In the projective plane, the two opposite directions of a line meet each other at a point on the line at infinity.
12.
This is the equation of a line according to the definition and the complement is called the " line at infinity ".
13.
By extending the geometry to a projective plane ( adding a line at infinity ) this apparent difference vanishes, and the commonality becomes evident.
14.
The lines will meet at a line at infinity ( a line that goes through zero on the plane at " z " = 0 ).
15.
The isogonal conjugate of the circumcircle is the line at infinity, given in trilinear coordinates by 0 } } and in barycentric coordinates by 0 } }.
16.
To illustrate the difference ( over the real numbers ), a parabola in the affine plane intersects the line at infinity, whereas an ellipse does not.
17.
Any pair of parallel planes in affine 3-space will intersect each other in a projective line ( a line at infinity ) in the plane at infinity.
18.
If the distance to the focus is fixed and the directrix is a line at infinity, so the eccentricity is zero, then the conic is a circle.
19.
Yaglom continues with his Galilean study to the " inversive Galilean plane " by including a special line at infinity and showing the topology with a stereographic projection.
20.
Though the line at infinity of the extended real plane may appear to have a different nature than the other lines of that projective plane, this is not the case.
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