Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally, this has meant using only the first four of Euclid's postulates.[1] The term was introduced by János Bolyai in 1832.[2] It is sometimes referred to as neutral geometry,[3] as it is neutral with respect to the parallel postulate. The first four of Euclid's postulates are now considered insufficient as a basis of Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead.[4]
^Faber 1983, pg. 131
^In "Appendix exhibiting the absolute science of space: independent of the truth or falsity of Euclid's Axiom XI (by no means previously decided)" (Faber 1983, pg. 161)
^Greenberg cites W. Prenowitz and M. Jordan (Greenberg, p. xvi) for having used the term neutral geometry to refer to that part of Euclidean geometry that does not depend on Euclid's parallel postulate. He says that the word absolute in absolute geometry misleadingly implies that all other geometries depend on it.
Absolutegeometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...
theorems of absolutegeometry hold in hyperbolic geometry as well as in Euclidean geometry. Absolutegeometry is inconsistent with elliptic geometry: in elliptic...
Euclidean geometry the resulting geometry is absolutegeometry. There are two kinds of absolutegeometry, Euclidean and hyperbolic. All theorems of absolute geometry...
the USA Absolute Software Corporation, specializes in security and data risk management Absolut Vodka, a brand of Swedish vodka Absolute (geometry), the...
Versions of a tropical geometry, of an absolutegeometry over a field with one element and an algebraic analogue of Arakelov geometry were realized in this...
Euclidean geometry is a model. Absolutegeometry Analytic geometry Birkhoff's axioms Cartesian coordinate system Hilbert's axioms Incidence geometry List of...
equivalent of the first four postulates) is known as absolutegeometry (or sometimes "neutral geometry"). Probably the best-known equivalent of Euclid's...
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined...
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic...
water will vibrate faster than at absolute zero. As stated above, rotation hardly influences the molecular geometry. But, as a quantum mechanical motion...
fundamental result in absolutegeometry because its proof does not depend upon the parallel postulate. In several high school treatments of geometry, the term "exterior...
approach of mono-anabelian geometry is bi-anabelian geometry, a term coined by Mochizuki in "Topics in Absolute Anabelian Geometry III" to indicate the classical...
theorems of the second. A good example is the relative consistency of absolutegeometry with respect to the theory of the real number system. Lines and points...
called the absolute pole of that line. The perpendiculars on the other side also intersect at a point. However, unlike in spherical geometry, the poles...
measurement. Ordered geometry is a fundamental geometry forming a common framework for affine, Euclidean, absolute, and hyperbolic geometry (but not for projective...
algebraic geometry. Versions of a tropical geometry, of an absolutegeometry over a field of one element and an algebraic analogue of Arakelov's geometry were...
then its absolute value is necessarily positive ( | x | = − x > 0 {\displaystyle |x|=-x>0} ). From an analytic geometry point of view, the absolute value...
References Absolute differential calculus An older name of Ricci calculus Absolutegeometry Also called neutral geometry, a synthetic geometry similar to...
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds....
human or social attributes of place identity and sense of place than on geometry. A populated place is called a settlement. A locality, settlement, or populated...
Global Information