Eric Lengyel: Created page with "'''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..."

2023-08-06T03:13:58Z

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]]

Flat point - Revision history