A Comparison of Different Line, Geometric Representations for Functions of a

Gladys E. C. Gibbens

ISBN 10: 1330190556 / ISBN 13: 9781330190555

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book introduces two methods for constructing a congruence of lines determined by a functional relation between two complex variables, enabling readers to visualize the properties of the function by studying the properties of the resulting congruence. In the first method, two complex variables are represented upon two distinct planes, parallel to each other and a unit apart. If points on the first plane are joined to points on the second plane that correspond to them via a given functional relation, a two-parameter family, or congruence, of straight lines is obtained. The second method uses a Riemann sphere. The two complex variables are projected upon the same sphere, and points of the sphere corresponding to each other via the function are joined by lines. The congruences obtained by either method always have real focal sheets and developables, making them more interesting than those obtained by the first method. The author demonstrates that there are other methods of constructing congruences of lines that impose less drastic restrictions upon the reference planes or spheres. The book then goes on to study the properties of the congruences resulting from these generalizations, including an extension of the method of the Riemann Sphere. By introducing complex variables into the study of lines and geometry, this book sheds new light on a subject of great mathematical interest. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781330190555_0

Bibliographic Details

• Title: A Comparison of Different Line, Geometric Representations for Functions of a
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1330190556
• ISBN 13: 9781330190555
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Geometry

About this title

Synopsis

Excerpt from A Comparison of Different Line, Geometric Representations for Functions of a Complex Variable a Dissertation Submitted to the Faculty of the Ogden Graduate School of Science, in Candidacy for the Degree of Doctor of Philosophy, (Department or Mathematics)

E. J. Wilczynski: Line-geometric representations for functions of a complex variable, Transactions of the American Mathematical Society, Vol. XX pp. 271-298.

About the Publisher

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.