Geometry, Axiomatic System, Parallel Postulate, János Bolyai, Euclidean Geometry
Bellum Publishing
(2011-07-14
)
eligible for voucher
ISBN-13:
978-613-5-77145-9
ISBN-10:
6135771450
EAN:
9786135771459
Book language:
English
Blurb/Shorttext:
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Absolute geometry is a geometry based on an axiom system 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. The theorems of absolute geometry hold in some non-Euclidean geometries, such as hyperbolic geometry, as well as in Euclidean geometry. Absolute geometry is an extension of ordered geometry, and thus, all theorems in ordered geometry hold in absolute geometry. The converse is not true. Absolute geometry assumes the first four of Euclid's Axioms, to be contrasted with affine geometry, which assumes Euclid's first, second, and fifth (parallel postulate) axioms. Ordered geometry is a common foundation of both absolute and affine geometry.