How Surfaces Intersect in Space

How Surfaces Intersect in Space
Author: J. Scott Carter
Publisher: World Scientific
Total Pages: 344
Release: 1995
Genre: Science
ISBN: 9789810220662

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

Mathematics of Surfaces

Mathematics of Surfaces
Author: Michael J. Wilson
Publisher: Springer Science & Business Media
Total Pages: 401
Release: 2003-09-09
Genre: Computers
ISBN: 3540200533

This book constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.

Flatland

Flatland
Author: Edwin A. Abbott
Publisher: David De Angelis
Total Pages: 106
Release: 2024-09-17
Genre: Fiction
ISBN:

A book that combines science fiction, satire of Victorian society and politics, proving to be a great literary allegory. The illustrated world is populated by Squares, Triangles, Circles and Lines living in a two-dimensional universe, all strictly divided by class and gender. The narrator is precisely one of them, a Square. He will guide readers into his world by explaining the brilliant implications of two-dimensional life. Later, however, he will tell of his discovery of other, more geometrically complex universes such as the three-dimensional one, represented by his encounter with a Sphere. Thus begins a true journey of knowledge, which will lead him to that which can hardly be conceived by the mind. A unique book that has become a cult object by the scientific community and beyond.

Visualizing Mathematics with 3D Printing

Visualizing Mathematics with 3D Printing
Author: Henry Segerman
Publisher: JHU Press
Total Pages: 201
Release: 2016-10-04
Genre: Mathematics
ISBN: 1421420368

The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.

The Fourth Dimension

The Fourth Dimension
Author: Rudolf Steiner
Publisher: SteinerBooks
Total Pages: 348
Release: 2001-06
Genre: Education
ISBN: 0880109491

8 Lectures in Dornach, Nov 26, 1923 to Dec 22, 1923 (CW 351) In 1923 Rudolf Steiner predicted the dire state of today's honeybee. He stated that, within fifty to eighty years, we would see the consequences of mechanizing the forces that had previously operated organically in the beehive. Such practices include breeding queen bees artificially. The fact that over sixty percent of the American honeybee population has died during the past ten years, and that this trend is continuing around the world, should make us aware of the importance of the issues discussed in these lectures. Steiner began this series of lectures on bees in response to a question from an audience of workers at the Goetheanum. From physical depictions of the daily activities of bees to the most elevated esoteric insights, these lectures describe the unconscious wisdom of the beehive and its connection to our experience of health, culture, and the cosmos. Bees is essential reading for anyone interested in understanding the true nature of the honeybee, as well as those who wish to heal the contemporary crisis of the beehive. Bees includes an essay by David Adams, "From Queen Bee to Social Sculpture: The Artistic Alchemy of Joseph Beuys." The art and social philosophy of Joseph Beuys (1921-1986) is among the most influential of the twentieth century. He was strongly influenced by Rudolf Steiner's lectures on bees. The elemental imagery and its relationship to human society played an important role in Beuys's sculptures, drawings, installations, and performance art. Adams' essay on Beuys adds a whole new dimension to these lectures, generally considered to be directed more specifically to biodynamic methods and beekeeping. This volume consists of 8 lectures (of 15) from Mensch und Welt. Das Wirken des Geistes in der Natur. Über das Wesen der Bienen (GA 351).

American Journal of Mathematics

American Journal of Mathematics
Author:
Publisher:
Total Pages: 458
Release: 1899
Genre: Electronic journals
ISBN:

The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.

Knotted Surfaces and Their Diagrams

Knotted Surfaces and Their Diagrams
Author: J. Scott Carter
Publisher: American Mathematical Society
Total Pages: 273
Release: 2023-12-06
Genre: Mathematics
ISBN: 1470476339

In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studied. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied. Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.

Regular Polytopes

Regular Polytopes
Author: H. S. M. Coxeter
Publisher: Courier Corporation
Total Pages: 372
Release: 2012-05-23
Genre: Mathematics
ISBN: 0486141586

Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.

Things to Make and Do in the Fourth Dimension

Things to Make and Do in the Fourth Dimension
Author: Matt Parker
Publisher: Farrar, Straus and Giroux
Total Pages: 465
Release: 2014-12-02
Genre: Games & Activities
ISBN: 0374710376

A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it.