Geometry And The Imagination
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Geometry And The Imagination
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Author : David Hilbert
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Geometry And The Imagination written by David Hilbert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books.
The Mathematical Imagination
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Author : Matthew Handelman
language : en
Publisher: Fordham Univ Press
Release Date : 2019-03-05
The Mathematical Imagination written by Matthew Handelman and has been published by Fordham Univ Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-05 with Philosophy categories.
This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.
Mathematics And The Imagination
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Author : Edward Kasner
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Mathematics And The Imagination written by Edward Kasner and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Sacred Geometry
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Author : Robert Lawlor
language : en
Publisher:
Release Date : 1989
Sacred Geometry written by Robert Lawlor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Geometry categories.
Geometry And The Imagination
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Author : David Hilbert
language : en
Publisher:
Release Date : 1956
Geometry And The Imagination written by David Hilbert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Geometry categories.
Geometry And The Imagination
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Author : A. Renwick Sheen
language : en
Publisher:
Release Date : 2002-01-01
Geometry And The Imagination written by A. Renwick Sheen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Geometry categories.
Geometry is a central subject in Steiner-Waldorf schools, weaving into different subject areas throughout the 12 years. Geometry helps children explore both the outward world, and the inner human world. It helps them develop spacial harmony, and their analytical thinking.This comprehensive book has sections on Pre-Geometry, First Lessons, Pentagon and Pentagram, The Four Rules of Arithmetic, The Five Regular Solids, The Conic Sections, and Projective Geometry.It will be a particularly valuable resource for teachers of Years 6 to 8, and into High School.
Matter Imagination And Geometry
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Author : Dmitriĭ Vladimirovich Nikulin
language : en
Publisher: Ashgate Publishing
Release Date : 2002
Matter Imagination And Geometry written by Dmitriĭ Vladimirovich Nikulin and has been published by Ashgate Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Philosophy categories.
"This book considers conditions of applicability of mathematics to the study of natural phenomena. The possibility of such an application is one of the fundamental assumptions underlying the enormous theoretical and practical success of modern science. Addressing problems of matter, substance, infinity, number, structure of cognitive faculties, imagination, and of construction of mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. The author explores questions in the history of philosophy and science, particularly in late antiquity and early modernity. The focus is on key thinkers Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
Geometry And The Imagination
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Author : A. Renwick Sheen
language : en
Publisher:
Release Date : 1970
Geometry And The Imagination written by A. Renwick Sheen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Geometry categories.
Shaping Space
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Author : Marjorie Senechal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-22
Shaping Space written by Marjorie Senechal 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 2013-03-22 with Mathematics categories.
This second edition is based off of the very popular Shaping Space: A Polyhedral Approach, first published twenty years ago. The book is expanded and updated to include new developments, including the revolutions in visualization and model-making that the computer has wrought. Shaping Space is an exuberant, richly-illustrated, interdisciplinary guide to three-dimensional forms, focusing on the suprisingly diverse world of polyhedra. Geometry comes alive in Shaping Space, as a remarkable range of geometric ideas is explored and its centrality in our cultre is persuasively demonstrated. The book is addressed to designers, artists, architects, engineers, chemists, computer scientists, mathematicians, bioscientists, crystallographers, earth scientists, and teachers at all levels—in short, to all scholars and educators interested in, and working with, two- and three-dimensinal structures and patterns.
Geometry And The Imagination
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Author : David Hilbert
language : en
Publisher:
Release Date : 1968
Geometry And The Imagination written by David Hilbert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.