Eric Lengyel: Created page with "'''Figure 1.''' The various properties of a plane. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''plane'' $$\mathbf g$$ is a quadrivector having the general form :$$\mathbf g = g_x \mathbf e_{4235} + g_y \mathbf e_{4315} + g_z \mathbf e_{4125} + g_w \mathbf e_{3215}$$ . A plane can be viewed as an infinitely large sphere containing the point at infinity. A plane in conformal geometric algebra is the precise..."

2023-08-06T03:14:26Z

Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a plane. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''plane'' $$\mathbf g$$ is a quadrivector having the general form :$$\mathbf g = g_x \mathbf e_{4235} + g_y \mathbf e_{4315} + g_z \mathbf e_{4125} + g_w \mathbf e_{3215}$$ . A plane can be viewed as an infinitely large sphere containing the point at infinity. A plane in conformal geometric algebra is the precise..."

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[[Image:plane.svg|400px|thumb|right|'''Figure 1.''' The various properties of a plane.]]
In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''plane'' $$\mathbf g$$ is a quadrivector having the general form

:$$\mathbf g = g_x \mathbf e_{4235} + g_y \mathbf e_{4315} + g_z \mathbf e_{4125} + g_w \mathbf e_{3215}$$ .

A plane can be viewed as an infinitely large [[sphere]] containing the [[point at infinity]]. A plane in conformal geometric algebra is the precise analog of a [http://rigidgeometricalgebra.org/wiki/index.php?title=Plane plane in rigid geometric algebra], with the only difference being that the representation of a plane in the conformal model contains an additional factor of $$\mathbf e_5$$ in each term.

== See Also ==

* [[Flat point]]
* [[Line]]
* [[Round point]]
* [[Dipole]]
* [[Circle]]
* [[Sphere]]

Plane - Revision history