Projective Vector Algebra (Classic Reprint): An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels: An Algebra of Vectors ... Congruence and of Parallels (Classic Reprint) - Tapa blanda
Sinopsis
A vector-based look at projective geometry that keeps operations simple and coordinate-free.
This book presents an algebra of vectors that represents projective geometry without relying on the usual axioms of congruence and parallels. It shows how projective collineations can be built from a distributive vector operation followed by a straightforward translation, making complex ideas easier to handle.
- Learn how line joins and plane equations arise directly from vector sums, without resorting to artificial coordinates.
- See the role of the T-plane and how projective concepts connect to familiar vector algebra.
- Explore involutoric and cyclic collineations and what they reveal about space and perspective.
- Discover practical ways these ideas illuminate problems in projective geometry through a clean, algebraic approach.
Ideal for readers of introductory projective geometry or anyone curious about a coordinate-free, vector-based treatment of the subject.
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Reseña del editor
Excerpt from Projective Vector Algebra: An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels
These suffice for the full validity of Desargues' theorem, a theorem whose aid will be most essential. (readers who are unfamiliar with this fundamental theorem can look up its proof in Prof.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
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.
Reseña del editor
Excerpt from Projective Vector Algebra: An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels
I. The reader will find in the widely known memoir of Hilbert on the Foundations of Geometry* various 'algebras of segments,' independent of one or of another group of axioms, the purpose of these algebras being, in Hilbert's case, to show the mutual independence of his set of axioms. More recently, in an excellent book, Schur has taken up von Staudt's calculus of projective segments (Wurfrechnung) in order to develop it analytically and to build upon it a complete system of metrical, euclidean and non-euclidean, geometry. This is admirably done in 4 and 5 of his work. Schur bases his definitions of equality, of addition and multiplication of projective segments, upon the correspondence known as 'prospectivity,' and, at first, avails himself only of the axioms of connection and of order [Schur's postulates I. to 8.]; for the further development of the subject, however, he has recourse [5] to the axioms of congruence or of 'motion,' postulates 9. to 13., and completes his investigation by adding an independent, 14th postulate concerning the use of compasses. The result is a most charming and lucid structure of the complete system of non-euclidean geometry (of an isotropic three-dimensional space of any constant curvature), the last touch to this true masterpiece being given in Schur's closing section by adding the archimedean postulate.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
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.
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Projective Vector Algebra (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book explores the fundamentals of projective vector algebra, focusing on the concepts of equality, addition, and subtraction of vectors. The author presents a simplified and elegant approach, accessible to beginners in geometry and physicists. Projective vector algebra builds upon the axioms of connection and order, establishing a system of metrical, Euclidean, and non-Euclidean geometry. The author's clear explanations and illustrative examples help readers grasp the subject's underlying principles. This book not only provides a solid foundation in projective vector algebra but also demonstrates its applicability in solving problems in various fields, highlighting its significance as a powerful tool for understanding and manipulating geometric concepts. 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. Nº de ref. del artículo: 9781330181966_0
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Projective Vector Algebra An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330181966
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Projective Vector Algebra An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330181966
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