Imaginaries In Geometry
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Imaginaries In Geometry
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Author : Pavel Alexandrovich Florensky
language : en
Publisher: Philosophy
Release Date : 2021
Imaginaries In Geometry written by Pavel Alexandrovich Florensky and has been published by Philosophy this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Philosophy categories.
This is the first complete English translation of Pavel Florensky's original and ambitious attempt to arrive at a geometric representation of imaginary numbers, in a context that had already captured the attention of other mathematicians, including Gauss, Argan, Cauchy and Bellavitis. Florensky did not limit his attempt solely to complex projective geometry, but extended it to encompass Ptolemaic-Dantean cosmology and Einstein's Principle of Relativity, as well as a new epistemological theory. The resulting treatise combines various disciplines and explores the relationship between an immanent realm of knowledge and a transcendent one.
An Essay On The Foundations Of Modern Geometry
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Author : Bertrand Russell
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
An Essay On The Foundations Of Modern Geometry written by Bertrand Russell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The author, a Nobel Laureate and one of the 20th century's most important logicians, asks and answers basic questions about the intersection of philosophy and higher mathematics. 1897 edition.
An Essay On The Foundations Of Geometry
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Author : Bertrand Russell
language : en
Publisher: Taylor & Francis
Release Date : 2022-09-15
An Essay On The Foundations Of Geometry written by Bertrand Russell and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-15 with Philosophy categories.
An Essay on the Foundations of Geometry was first published in 1897 when Bertrand Russell was 25 years old. It marks his first major foray into analytic philosophy, a movement in which Russell is one of the founding members and figurehead. It provides a brilliant insight into Russell's early philosophical thought and an engaging and authoritative introduction to the philosophical and logical foundations of geometry - a version of which was fundamental to Einstein's theory of relativity. Russell explores and introduces the concepts of geometry and their philosophical implications, including a historical overview of geometrical theory, making it an invaluable resource not only for students of philosophy but anyone interested in the origins of the thought of one of the twentieth century's most important and widely-read philosophers. This Routledge Classics edition includes a new Foreword by Michael Potter.
An Essay On The Foundations Of Geometry
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Author : A. W. Russell
language : en
Publisher: CUP Archive
Release Date : 2017-07-29
An Essay On The Foundations Of Geometry written by A. W. Russell and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-29 with History categories.
Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.
The Theory Of The Imaginary In Geometry
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Author : J. Hatton
language : en
Publisher: CreateSpace
Release Date : 2015-07-15
The Theory Of The Imaginary In Geometry written by J. Hatton and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with categories.
THE word theory in the title is to be understood in a very non-technical sense. Indeed, apart from the idea of the invariant elements of an elliptic involution on a straight line, no theory is found at all. The purpose of the book is rather to furnish a certain graphical representation of imaginaries under a number of conventions more or less well known. Three concepts run through the work: first, an incompletely defined idea of the nature of an imaginary; second, the analogy with the geometry of reals; third, the use of coordinate methods, assuming the algebra of imaginaries. Given a real point O and a real constant k, an imaginary point P is defined by the equation OP2 = -k - 2. The two imaginary points P and P' are the double points of an involution having O for center, and ik for parameter. The algebra of imaginaries is now assumed, and a geometry of imaginary distances on a straight line is built upon it. The reader is repeatedly reminded that in themselves there is no difference between real and imaginary points; that differences exist solely in their relations to other points. In the extension to two dimensions both x and ix are plotted on a horizontal line, while x and xy are plotted on a vertical line. Imaginary lines are dotted, and points having one or both coordinates imaginary are enclosed by parentheses, but otherwise the same figures are used for proofs, either by the methods of elementary geometry, or by coordinate methods.In the algebra of segments it is shown that an imaginary distance O'D' can be expressed in the form iOD, wherein OD is a real segment, or at most by OD times some number. Now follows a long development of the extension of cross ratios, etc., to imaginaries. In fact every word of this is found implicitly in any treatment of the invariance of cross ratios under linear fractional transformation.In Chapter II the conic with a real branch is introduced, beginning with involutions of conjugate points on lines having imaginary points on the conic. If the coefficients in the equation of a circle are real, the usual graph of x2 + y2 = a2 for real x and real y is followed by replacing y by iy, then proceeding as before. The former locus is called the (1, 1) branch, and the latter the (1, i) branch of the circle. Similarly, it has a (i, 1) branch, and another, (i, i) , but the latter has no graph. This idea is applied in all detail to ellipses, hyperbolas, and parabolas; in the case of the central conies it is also followed by replacing rectangular coordinates by a pair of conjugate diameters. The ordinary theorems of poles and polars, and the theorems of Pascal, Brianchon, Desargues, Carnot are shown to apply. Indeed, after having established the applicability of cross ratios in the earlier chapters, all these proofs can be applied in the same manner as to reals, without changing a word....-An excerpt from Bulletin of the American Mathematical Society, Vol. 27 [1921]
Around Caspar Wessel And The Geometric Representation Of Complex Numbers
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Author : Jesper Lützen
language : en
Publisher: Kgl. Danske Videnskabernes Selskab
Release Date : 2001
Around Caspar Wessel And The Geometric Representation Of Complex Numbers written by Jesper Lützen and has been published by Kgl. Danske Videnskabernes Selskab this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Cartography categories.
An Imaginary Tale
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Author : Paul Nahin
language : en
Publisher: Princeton University Press
Release Date : 2016-03-15
An Imaginary Tale written by Paul Nahin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-15 with Mathematics categories.
In the title, "[the square root of minus one]" appears as a radical over "-1."
Lectures On The Geometry Of Position
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Author : Theodor Reye
language : en
Publisher:
Release Date : 1898
Lectures On The Geometry Of Position written by Theodor Reye and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1898 with Geometry categories.
Model Theory And Algebraic Geometry
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Author : Elisabeth Bouscaren
language : en
Publisher: Springer
Release Date : 2009-03-14
Model Theory And Algebraic Geometry written by Elisabeth Bouscaren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-14 with Mathematics categories.
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Bulletin Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1899
Bulletin Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1899 with Mathematics categories.