Non-Euclidean geometry Geometry and topology index History Topics Index In about 300 BC Euclid wrote The Elements, a book which was to become one of the most famous books ever written. Euclid stated five postulates on which he based all his theorems: To draw a straight line from any point to any other. To produce a finite straight line continuously in a straight line. To describe a circle with ...

NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the Poincare Disk and the Upper Half-Plane Models of Hyperbolic Geometry for use in High School and Undergraduate Education. Hyperbolic Geometry is a geometry of Einstein's General Theory of Relativity and Curved Hyperspace.

Non-Euclidean Geometry - Mathematics and the Liberal Arts See the page The Parallel Postulate. To expand search, see Geometry. Laterally related topics: Symmetry, Analytic Geometry, Trigonometry, Pattern, Geometric Theorems, The Pyramid, Similarity, The Triangle, The Method of Exhaustion, Projective Geometry, Algebraic Geometry, The Parallel Postulate, The Regular Solids, Irrationals, The ...

The Ontology and Cosmology of Non-Euclidean Geometry Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. David Hume, An Enquiry Concerning Human Understanding, Section IV, Part I, p. 20 1. Introduction Until recently, Albert Einstein's complaints in his later years about the intelligibility of Quantum ...

A formula for resolving the arc distance and bearings, plus a link to a spreadsheet to resolve same.

Linguistics Mathematics Philosophy Physics Psychology Sociology E-Library of Science Geometries An axiom is said smarandachely denied if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). A Smarandache Geometry is a geometry which has at least one smarandachely denied axiom (1969). Thus, as a particular case, ...

Seminar on the History of Hyperbolic Geometry Greg Schreiber In this course we traced the development of hyperbolic (non-Euclidean) geometry from ancient Greece up to the turn of the century. This was accomplished by focusing chronologically on those mathematicians who made the most significant contributions to the subject. We began with an exposition of Euclidean geometry, first from Euclid's ...