The Method of Coordinates / Edition 1

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Overview


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
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Editorial Reviews

From the Publisher
"All through both volumes [‘Functions & Graphs’ and ‘The Methods of Coordinates’], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done."

—- H. Wu, The Mathematical Intelligencer

"This book is a concise and compact treatment of the essential ideas of coordinate geometry. The authors demonstrate powerfully how geomtric ides may be communicated and studied effectively without the aid of pictures. Graphics are of course of vital importance int he methods of Euclidean geometry. However, the methods of coordinate geometry are able to transform pure geometric ideas into algebraic manipulations where the meaning is very clear once the formalism is learnt. In particular the book demonstrates the value of conveying information in the form of images embedded in formulas. This is very useful in the transmission of information by electronic means. . . This book is a valuable tool for teaching the redimentary concepts of analytical geometry. It contains a number of excellent examples and exercises which go further than a mere introductory programme. the exercises, while not numerous, are very thought-provoking and are bound to pose a serious challenge to the interested student."

—-The Mathematical Gazette

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Product Details

  • ISBN-13: 9780817635336
  • Publisher: Birkhauser Verlag
  • Publication date: 1/1/1990
  • Edition description: 1990
  • Edition number: 1
  • Pages: 74
  • Product dimensions: 9.00 (w) x 6.00 (h) x 0.17 (d)

Table of Contents

Foreword v
Introduction 1
Part 1
Chapter 1 The Coordinates of Points on a Line 5
1. The Number Axis 5
2. The Absolute Value of a Number 8
3. The Distance Between Two Points 9
Chapter 2 The Coordinates of Points in the Plane 12
4. The Coordinate Plane 12
5. Relations Connecting Coordinates 15
6. The Distance Between Two Points 17
7. Defining Figures 20
8. We Begin to Solve Problems 23
9. Other Systems of Coordinates 27
Chapter 3 The Coordinates of a Point in Space 32
10. Coordinate Axes and Planes 32
11. Defining Figures in Space 36
Part 2
Chapter 1 Introduction 41
1. Some General Considerations 41
2. Geometry as an Aid in Calculation 42
3. The Need for Introducing Four-Dimensional Space 45
4. The Peculiarities of Four-Dimensional Space 47
5. Some Physics 48
Chapter 2 Four-Dimensional Space 50
6. Coordinate Axes and Planes 51
7. Some Problems 56
Chapter 3 The Four-Dimensional Cube 58
8. The Definition of the Sphere and the Cube 58
9. The Structure of the Four-Dimensional Cube 60
10. Problems on the Cube 67
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