Eric Lengyel: Created page with "'''Figure 1.''' The various properties of a line. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''line'' $$\boldsymbol l$$ is a trivector having the general form :$$\boldsymbol l = v_x \mathbf e_{415} + v_y \mathbf e_{425} + v_z \mathbf e_{435} + m_x \mathbf e_{235} + m_y \mathbf e_{315} + m_z \mathbf e_{125}$$ . A line can be viewed as an infinitely large circle that contains the point at infinity. A line in..."

2023-08-06T03:14:15Z

Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a line. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''line'' $$\boldsymbol l$$ is a trivector having the general form :$$\boldsymbol l = v_x \mathbf e_{415} + v_y \mathbf e_{425} + v_z \mathbf e_{435} + m_x \mathbf e_{235} + m_y \mathbf e_{315} + m_z \mathbf e_{125}$$ . A line can be viewed as an infinitely large circle that contains the point at infinity. A line in..."

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

:$$\boldsymbol l = v_x \mathbf e_{415} + v_y \mathbf e_{425} + v_z \mathbf e_{435} + m_x \mathbf e_{235} + m_y \mathbf e_{315} + m_z \mathbf e_{125}$$ .

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

== See Also ==

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

Line - Revision history