Axioms of Projective Geometry
Any given geometry may be deduced from an appropriate set of axioms. Projective geometries are characterised by the "elliptic parallel" axiom, that any two planes always meet in just one line, or in the plane, any two lines always meet in just one point. In other words, there are no such things as parallel lines or planes in projective geometry. Many alternative sets of axioms for projective geometry have been proposed (see for example Coxeter 2003, Hilbert & Cohn-Vossen 1999, Greenberg 1980).
Read more about this topic: Projective Geometry
Famous quotes containing the words axioms of, axioms and/or geometry:
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)
“The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematising the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray’s Anatomy.”
—J.G. (James Graham)