 Comparison of Euclidean, spherical, and hyperbolic geometries

▪ TableComparison of Euclidean, spherical, and hyperbolic geometriesGiven a line and a point not on the line, there exist(s) ____________ through the given pointand parallel to the given line.a) exactly one line (Euclidean)b) no lines (spherical)c) infinitely many lines (hyperbolic)Euclid s fifth postulate is ____________.a) true (Euclidean)b) false (spherical)c) false (hyperbolic)The sum of the interior angles of a triangle ______ 180 degrees.a) = (Euclidean)b) > (spherical)c) < (hyperbolic)See as table:
* * *
Universalium. 2010.
Look at other dictionaries:
nonEuclidean geometry — geometry based upon one or more postulates that differ from those of Euclid, esp. from the postulate that only one line may be drawn through a given point parallel to a given line. [1870 75; NON + EUCLIDEAN] * * * Any theory of the nature of… … Universalium
Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… … History of philosophy
Shape of the Universe — Edge of the Universe redirects here. For the Bee Gees song, see Edge of the Universe (song). The local geometry of the universe is determined by whether Omega is less than, equal to or greater than 1. From top to bottom: a spherical universe, a… … Wikipedia
mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium
Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… … Wikipedia
Geometrization conjecture — Thurston s geometrization conjecture states that compact 3 manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3 manifolds of the uniformization theorem for… … Wikipedia
History of geometry — Geometry (Greek γεωμετρία ; geo = earth, metria = measure) 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. Classic geometry… … Wikipedia
Ibn alHaytham — Infobox Muslim scholars  notability = Muslim scientist era = Islamic Golden Age color = #cef2e0   image caption = Ibn al Haytham drawing taken from a 1982 Iraqi 10 dinar note.   name = UnicodeAbū ‘Alī al Ḥasan ibn al Ḥasan ibn al Haytham… … Wikipedia
Alhazen — For the Moon crater, see Alhazen (crater). For the asteroid, see 59239 Alhazen. Alhazen Alhazen (Ibn al Haytham) … Wikipedia
List of interactive geometry software — Interactive geometry software (IGS, or dynamic geometry environments, DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting… … Wikipedia