https://conformalgeometricalgebra.org/wiki/index.php?title=Flat_point&feed=atom&action=historyFlat point - Revision history2024-03-29T14:54:20ZRevision history for this page on the wikiMediaWiki 1.40.0https://conformalgeometricalgebra.org/wiki/index.php?title=Flat_point&diff=52&oldid=prevEric 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<p>Created page with "<a href="/wiki/index.php?title=File:Point.svg" title="File:Point.svg">400px|thumb|right|'''Figure 1.''' The various properties of a flat point.</a> 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 <a href="/wiki/index.php?title=Dipole" title="Dipole">dipole</a> that has one end at the <a href="/wiki/index.php?title=Point_at_infinity&action=edit&redlink=1" class="new" title="Point at infinity (page does not exist)">point at infinity</a>. A flat point in conformal geometric algebra is the precise..."</p>
<p><b>New page</b></p><div>[[Image:point.svg|400px|thumb|right|'''Figure 1.''' The various properties of a flat point.]]<br />
In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''flat point'' $$\mathbf p$$ is a bivector having the general form<br />
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:$$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p_z \mathbf e_{35} + p_w \mathbf e_{45}$$ .<br />
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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.<br />
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== See Also ==<br />
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* [[Line]]<br />
* [[Plane]]<br />
* [[Round point]]<br />
* [[Dipole]]<br />
* [[Circle]]<br />
* [[Sphere]]</div>Eric Lengyel