in a gyrovector space ( , ?, ?).

Aut

An automorphism group.

Aut 0

A subgroup of an automorphism group.

CM

Center of momentum.

c

The vacuum speed of light,

gyr

Gyrator. gyr[ a, b] the gyration (gyroautomorphism) generated by a and b.

s

Gyrovector space analogue of the vacuum speed of light

UNLIMITED FREE
ACCESS
TO THE WORLD'S BEST IDEAS

SUBMIT
Already a GlobalSpec user? Log in.

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.

Customize Your GlobalSpec Experience

Category: Energy Management Software
Finish!
Privacy Policy

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.