The Method of Coordinates (Dover Books on Mathematics)

Gelfand, I. M.; Glagoleva, E. G.; Kirillov, A. A.

ISBN 10: 0486425657 / ISBN 13: 9780486425658

Editore: Dover Publications, 2011

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Dati bibliografici

• Titolo: The Method of Coordinates (Dover Books on Mathematics)
• Editore: Dover Publications
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 0486425657
• ISBN 13: 9780486425658
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space.
Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of "road signs" in the margins, alerting students to passages requiring particular attention, and an abundance of ingenious problems — with solutions, answers, and hints — promote habits of independent work

Contenuti

Foreword; Introduction; Part 1. Chapter 1. The Coordinates of Points on a Line 1. The Number Axis 2. The Absolute Value of a Number 3. The Distance Between Two Points Chapter 2. The Coordinates of Points in the Plane 4. The Coordinate Plane 5. Relations Connecting Coordinates 6. The Distance Between Two Points 7. Defining Figures 8. We Begin to Solve Problems 9. Other Systems of Coordinates Chapter 3. The Coordinates of a Point in Space 10. Coordinate Axes and Planes 11. Defining Figures in Space Part 2. Chapter 1. Introduction 1. Some General Considerations 2. Geometry as an Aid in Calculation 3. The Need for Introducing Four-Dimensional Space 4. The Peculiarities of Four-Dimensional Space 5. Some Physics Chapter 2. Four-Dimensional Space 6. Coordinate Axes and Planes 7. Some Problems Chapter 3. The Four-Dimensional Cube 8. The Definition of the Sphere and the Cube 9. The Definition of the Sphere and the Cube 10. Problems on the Cube