Explore advanced geometry across dimensions with clear, rigorous problems and proofs.
A rigorous tour through high-level geometry, from plane figures to fourfold space. This edition gathers topics like inversions, quadrics, and complex geometric constructions, with a focus on concrete methods and worked examples. It’s suited for readers who want to see how classic theorems extend into higher dimensions and how different geometric ideas connect.
- Learn how conics, quadric surfaces, and Veronese surfaces relate to spaces of three, four, and five dimensions.
- See practical problem solving in action with exercises on circles, spheres, and their tangent and polar relations.
- Explore the algebraic and synthetic approaches that unify space geometry with projective and descriptive methods.
- Understand how transformations like harmonic inversion and duality reveal hidden structures in complex figures.
Ideal for students and researchers of advanced geometry, and for anyone who enjoys seeing geometric ideas extended beyond the ordinary plane.
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Excerpt from Principles of Geometry, Vol. 4
The book, for which indeed, mostly, the earlier volumes were undertaken, still bears many marks of the difficulty of compressing the matter into brief compass. But the writer hopes that it may seem to the reader as remarkable as it does to him, that it should be possible to comprehend under one point of view, and that so simple, the introduction to nearly all the surfaces ordinarily studied in the geometry of three dimensions, as well as the usual line geometry. Chapters V, VI, VII seek to make clear that this is so. To these the earlier chapters are auxiliary. But Chapters II and IV have been introduced as much for their own interest as for their illustrative value; the results obtained in these two chapters are not required in the subsequent pages. It is hoped that the Table of Contents, and the Index, may make it easy to use the volume. It will of course be understood that the volume is throughout intended to be introductory and illustrative; hardly anywhere is it complete.
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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.
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Librería: Forgotten Books, London, Reino Unido
Paperback. Condición: New. Print on Demand. This book delves into the fascinating connections between geometry in different dimensions, showcasing the elegance and interconnectedness of mathematical principles. By exploring relationships between theorems in two, three, four, and even five dimensions, the author reveals how seemingly disparate concepts are intricately linked. Through a series of detailed examples and insightful commentary, the book guides readers through a journey of discovery, starting with the familiar geometry of circles and lines in a plane and culminating in the complexities of higher-dimensional spaces. Readers will encounter intriguing geometric figures, such as the "double-six" theorem and Kummer's surface, and witness how their properties can be understood through the lens of different dimensions. The author's approach not only illuminates the intrinsic beauty of these geometric objects but also demonstrates the power of unifying mathematical concepts across various dimensions. Ultimately, this book offers a profound appreciation for the depth and interconnectedness of geometry, revealing how the exploration of higher dimensions can shed new light on even the most fundamental geometric principles. 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: 9781330337486_0
Cantidad disponible: Más de 20 disponibles
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330337486
Cantidad disponible: 15 disponibles
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330337486
Cantidad disponible: 15 disponibles
Librería: Revaluation Books, Exeter, Reino Unido
Paperback. Condición: Brand New. 268 pages. 8.90x5.60x0.40 inches. This item is printed on demand. Nº de ref. del artículo: zk1330337484
Cantidad disponible: 1 disponibles