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Moderne Geometrie mit Anwendungen von George A. Jennings (1997
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eBay-Artikelnr.:155148204504
Artikelmerkmale
- Artikelzustand
- Sehr gut
- Hinweise des Verkäufers
- “No Writing or Highlighting Found. Cover, Spine & Interior Are Clean & Intact.”
- Subject
- Geometry
- Personalized
- No
- Custom Bundle
- No
- Subject Area
- Applied Geography
- ISBN
- 9780387942223
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
038794222X
ISBN-13
9780387942223
eBay Product ID (ePID)
8038307820
Product Key Features
Number of Pages
VIII, 204 Pages
Publication Name
Modern Geometry with Applications
Language
English
Publication Year
1994
Subject
Geometry / General
Type
Textbook
Subject Area
Mathematics
Series
Universitext Ser.
Format
Trade Paperback
Dimensions
Item Height
0.2 in
Item Weight
22.9 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
93-027818
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
1 Euclidean Geometry.- 1.1 Euclidean Space.- 1.2 Isometries and Congruence.- 1.3 Reflections in the Plane.- 1.4 Reflections in Space.- 1.5 Translations.- 1.6 Rotations.- 1.7 Applications and Examples.- 1.8 Some Key Results of High School Geometry: The Parallel Postulate, Angles of a Triangle, Similar Triangles, and the Pythagorean Theorem.- 1.9 SSS, ASA, and SAS.- 1.10 The General Isometry.- 1.11 Appendix: The Planimeter.- 2 Spherical Geometry.- 2.1 Geodesics.- 2.2 Geodesics on Spheres.- 2.3 The Six Angles of a Spherical Triangle.- 2.4 The Law of Cosines for Sides.- 2.5 The Dual Spherical Triangle.- 2.6 The Law of Cosines for Angles.- 2.7 The Law of Sines for Spherical Triangles.- 2.8 Navigation Problems.- 2.9 Mapmaking.- 2.10 Applications of Stereographic Projection.- 3 Conics.- 3.1 Conic Sections.- 3.2 Foci of Ellipses and Hyperbolas.- 3.3 Eccentricity and Directrix; the Focus of a Parabola.- 3.4 Tangent Lines.- 3.5 Focusing Properties of Conics.- 3.6 Review Exercises: Standard Equations for Smooth Conics.- 3.7 LORAN Navigation.- 3.8 Kepler's Laws of Planetary Motion.- 3.9 Appendix: Reduction of a Quadratic Equation to Standard Form.- 4 Projective Geometry.- 4.1 Perspective Drawing.- 4.2 Projective Space.- 4.3 Desargues' Theorem.- 4.4 Cross Ratios.- 4.5 Projections in Coordinates.- 4.6 Homogeneous Coordinates and Duality.- 4.7 Homogeneous Polynomials, Algebraic Curves.- 4.8 Tangents.- 4.9 Dual Curves.- 4.10 Pascal's and Brianchon's Theorems.- 5 Special Relativity.- 5.1 Spacetime.- 5.2 Galilean Transformations.- 5.3 The Failure of the Galilean Transformations.- 5.4 Lorentz Transformations.- 5.5 Relativistic Addition of Velocities.- 5.6 Lorentz-FitzGerald Contractions1.- 5.7 Minkowski Geometry.- 5.8 The Slowest Path is a Line.- 5.9 Hyperbolic Angles and theVelocity Addition Formula.- 5.10 Appendix: Circular and Hyperbolic Functions.- References.
Synopsis
This book is an introduction to the theory and applications of "modern geometry" ~ roughly speaking, geometry that was developed after Euclid. It covers three major areas of non-Euclidean geometry and their applica tions: spherical geometry (used in navigation and astronomy), projective geometry (used in art), and spacetime geometry (used in the Special The ory of Relativity). In addition it treats some of the more useful topics from Euclidean geometry, focusing on the use of Euclidean motions, and includes a chapter on conics and the orbits of planets. My aim in writing this book was to balance theory with applications. It seems to me that students of geometry, especially prospective mathe matics teachers, need to be aware of how geometry is used as well as how it is derived. Every topic in the book is motivated by an application and many additional applications are given in the exercises. This emphasis on applications is responsible for a somewhat nontraditional choice of top ics: I left out hyperbolic geometry, a traditional topic with practically no applications that are intelligible to undergraduates, and replaced it with the spacetime geometry of Special Relativity, a thoroughly non-Euclidean geometry with striking implications for our own physical universe. The book contains enough material for a one semester course in geometry at the sophomore-to-senior level, as well as many exercises, mostly of a non routine nature (the instructor may want to supplement them with routine exercises of his/her own)., This is a thorough analysis of the fundamentals of plane geometry. The reader is provided with an abundance of geometric facts such as results of Euclidean and spherical geometry, conic sections, projective geometry, and Minkowski geometry to name a few. The book covers unusual material and provides fresh examples and interesting exercises., This book is an introduction to the theory and applications of "modern geometry" roughly speaking, geometry that was developed after Euclid. It covers three major areas of non-Euclidean geometry and their applica- tions: spherical geometry (used in navigation and astronomy), projective geometry (used in art), and spacetime geometry (used in the Special The- ory of Relativity). In addition it treats some of the more useful topics from Euclidean geometry, focusing on the use of Euclidean motions, and includes a chapter on conics and the orbits of planets. My aim in writing this book was to balance theory with applications. It seems to me that students of geometry, especially prospective mathe- matics teachers, need to be aware of how geometry is used as well as how it is derived. Every topic in the book is motivated by an application and many additional applications are given in the exercises. This emphasis on applications is responsible for a somewhat nontraditional choice of top- ics: I left out hyperbolic geometry, a traditional topic with practically no applications that are intelligible to undergraduates, and replaced it with the spacetime geometry of Special Relativity, a thoroughly non-Euclidean geometry with striking implications for our own physical universe. The book contains enough material for a one semester course in geometry at the sophomore-to-senior level, as well as many exercises, mostly of a non- routine nature (the instructor may want to supplement them with routine exercises of his/her own).
LC Classification Number
QA440-699
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- t***u (893)- Bewertung vom Käufer.Vor über einem JahrBestätigter KaufExcellent seller! Quality patches.Alcoholics Anonymous Clean & Sober Embroidered Recovery Patch Set (Nr. 165720012028)