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Wednesday, April 10, 2019

The Advanced Geometry of Plane Curves and Their Applications




File Size: 7.93 Mb

Description
Most textbooks on plane geometry show a certain onesideclness and concentrate the attention to an unduly great extent on conics, probably because these are so well suited to the illustration of general principles. Those properties, however, which require the introduction of differential quotients and integrals in the formulae are hardly mentioned at all in textbooks on analytical geometry and can be found in textbooks on the differential- and integralcalculus. Non-algebraic curves, finally, are mostly treated in textbooks on kinematics.

The present book is an attempt to combine the various parts of plane geometry. It gives a compilation of the most important properties of algebraic and transcendent curves together with their applications in physics and in technics; in the choice of the latter the author has been led by his own experience in
physical engineering.

Content:-
CHAPTER I. The plane
CHAPTER II. The geometrical interpretation of analytic operations applied to complex numbers
CHAPTER III. The straight line
CHAPTER IV. The triangle
CHAPTER V. The circle
CHAPTER VI. Algebraic curves
CHAPTER VII. Ellipse
CHAPTER VIII. Hyperbola
CHAPTER IX. Parabola
CHAPTER X. Involutes, evolutes and anticaustics
CHAPTER XI. Pedals and other derived curves
CHAPTER XII. Areas and other integrals
CHAPTER XIII. Envelopes
CHAPTER XIV. Orthogonal trajectories
CHAPTER XV. Kinked curves
CHAPTER XVI. Spirals
CHAPTER XVII. Lemniscate
CHAPTER XVIII. Cycloid
CHAPTER XIX. Epi- and hypocycloids
CHAPTER XX. Cardioid and limaron
CHAPTER XXI. Gear wheel tooth profiles
Appendix I: Analytical formula
Appendix II: Table of plane curves
Appendix III: Table of operations
Appendix IV: Table of derived curves
Appendix V: Historical notes
Index

Author Details
"C. Zwikker"




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