Absolute Geometry

Absolute geometry is a geometry based on an axiom system for Euclidean geometry that does not assume the parallel postulate or any of its alternatives. The term was introduced by János Bolyai in 1832. It is sometimes referred to as neutral geometry, as it is neutral with respect to the parallel postulate.

Other articles related to "geometry, absolute geometry":

Axiomatic Basis of Non-Euclidean Geometry
... Euclidean geometry can be axiomatically described in several ways ... Other systems, using different sets of undefined terms obtain the same geometry by different paths ... postulate, in whatever form it takes, and leaving all the other axioms intact, produces absolute geometry ...
Absolute Geometry - Incompleteness
... Absolute geometry is an incomplete axiomatic system, in the sense that one can add extra independent axioms without making the axiom system inconsistent ... One can extend absolute geometry by adding different axioms about parallel lines and get incompatible but consistent axiom systems, giving rise to Euclidean or hyperbolic geometry ... Thus every theorem of absolute geometry is a theorem of hyperbolic geometry and Euclidean geometry ...

Famous quotes containing the words geometry and/or absolute:

... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.
Louise Bourgeois (b. 1911)

War is bestowed like electroshock on the depressive nation; thousands of volts jolting the system, an artificial galvanizing, one effect of which is loss of memory. War comes at the end of the twentieth century as absolute failure of imagination, scientific and political. That a war can be represented as helping a people to “feel good” about themselves, their country, is a measure of that failure.