Flat point: Difference between revisions
Jump to navigation
Jump to search
Eric Lengyel (talk | contribs) (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a flat point. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''flat point'' $$\mathbf p$$ is a bivector having the general form :$$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p_z \mathbf e_{35} + p_w \mathbf e_{45}$$ . A flat point can be viewed as a dipole that has one end at the point at infinity. A flat point in conformal geometric algebra is the precise...") |
(No difference)
|
Latest revision as of 03:13, 6 August 2023
In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a flat point $$\mathbf p$$ is a bivector having the general form
- $$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p_z \mathbf e_{35} + p_w \mathbf e_{45}$$ .
A flat point can be viewed as a dipole that has one end at the point at infinity. A flat point in conformal geometric algebra is the precise analog of a point in rigid geometric algebra, with the only difference being that the representation of a flat point in the conformal model contains an additional factor of $$\mathbf e_5$$ in each term.