Geometry: Deductive Structure
... The effort to turn the Parallel Postulate into a theorem led to other kinds of geometry, the non-Euclidean geometries, discussed briefly in ACISD geometry classes. Attention should be given to the issue of the uncountable collection of Euclidean geometry postulates. In an effort to gain some strange ...
... The effort to turn the Parallel Postulate into a theorem led to other kinds of geometry, the non-Euclidean geometries, discussed briefly in ACISD geometry classes. Attention should be given to the issue of the uncountable collection of Euclidean geometry postulates. In an effort to gain some strange ...
Modern Geometries: Non-Euclidean, Projective, and Discrete
... 5. If a straight line meet two other straight lines so that as to make the interior angles on one side less than two right angles, the other straight lines meet on that side of the first line. ...
... 5. If a straight line meet two other straight lines so that as to make the interior angles on one side less than two right angles, the other straight lines meet on that side of the first line. ...
Euclidean and Non-Euclidean Geometries: Development and History
... have been so profound,” wrote the great Canadian geometer H.S.M. Coxeter, “that we can hardly imagine how shocking the possibility of a geometry different from Euclid’s must have seemed in 1820.” (Greenberg, xxv) ...
... have been so profound,” wrote the great Canadian geometer H.S.M. Coxeter, “that we can hardly imagine how shocking the possibility of a geometry different from Euclid’s must have seemed in 1820.” (Greenberg, xxv) ...
History of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- ""earth"", -metron ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)