Before we introduce projective geometry let us briefly consider
spherical geometry (
), which is the geometry on the surface of a sphere.
- 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,
is the line with pole
.
- 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:
- Two points define a line:
- Two lines define a point:
Subhashis Banerjee
2008-01-20