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A New Basis for the Metric Theory of Congruences: A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the ... Department of Mathematics (Classic Reprint) - Softcover
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Excerpt from A New Basis for the Metric Theory of Congruences: A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the Degree of Doctor of Philosophy, Department of Mathematics
In the third section we Obtain new proofs of some of the most important general theorems on congruences. These results are typical-of those Obtained by means of the Kummer theory. The fourth section takes up the axis and ray congruences and the cor responding curves on the focal surfaces, all of which were recently discovered by Wilczynski.1 A number of new theorems concerning these configurations, mainly metric in character, are proven in this section. In the final section we discuss the equations of the Darboux conics of a point on one of the focal surfaces and consider some special cases.
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- PublisherForgotten Books
- Publication date2018
- ISBN 10 1331996716
- ISBN 13 9781331996712
- BindingPaperback
- LanguageEnglish
- Number of pages36
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A New Basis for the Metric Theory of Congruences (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book offers a pioneering method of understanding congruences, leveraging the fundamental ideas established by Kummer. Expanding on this classical theory, the author presents an innovative framework utilizing local coordinate systems that closely align with the congruence's general line. The book delves into the differential equations that define congruences, providing detailed derivations of their coefficients through the fundamental quantities of the surfaces involved. It also skillfully demonstrates the use of these equations to explore the relationships between congruences and their focal surfaces. Throughout the book, the author demonstrates mastery of the subject matter, guiding readers through complex concepts with clarity and precision. The work offers a unique perspective on congruences, blending geometric intuition with analytical rigor. Its in-depth exploration of congruence properties, such as the existence of focal surfaces and the behavior of developables, provides valuable insights into their behavior. By establishing new proofs for important theorems and examining special cases like axis and ray congruences, the author deepens our understanding of these mathematical constructs. This book will undoubtedly appeal to mathematicians seeking to expand their knowledge of differential geometry and the theory of congruences. Its rigorous approach and novel contributions make it an invaluable resource for researchers and advanced students in the field. The author's meticulous analysis provides a comprehensive understanding of the subject, offering a solid foundation for further exploration and the development of new theories. 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. print-on-demand item. Seller Inventory # 9781331996712_0
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A New Basis for the Metric Theory of Congruences A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the Department of Mathematics Classic Reprint
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A New Basis for the Metric Theory of Congruences A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the Department of Mathematics Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781331996712
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A New Basis for the Metric Theory of Congruences : A Dissertation Submitted to the Faculty of the Ogden Graduate School of Science in Candidacy for the Degree of Doctor of Philosophy, Department of Mathematics (Classic Reprint)
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Condition: Sehr gut. Zustand: Sehr gut - Gepflegter, sauberer Zustand. | Seiten: 40 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 26042980/2
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