The Fourth Dimension Simply Explained

by Henry P. Manning, Thomas F. Banchoff (Introduction)

Overview

Twenty-two essays examine the fourth dimension: how it may be studied, its relationship to non-Euclidean geometry, analogues to three-dimensional space, its absurdities and curiosities, and its simpler properties. 1910 edition.

Product Details

ISBN-13:	9780486438894
Publisher:	Dover Publications
Publication date:	02/18/2005
Series:	Dover Science Books
Pages:	272
Product dimensions:	5.38(w) x 8.42(h) x 0.54(d)

Table of Contents

	Introduction	7
I	An Elucidation of the Fourth Dimension	43
II	Non-Euclidean Geometry and the Fourth Dimension	52
III	Fourth Dimension Absurdities	60
IV	The Boundary of the Four-Dimensional Unit and Other Features of Four-Dimensional Space	70
V	How the Fourth Dimension May be Studied	81
VI	Space and Hyperspace	91
VII	An Interpretation of the Fourth Dimension	100
VIII	Length, Breadth, Thickness, and Then What?	110
IX	The Fourth Dimension Algebraically Considered	118
X	Difficulties in Imagining the Fourth Dimension	125
XI	Some Fourth Dimension Curiosities	134
XII	Characteristics of the Fourth Dimension	144
XIII	The Fourth Dimension, the Playground of Mathematics	154
XIV	The True and the False in the Theory of Four Dimensions	163
XV	The Ascending Series of Dimensions	172
XVI	The Mind's Eye and the Fourth Dimension	182
XVII	Other Dimensions Than Ours	192
XVIII	The Meaning of the Term "Fourth Dimension"	201
XIX	A Pupil in Geometry Quizzes His Teacher About the Fourth Dimension	211
XX	Possible Measurements and Forms in a System of Four Dimensions	220
XXI	The Fairyland of the Fourth Dimension	232
XXII	The Properties of Four-Dimensional Space	242