## On Quadrics and Pseudoquadrics Inversions in Hyperpseudospheres

**Authors:** Robert B. Easter

This note on quadrics and pseudoquadrics inversions in hyperpseudospheres shows that the inversions produce different results in a three-dimensional spacetime. Using Geometric Algebra, all quadric and pseudoquadric entities and operations are in the G(4,8) Double Conformal Space-Time Algebra (DCSTA). Quadrics at zero velocity are purely spatial entities in x y z-space that are hypercylinders in w x y z-spacetime. Pseudoquadrics represent quadrics in a three-dimensional (3D) x y w, y z w, or z x w spacetime with the pseudospatial w-axis that is associated with time w=c t. The inversion of a quadric in a hyperpseudosphere can produce a Darboux pseudocyclide in a 3D spacetime that is a quartic hyperbolic (infinite) surface, which does not include the point at infinity. The inversion of a pseudoquadric in a hyperpseudosphere can produce a Darboux pseudocyclide in a 3D spacetime that is a quartic finite surface. A quadric and pseudoquadric can represent the same quadric surface in space, and their two different inversions in a hyperpseudosphere represent the two types of reflections of the quadric surface in a hyperboloid.

**Comments:** 4 Pages.

**Download:** **PDF**

### Submission history

[v1] 2016-08-09 15:55:41

**Unique-IP document downloads:** 31 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*