Author: Dmitriĭ Vladimirovich Nikulin
Publisher: Ashgate Publishing
ISBN:
Category : Philosophy
Languages : en
Pages : 328
Get Book Here
Book Description
"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
Author: D. Hilbert
Publisher: American Mathematical Soc.
ISBN: 1470463024
Category : Education
Languages : en
Pages : 357
Get Book Here
Book Description
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.
Author: Matthew Handelman
Publisher: Fordham Univ Press
ISBN: 0823283852
Category : Philosophy
Languages : en
Pages : 287
Get Book Here
Book Description
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.
Author: Dmitri Nikulin
Publisher:
ISBN: 9781315192406
Category : Electronic books
Languages : en
Pages :
Get Book Here
Book Description
"This title was first published in 2002: This text considers the 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 and mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. Exploring questions in the history of philosophy and science of late antiquity and early modernity, the key thinkers of focus are 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."--Provided by publisher.
Author: Dmitri Nikulin
Publisher: Routledge
ISBN: 9781138724549
Category :
Languages : en
Pages :
Get Book Here
Book Description
This title was first published in 2002: This text considers the 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 and mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. Exploring questions in the history of philosophy and science of late antiquity and early modernity, the key thinkers of focus are 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.
Author: Vincenzo De Risi
Publisher: Birkhäuser
ISBN: 3319121022
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
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).
Author: Marc Frantz
Publisher: Princeton University Press
ISBN: 140083905X
Category : Mathematics
Languages : en
Pages : 259
Get Book Here
Book Description
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)
Author: Edward Kasner
Publisher: Courier Corporation
ISBN: 0486320278
Category : Mathematics
Languages : en
Pages : 402
Get Book Here
Book Description
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.
Author: Dmitri Nikulin
Publisher: Oxford University Press
ISBN: 0190662387
Category : Philosophy
Languages : en
Pages : 297
Get Book Here
Book Description
This book is a philosophical study of two major thinkers who span the period of late antiquity. While Plotinus stands at the beginning of its philosophical tradition, setting the themes for debate and establishing strategies of argument and interpretation, Proclus falls closer to its end, developing a grand synthesis of late ancient thought. The book discusses many central topics of philosophy and science in Plotinus and Proclus, such as the one and the many, number and being, the individuation and constitution of the soul, imagination and cognition, the constitution of number and geometrical objects, indivisibility and continuity, intelligible and bodily matter, and evil. It shows that late ancient philosophy did not simply embrace and borrow from the major philosophical traditions of earlier antiquity--Platonism, Aristotelianism, Stoicism--by providing marginal comments on widely-known philosophical texts. Rather, Neoplatonism offered a set of highly original and innovative insights into the nature of being and thought, which can be distinguished in much subsequent philosophical thought, up until modernity.
Author: David W. Wood
Publisher: Brill Rodopi
ISBN: 9789042034914
Category : Mathematics
Languages : en
Pages : 304
Get Book Here
Book Description
This is the first major study in any language on J.G. Fichte's philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to "ordinary" Euclidean geometry, in his "Erlanger Logik "of 1805 Fichte posits a model of an "ursprungliche" or original geometry - that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that are grasped through geometrical or intelligible intuition. Accordingly, this study classifies Fichte's philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the "Wissenschaftslehre "itself may be read as an attempt at a new philosophical mathesis, or "mathesis of the mind." "This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched." Professor Dr. Marco Ivaldo (University of Naples) "This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the "Wissenschaftslehre "and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious." Professor Dr. Emmanuel Cattin (Universite Blaise-Pascal, Clermont-Ferrand)
