-
Projective planes in
which the "theorem" is
valid are
called pappian planes. If one
considers a
pappian plane containing a
hexagon as just
described but with...
- collinear. A
plane in
which Pappus's
theorem is
universally true is
called Pappian.
Hessenberg (1905)
showed that Desargues's
theorem can be
deduced from...
-
examples are the
nondegenerate conics. However, a
conic is only
defined in a
pappian plane,
whereas an oval may
exist in any type of
projective plane. In the...
- real 4-manifold. It and
projective planes over
other fields (known as
pappian planes)
serve as
fundamental examples in
algebraic geometry. The quaternionic...
-
mathematician Beniamino Segre, is the statement: Any oval in a
finite pappian projective plane of odd
order is a
nondegenerate projective conic section...
- be non-degenerate; this is true over both the
Euclidean plane and any
pappian projective plane. Indeed,
given any five
points there is a
conic p****ing...
- mappings. As a
projective mapping in a
projective plane over a
field (
pappian plane) is
uniquely determined by
prescribing the
images of
three lines...
-
spaces of
dimension d ≥ 3 (i.e., the
point set is finite, the
space is
pappian), the
following result is true: If O {\displaystyle {\mathcal {O}}} is...
- planes. If
transitive is
replaced by
sharply transitive, the
plane is
pappian. Hughes,
Daniel R.; Piper, Fred C. (1973),
Projective Planes, Springer-Verlag...
-
Panglossian – Pangloss, Voltaire's
fictional character pappian –
Pappus of
Alexandria (as in
pappian plane)
Paracelsian –
Paracelsus parkinsonian – James...
