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A Geometry Of The Imagination
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Book Synopsis Geometry and the Imagination by : D. Hilbert
Download or read book Geometry and the Imagination written by D. Hilbert and published by American Mathematical Soc.. This book was released on 2021-03-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! 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. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. 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 R 3 R3. 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: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. 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. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! 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.
Book Synopsis The Mathematical Imagination by : Matthew Handelman
Download or read book The Mathematical Imagination written by Matthew Handelman and published by Fordham Univ Press. This book was released on 2019-03-05 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Matter, Imagination, and Geometry by : Dmitriĭ Vladimirovich Nikulin
Download or read book Matter, Imagination, and Geometry written by Dmitriĭ Vladimirovich Nikulin and published by Ashgate Publishing. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Book Synopsis Geometry and the Imagination by : A. Renwick Sheen
Download or read book Geometry and the Imagination written by A. Renwick Sheen and published by . This book was released on 2002-01-01 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematics and the Imagination by : Edward Kasner
Download or read book Mathematics and the Imagination written by Edward Kasner and published by Courier Corporation. This book was released on 2013-04-22 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Foundations of Geometry by : David Hilbert
Download or read book The Foundations of Geometry written by David Hilbert and published by Read Books Ltd. This book was released on 2015-05-06 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Download or read book Viewpoints written by Marc Frantz and published by Princeton University Press. This book was released on 2011-07-05 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)
Book Synopsis Mathematics for the Imagination by : Peter Higgins
Download or read book Mathematics for the Imagination written by Peter Higgins and published by OUP Oxford. This book was released on 2002-09-26 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind. This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems. A highly involving book which encourages the reader to enter into the spirit of mathematical exploration.
Book Synopsis Maps of the Imagination by : Peter Turchi
Download or read book Maps of the Imagination written by Peter Turchi and published by Trinity University Press. This book was released on 2011-06-01 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maps of the Imagination takes us on a magic carpet ride over terrain both familiar and exotic. Using the map as a metaphor, fiction writer Peter Turchi considers writing as a combination of exploration and presentation, all the while serving as an erudite and charming guide. He compares the way a writer leads a reader though the imaginary world of a story, novel, or poem to the way a mapmaker charts the physical world. "To ask for a map," says Turchi, "is to say, ‘Tell me a story.’ " With intelligence and wit, the author looks at how mapmakers and writers deal with blank space and the blank page; the conventions they use or consciously disregard; the role of geometry in maps and the parallel role of form in writing; how both maps and writing serve to re-create an individual’s view of the world; and the artist’s delicate balance of intuition with intention. A unique combination of history, critical cartography, personal essay, and practical guide to writing, Maps of the Imagination is a book for writers, for readers, and for anyone interested in creativity. Colorful illustrations and Turchi’s insightful observations make his book both beautiful and a joy to read.
Download or read book Sacred Geometry written by Robert Lawlor and published by . This book was released on 1994 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematizing Space by : Vincenzo De Risi
Download or read book Mathematizing Space written by Vincenzo De Risi and published by Birkhäuser. This book was released on 2015-01-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
Book Synopsis Conceptual Spaces by : Peter Gardenfors
Download or read book Conceptual Spaces written by Peter Gardenfors and published by MIT Press. This book was released on 2004-01-30 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.
Book Synopsis The Shape of Space by : Jeffrey R. Weeks
Download or read book The Shape of Space written by Jeffrey R. Weeks and published by CRC Press. This book was released on 2001-12-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
Book Synopsis Mythic Imagination Today by : Terry Marks-Tarlow
Download or read book Mythic Imagination Today written by Terry Marks-Tarlow and published by BRILL. This book was released on 2021-01-18 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mythic Imagination Today is an illustrated guide to the interpenetration of mythology and science throughout the ages. This monograph brings alive our collective need for story as a guide to the rules, roles, and relationships of everyday life.
Book Synopsis Shaping Space by : Marjorie Senechal
Download or read book Shaping Space written by Marjorie Senechal and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Embodied Image by : Juhani Pallasmaa
Download or read book The Embodied Image written by Juhani Pallasmaa and published by John Wiley & Sons. This book was released on 2011-05-16 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Embodied Image The Embodied Image: Imagination and Imagery in Architecture Juhani Pallasmaa All artistic and architectural effects are evoked, mediated and experienced through poeticised images. These images are embodied and lived experiences that take place in ‘the flesh of the world’, becoming part of us, at the same time that we unconsciously project aspects of ourselves on to a conceived space, object or event. Artistic images have a life and reality of their own and they develop through unexpected associations rather than rational and causal logic. Images are usually thought of as retinal pictures but profound poetic images are multi-sensory and they address us in an embodied and emotive manner. Architecture is usually analysed and taught as a discipline that articulates space and geometry, but the mental impact of architecture arises significantly from its image quality that integrates the various aspects and dimensions of experience into a singular, internalised and remembered entity. The material reality is fused with our mental and imaginative realm. The book is organised into five main parts that look at in turn: the image in contemporary culture; language, thought and the image; the many faces of the image; the poetic image; and finally the architectural image. The Embodied Image is illustrated with over sixty images in pairs, which are diverse in subject. They range from scientific images to historic artistic and architectural masterpieces. Artworks span Michelangelo and Vermeer to Gordon Matta- Clark and architecture takes in Modern Masters such as Mies van der Rohe, Le Corbusier and Alvar Aalto, as well as significant contemporary works by Steven Holl and Daniel Libeskind.
Book Synopsis Mathematics, Education, and Other Endangered Species by : Shlomo Vinner
Download or read book Mathematics, Education, and Other Endangered Species written by Shlomo Vinner and published by Springer. This book was released on 2019-04-26 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the critical roles and effects of mathematics education. The exposition draws from the author’s forty-year mathematics career, integrating his research in the psychology of mathematical thinking into an overview of the true definition of math. The intention for the reader is to undergo a “corrective” experience, obtaining a clear message on how mathematical thinking tools can help all people cope with everyday life. For those who have struggled with math in the past, the book also aims to clarify that math learning difficulties are likely a result of improper pedagogy as opposed to any lack of intelligence on the part of the student. This personal treatise will be of interest to a variety of readers, from mathematics teachers and those who train them to those with an interest in education but who may lack a solid math background.
