File:Plane meet plane.svg and Flat point: Difference between pages
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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...") |
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[[Image:point.svg|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 analog of a [http://rigidgeometricalgebra.org/wiki/index.php?title=Point 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. | |||
== See Also == | |||
* [[Line]] | |||
* [[Plane]] | |||
* [[Round point]] | |||
* [[Dipole]] | |||
* [[Circle]] | |||
* [[Sphere]] | |||
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.
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