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Geometry by Its History [electronic resource] / by Alexander Ostermann, Gerhard Wanner.

By: Ostermann, Alexander [author.].
Contributor(s): Wanner, Gerhard [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Undergraduate Texts in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: XII, 437p. 452 illus., 61 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642291630.Subject(s): Mathematics | Geometry, algebraic | Geometry | Mathematics | Geometry | Algebraic Geometry | History of Mathematical SciencesDDC classification: 516 Online resources: Click here to access online
Contents:
Preface -- Part I: Classical Geometry -- Thales and Pythagoras -- The Elements of Euclid -- Conic Sections -- Further Results on Euclidean Geometry -- Trigonometry -- Part II: Analytic Geometry -- Descartes' Geometry -- Cartesian Coordinates -- To be Constructible, or not to be -- Spatial Geometry and Vector Algebra -- Matrices and Linear Mappings -- Projective Geometry -- Solutions to Exercises --  References -- Figure Source and Copyright -- Index.
In: Springer eBooksSummary: In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in  geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19th century. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
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Preface -- Part I: Classical Geometry -- Thales and Pythagoras -- The Elements of Euclid -- Conic Sections -- Further Results on Euclidean Geometry -- Trigonometry -- Part II: Analytic Geometry -- Descartes' Geometry -- Cartesian Coordinates -- To be Constructible, or not to be -- Spatial Geometry and Vector Algebra -- Matrices and Linear Mappings -- Projective Geometry -- Solutions to Exercises --  References -- Figure Source and Copyright -- Index.

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in  geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19th century. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

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