On the Hypotheses Which Lie at the Bases of Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Hypotheses Which Lie at the Bases of Geometry write by Bernhard Riemann. This book was released on 2016-04-19. On the Hypotheses Which Lie at the Bases of Geometry available in PDF, EPUB and Kindle. This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Proceedings of the Indiana Academy of Science
Proceedings of the Indiana Academy of Science - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proceedings of the Indiana Academy of Science write by Indiana Academy of Science. This book was released on 1898. Proceedings of the Indiana Academy of Science available in PDF, EPUB and Kindle.
Geometry - Intuition and Concepts
Geometry - Intuition and Concepts - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry - Intuition and Concepts write by Jost-Hinrich Eschenburg. This book was released on 2022-10-31. Geometry - Intuition and Concepts available in PDF, EPUB and Kindle. This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
God Created The Integers
God Created The Integers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook God Created The Integers write by Stephen Hawking. This book was released on 2007-03-29. God Created The Integers available in PDF, EPUB and Kindle. Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.
An Aristotelian Realist Philosophy of Mathematics
An Aristotelian Realist Philosophy of Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Aristotelian Realist Philosophy of Mathematics write by J. Franklin. This book was released on 2014-04-09. An Aristotelian Realist Philosophy of Mathematics available in PDF, EPUB and Kindle. Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
