Two-Dimensional Geometries

A Problem-Solving Approach

AvC. Herbert Clemens

Inbunden, Engelska, 2019

Del i serien Pure and Applied Undergraduate Texts

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Beskrivning

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

Utgivningsdatum:2019-03-30
Mått:178 x 254 x undefined mm
Vikt:450 g
Format:Inbunden
Språk:Engelska
Serie:Pure and Applied Undergraduate Texts
Antal sidor:142
Förlag:American Mathematical Society
ISBN:9781470447601

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

C. Herbert Clemens, Ohio State University, Columbus, OH.

Innehållsförteckning

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