Projective Geometry (Classic Reprint) - Couverture souple

Dowling, L. Wayland

Couverture souple

ISBN 10 : 1451000693 ISBN 13 : 9781451000696

Editeur : Forgotten Books, 2018

Synopsis

Master poles, polars, and quadric transformations in projective geometry.

A clear, structured introduction shows how polarities in a plane give rise to powerful transformations and the role of conics in these mappings. Learn how degeneracy, perspective, and inversions intertwine to shape geometric relationships. This edition explains the core ideas of poles and polars, fundamental lines and points, and how a quadric transformation connects lines to conics. It also covers inversions with respect to a circle, circular transformations, and the birational and involutoric properties that govern these maps, all with concrete descriptions and historical context.

• How two polarities create quadric transformations and when such maps are degenerate or non-degenerate.
• The concept of inversion with respect to a circle and how centers, radii, and polarity interact.
• What makes circular transformations birational and, in some cases, involutoric.
• Key exercises and historical notes that illuminate the development of these ideas.

Ideal for readers seeking a solid, accessible entry into the geometric transformations that underpin projective geometry and its applications.

A propos du livre

Présentation de l'éditeur

The existence of ideal elements must be assumed (A rt. 7); and theD edekind postulate, or an equivalent, must be used in order to arrive at continuously protective forms. The treatment of theD edekind postulate for this purpose (A rt. 39) is confessedly meager, and many teachers may feel the need of expanding it, or indeed of restating it, as occasion seems to demand. No attempt has been made to introduce new or strange terms, the only exception, so far as the author is aware, is the use of the word confocal to indicate those elements of a double polarity which are the supports of coinciding involutions of conjugate elements (A rt. 159). While this book has grown out of lectures given to students preparing to teach geometry, the subject matter is by no means of interest to this class of students alone. The engineer and the artisan must of necessity become familiar with the elementary processes of projection and section, and these processes are the same whether they lead to properties of geometrical figures or to methods in mechanical drawing. The author takes this occasion to express his gratitude toP rofessor Thomas F. Holgate, now Acting President of Northwestern University, for inspiration and enthusiasm acquired under his instruction at Clark University; and also his indebtedness for many helpful suggestions during the preparation of the manuscript for this book. Especial acknowledgment is due toP rofessor Henry S. White, of Vassar College, who read the manuscript and whose kindly comments and criticisms have materially improved the book in a number of points. The author wishes also to express his thanks toP rofessor Charles S. Slichter, of the University of Wisconsin for his sympathetic interest during the preparation of the manuscript and for his aid in seeing the book through the press. L. WAYLAND BOWLING. UNIVERSITY OF WISCONSIN, June,
(Typographical errors above are due to OCR software and don't occur in the book.)

About

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1451000693
• ISBN 13: 9781451000696
• Reliure: Broché
• Nombre de pages: 231
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