Chasles And The Projective Geometry
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Chasles And The Projective Geometry
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Author : Paolo Bussotti
language : en
Publisher: Springer Nature
Release Date : 2024-07-17
Chasles And The Projective Geometry written by Paolo Bussotti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-17 with Mathematics categories.
This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles' extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed "parabolic," to the graphic context, so expressing the metric properties by means of this specific polarity—a foundational argument. Beyond the celebrated "Chasles theorem," he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles' philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles’ synthetic solution for the intricate problem of ellipsoid attraction—the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions. Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles' groundbreaking contributions. Providing a comprehensive understanding of Chasles' distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.
Chasles And The Projective Geometry
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Author : Paolo Bussotti
language : en
Publisher: Birkhäuser
Release Date : 2024-04-29
Chasles And The Projective Geometry written by Paolo Bussotti and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-29 with Mathematics categories.
This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles' extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed "parabolic," to the graphic context, so expressing the metric properties by means of this specific polarity—a foundational argument. Beyond the celebrated "Chasles theorem," he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles' philosophy of duality is explained. It is grounded on the duality principles of projective geometry. Finally, the author presents Chasles’ synthetic solution for the intricate problem of ellipsoid attraction—the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions. Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles' groundbreaking contributions. Providing a comprehensive understanding of Chasles' distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.
Projective Geometry
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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2024-04-30
Projective Geometry written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-30 with Computers categories.
What is Projective Geometry Projective geometry is a branch of mathematics that focuses on the study of geometric qualities that remain unchanged regardless of the transformations that are being applied to them. This indicates that, in contrast to simple Euclidean geometry, projective geometry is characterized by a distinct environment, a space that is the subject of the project, and a limited collection of fundamental geometric notions. For a given dimension, the fundamental intuitions are that projective space has a greater number of points than Euclidean space does, and that geometric transformations are allowed that change the extra points into Euclidean points, and vice versa. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Projective geometry Chapter 2: Projective plane Chapter 3: Projective space Chapter 4: Affine geometry Chapter 5: Desargues's theorem Chapter 6: Duality (projective geometry) Chapter 7: Complete quadrangle Chapter 8: Homography Chapter 9: Desargues configuration Chapter 10: Conic section (II) Answering the public top questions about projective geometry. (III) Real world examples for the usage of projective geometry in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Projective Geometry.
A History Of Geometrical Methods
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Author : Julian Lowell Coolidge
language : en
Publisher: Courier Corporation
Release Date : 2013-02-27
A History Of Geometrical Methods written by Julian Lowell Coolidge and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-27 with Mathematics categories.
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
Mathematics Of The 19th Century
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Author : Andrei N. Kolmogorov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematics Of The 19th Century written by Andrei N. Kolmogorov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka, Moscow 1978; En glish translation by Birkhiiuser Verlag, Basel-Boston-Berlin 1992). Circumstances beyond the control of the editors necessitated certain changes in the sequence of historical exposition of individual disciplines. The second volume contains two chapters: history of geometry and history of analytic function theory (including elliptic and Abelian functions); the size of the two chapters naturally entailed di viding them into sections. The history of differential and integral calculus, as well as computational mathematics, which we had planned to include in the second volume, will form part of the third volume. We remind our readers that the appendix of each volume contains a list of the most important literature and an index of names. The names of journals are given in abbreviated form and the volume and year of publication are indicated; if the actual year of publication differs from the nominal year, the latter is given in parentheses. The book History of Mathematics from Ancient Times to the Early Nineteenth Century [in Russian], which was published in the years 1970-1972, is cited in abbreviated form as HM (with volume and page number indicated). The first volume of the present series is cited as Bk. 1 (with page numbers).
Elements Of Projective Geometry
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Author : Luigi Cremona
language : en
Publisher:
Release Date : 1893
Elements Of Projective Geometry written by Luigi Cremona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1893 with Mathematics categories.
One of the best, most complete treatments of projective geometry, this treatise features detailed proofs, plus complete solutions for more than 150 examples and problems and numerous diagrams. 1913 edition.
Worlds Out Of Nothing
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Author : Jeremy Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-01
Worlds Out Of Nothing written by Jeremy Gray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-01 with Mathematics categories.
Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
Roads To Geometry
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Author : Edward C. Wallace
language : en
Publisher: Waveland Press
Release Date : 2015-10-23
Roads To Geometry written by Edward C. Wallace and has been published by Waveland Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-23 with Mathematics categories.
Now available from Waveland Press, the Third Edition of Roads to Geometry is appropriate for several kinds of students. Pre-service teachers of geometry are provided with a thorough yet accessible treatment of plane geometry in a historical context. Mathematics majors will find its axiomatic development sufficiently rigorous to provide a foundation for further study in the areas of Euclidean and non-Euclidean geometry. By using the SMSG postulate set as a basis for the development of plane geometry, the authors avoid the pitfalls of many “foundations of geometry” texts that encumber the reader with such a detailed development of preliminary results that many other substantive and elegant results are inaccessible in a one-semester course. At the end of each section is an ample collection of exercises of varying difficulty that provides problems that both extend and clarify results of that section, as well as problems that apply those results. At the end of chapters 3–7, a summary list of the new definitions and theorems of each chapter is included.
The History Of The Geometry Curriculum In The United States
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Author : Nathalie Sinclair
language : en
Publisher: IAP
Release Date : 2008-02-01
The History Of The Geometry Curriculum In The United States written by Nathalie Sinclair and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-01 with Education categories.
This volume investigates the evolution of the geometry curriculum in the United States over the past 150 years. A primary goal is to increase awareness of the shape and nature of the current geometry curriculum by explaining how things have come to be as they are. Given the limited access to first-hand accounts of the enacted geometry curriculum during the past 150 years, the monograph relies on textbooks to provide a record of the implemented curriculum at any given point in time. Policy documents can provide insight into the choices made in textbooks by hinting at the issues considered and the recommendations made. The monograph is organized in a chronological sequence of "notable events" leading to discernable changes in thinking about the geometry curriculum over the past century and a half—roughly the extent of time during which geometry has been taught in American schools. Notable events include important reports or commissions, influential texts, new schools of thought, and developments in learning technologies. These events affected, among other things: content and aims of the geometry curriculum; the nature of mathematical activity as construed by both mathematicians and mathematics educators; and, the resources students are given for engaging in mathematical activity. Before embarking through the notable events, it is necessary to consider the "big bang" of geometry, namely the moment in time that shaped the future life of the geometry curriculum. This corresponds to the emergence of Euclidean geometry. Given its influence on the shape of the geometry curriculum, familiarity with the nature of the geometry articulated in Euclid’s Elements is essential to understanding the many tensions that surround the school geometry curriculum. Several themes emerge over the course of the monograph, and include: the aims and means of the geometry curriculum, the importance of proof in geometry, the role of visualization and tactile experiences, the fusion between solid and plane geometry, the curricular connections between geometry and algebra, and the use of motion and continuity. The intended audience would include curriculum developers, researchers, teachers, and curriculum supervisors.
The Oxford Handbook Of Generality In Mathematics And The Sciences
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Author : Karine Chemla
language : en
Publisher: Oxford University Press
Release Date : 2016
The Oxford Handbook Of Generality In Mathematics And The Sciences written by Karine Chemla and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
This collection of original essays aims to inquire into the diversity of Generality. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts.