Flat point

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 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