Robert C. Yates. CURVES AND THEIR PROPERTIES. THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS, Printed in the United States of America, 1974.
Some mathematical works of considerable vintage have a timeless quality about them. Like classics in any field, they still bring joy and guidance to the reader. Books of this kind, if no longer readily available, are being sought out by the National Council of Teachers of Mathematics, which has begun to publish a series of such classics. The present title is the fourth volume of the series.
A Handbook on Curves and Their Properties was first published in 1952 when the author was teaching at the United States Military Academy at West Point. A photo-lithoprint reproduction was issued in 1959 by Edwards Brothers, Inc., Lithoprinters, of Ann Arbor, Michigan. The present reprint edition has been similarly produced, by photo-offset, from a copy of the 1959 edition. Except for providing new front matter, including a biographical sketch of the author and this Foreword by way of explanation, no attempt has been made to modernize the book in any way. To do so would surely detract from, rather than add to, its value.
CONTENTS
Astroid ..........................................1
Cardioid..........................................4
Cassinian Curves..................................8
Catenary.....................12
Caustics.....................15
Circle......................21
Cissoid.....................26
Conchoid.....................31
Cones......................34
Conies......................36
Cubic Parabola..................56
Curvature....................60
Cycloid.....................65
Deltoid.....................71
Envelopes....................75
Ері- and Hypo-Cycloids..............81
Evolutes.....................86
Exponential Curves................93
Folium of Descartes...............98
Functions with Discontinuous Properties ..........100
Glissettes....................108
Hyperbolic Functions...............113
Instantaneous Center of Rotation and the
Construction of Some Tangents.........119
Intrinsic Equations ..............................123
Inversion....................127
Involutes....................135
Isoptic Curves..................138
Kieroid.....................141
Lemniscate of Bernoulli.............143
Limacon of Pascal................148
Nephroid.....................152
Parallel Curves ..................................155
Pedal Curves...................160
Pedal Equations.................166
Pursuit Curve ....................................170
Radial Curves ....................................172
Roulettes....................175
Semi-Cubic Parabola ..............................186
Sketching....................188
Spirals.....................206
Strophoid....................217
Tractrix.....................221
Trigonometric Functions ..........................225
Trochoids....................233
Witch of Agnesi.................237
