Proper Velocity Addition Formula
The proper velocity addition formula:
where is the beta factor given by .
This formula provides a proper-velocity gyrovector space model of hyperbolic geometry that uses a whole space compared to other models of hyperbolic geometry which use discs or half-planes.
In the unidirectional case this becomes commutative and simplifies to a Lorentz-factor product times a coordinate-velocity sum, e.g. to wAC = γABγBC(vAB+vBC), as discussed in the application section below.
Read more about this topic: Proper Velocity
Famous quotes containing the words proper, addition and/or formula:
“You can marry Lorraine, my fortune will be restored to her, and you can live contentedly together ever after. Now that’s a proper ending to a story, isn’t it?”
—Garrett Fort (1900–1945)
“Napoleon wanted to turn Paris into Rome under the Caesars, only with louder music and more marble. And it was done. His architects gave him the Arc de Triomphe and the Madeleine. His nephew Napoleon III wanted to turn Paris into Rome with Versailles piled on top, and it was done. His architects gave him the Paris Opera, an addition to the Louvre, and miles of new boulevards.”
—Tom Wolfe (b. 1931)
“In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the child’s age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.”
—Alicia F. Lieberman (20th century)