The Fourth Dimension Simply Explained

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Overview

To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable — or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension.
This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by Scientific American, these essays ...

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The Fourth Dimension Simply Explained

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Overview

To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable — or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension.
This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by Scientific American, these essays are so well reasoned and lucidly written that they were judged to merit publication in book form. Their easily understood explanations cover such topics as how the fourth dimension may be studied, the relationship of non-Euclidean geometry to the fourth dimension, analogues to three-dimensional space, some four-dimensional absurdities and curiosities, possible measurements and forms in the fourth dimension, and extensive considerations of four-dimensional space's simpler properties.
Since each essay is independently conceived, all of the writers offer fresh viewpoints and original examples. Because of this, some of the most important principles relating to the fourth dimension are viewed from several different angles at once — an invaluable aid to visualizing these abstruse but fascinating ideas. New Introduction by Thomas F. Banchoff, Brown University. 82 figures.

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Product Details

  • ISBN-13: 9780486438894
  • Publisher: Dover Publications
  • Publication date: 2/18/2005
  • Pages: 272
  • Product dimensions: 5.38 (w) x 8.42 (h) x 0.54 (d)

Table of Contents

Introduction
I. An Elucidation of the Fourth Dimension
II. Non-Euclidean Geometry and the Fourth Dimension
III. Fourth Dimension Absurdities
IV. The Boundary of the Four-Dimensional Unit and Other Features of Four-Dimensional Space
V. How the Fourth Dimension May Be Studied
VI. Space and Hyperspace
VII. An Interpretation of the Fourth Dimension
VIII. Length, Breadth, Thickness, and Then What?
IX. The Fourth Dimension Algebraically Considered
X. Difficulties in Imagining the Fourth Dimension
XI. Some Fourth Dimension Curiosities
XII. Characteristics of the Fourth Dimension
XIII. The Fourth Dimension, the Playground of Mathematics
XIV. The True and the False in the Theory of Four Dimensions
XV. The Ascending Series of Dimensions
XVI. The Mind's Eye and the Fourth Dimension
XVII. Other Dimensions Than Ours
XVIII. The Meaning of the Term "Fourth Dimension"
XIX. A Pupil in Geometry Quizzes His Teacher About the Fourth Dimension
XX. Possible Measurements and Forms in a System of Four Dimensions
XXI. The Fairyland of the Fourth Dimension
XXII. The Properties of Four-Dimensional Space
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