Synopses & Reviews
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 and#8212; with solutions, answers, and hints and#8212; promote habits of independent work
Synopsis
Two-part treatment begins with discussions of coordinates of points on a line, coordinates of points in a plane, and coordinates of points in space. Part two examines geometry as an aid to calculation and peculiarities of four-dimensional space. Abundance of ingenious problems — includes solutions, answers, and hints. 1967 edition.
Table of Contents
and#160; Foreword; Introduction; Part 1.
Chapter 1. The Coordinates of Points on a Line
and#160; 1. The Number Axis
and#160; 2. The Absolute Value of a Number
and#160; 3. The Distance Between Two Points
Chapter 2. The Coordinates of Points in the Plane
and#160; 4. The Coordinate Plane
and#160; 5. Relations Connecting Coordinates
and#160; 6. The Distance Between Two Points
and#160; 7. Defining Figures
and#160; 8. We Begin to Solve Problems
and#160; 9. Other Systems of Coordinates
Chapter 3. The Coordinates of a Point in Space
and#160; 10. Coordinate Axes and Planes
and#160; 11. Defining Figures in Space
and#160; Part 2.
Chapter 1. Introduction
and#160; 1. Some General Considerations
and#160; 2. Geometry as an Aid in Calculation
and#160; 3. The Need for Introducing Four-Dimensional Space
and#160; 4. The Peculiarities of Four-Dimensional Space
and#160; 5. Some Physics
Chapter 2. Four-Dimensional Space
and#160; 6. Coordinate Axes and Planes
and#160; 7. Some Problems
Chapter 3. The Four-Dimensional Cube
and#160; 8. The Definition of the Sphere and the Cube
and#160; 9. The Definition of the Sphere and the Cube
and#160; 10. Problems on the Cube