Two-Dimensional Geometries

A Problem-Solving Approach

Inbunden, Engelska, 2019

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This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving them room to discover and partially construct the story themselves. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space.

Produktinformation

Utgivningsdatum2019-03-30
Mått178 x 254 x undefined mm
Vikt450 g
FormatInbunden
SpråkEngelska
SeriePure and Applied Undergraduate Texts
Antal sidor142
FörlagAmerican Mathematical Society
ISBN9781470447601

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

IntroductionNeutral geometry: Euclid's postulates for plane geometryEuclidean (plane) geometry: Rectangles and cartesian coordinatesConcurrence and circles in Euclidean geometrySpherical geometry: Surface area and volume of the $R$-sphere in Euclidean 3-spaceUsual dot-product for three-dimensional Euclidean space: Euclidean three-space as a metric spaceTransformations$K$-geometry: Changing coordinatesUniform coordinates for the two-dimensional geometriesReturn to spherical geometry: Spherical geometry from an advanced viewpointHyperbolic geometry: The curvature $K$ becomes negativeDefinitionsBibliographyIndex