**The space :****lines in :**If one begins at a point in and travels straight ahead on the surface, one will trace out a*great circle*. Viewed as a set in this is the intersection of with a plane through the origin. We will call this great circle a line in :

Let be a unit vector. Then,- Two points
and
are
*antipodal*if . - Lines in cannot be parallel. Any two lines intersect at a pair of antipodal points.
- A point on a line:
or or
- Two points define a line:
- Two lines define a point:

Subhashis Banerjee 2008-01-20