Buch, Englisch, 558 Seiten, Format (B × H): 241 mm x 164 mm, Gewicht: 1074 g
Reihe: Textbooks in Mathematics
Buch, Englisch, 558 Seiten, Format (B × H): 241 mm x 164 mm, Gewicht: 1074 g
Reihe: Textbooks in Mathematics
ISBN: 978-1-4987-6080-5
Verlag: Taylor & Francis Inc
Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.
Features:
- Second edition of a successful textbook for the first undergraduate course
- Every major concept is introduced in its historical context and connects the idea with real life
- Focuses on experimentation
- Projects help enhance student learning
- All major software programs can be used; free software from author
Zielgruppe
Academic
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Geometry and the Axiomatic Method
Early Origins of Geometry
Thales and Pythagoras
Project 1 - The Ratio Made of Gold
The Rise of the Axiomatic Method
Properties of the Axiomatic Systems
Euclid's Axiomatic Geometry
Project 2 - A Concrete Axiomatic System
Euclidean Geometry
Angles, Lines, and Parallels ANGLES, LINES, AND PARALLELS 51
Congruent Triangles and Pasch's Axiom
Project 3 - Special Points of a Triangle
Measurement and Area
Similar Triangles
Circle Geometry
Project 4 - Circle Inversion and Orthogonality
Analytic Geometry
The Cartesian Coordinate System
Vector Geometry
Project 5 - Bezier Curves
Angles in Coordinate Geometry
The Complex Plane
Birkhoff's Axiomatic System
Constructions
Euclidean Constructions
Project 6 - Euclidean Eggs
Constructibility
Transformational Geometry
Euclidean Isometries
Reflections
Translations
Rotations
Project 7 - Quilts and Transformations
Glide Reflections
Structure and Representation of Isometries
Project 8 - Constructing Compositions
Symmetry
Finite Plane Symmetry Groups
Frieze Groups
Wallpaper Groups
Tilting the Plane
Project 9 - Constructing Tesselations
Hyperbollic Geometry
Background and History
Models of Hyperbolic Geometry
Basic Results in Hyperbolic Geometry
Project 10 - The Saccheri Quadrilateral
Lambert Quadrilaterals and Triangles
Area in Hyperbolic Geometry
Project 11 - Tilting the Hyperbolic Plane
Elliptic Geometry
Background and History
Perpendiculars and Poles in Elliptic Geometry
Project 12 - Models of Elliptic Geometry
Bas
