Beautiful Geometry


Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

View: 3650

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries


Author: Paulus Gerdes


ISBN: 1435726294


Page: 202

View: 4411

The book "Lunda Geometry" explains how the mathematical concepts of mirror curves and Lunda-designs were discovered in the context of the author's research of 'sona', illustrations traditionally made in the sand by Cokwe storytellers from eastern Angola (a region called Lunda) and neighboring regions of Congo and Zambia. Examples of mirror curves from several cultures are presented. Lunda-designs are aesthetically attractive and display interesting symmetry properties. Examples of Lunda-patterns and Lunda-polyominoes are presented. Some generalizations of the concept of Lunda-design are discussed, like hexagonal Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs. Lunda-designs of Celtic knot designs are constructed.Several chapters were published in journals like 'Computers & Graphics' (Oxford), 'Visual Mathematics' (Belgrade), and 'Mathematics in School' (UK).

Matroids: A Geometric Introduction


Author: Gary Gordon,Jennifer McNulty

Publisher: Cambridge University Press

ISBN: 0521145686

Category: Language Arts & Disciplines

Page: 393

View: 4485

This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Birational Geometry, Rational Curves, and Arithmetic


Author: Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel

Publisher: Springer Science & Business Media

ISBN: 146146482X

Category: Mathematics

Page: 319

View: 7115

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Models of the Real Projective Plane

Computer Graphics of Steiner and Boy Surfaces


Author: Francois Apery

Publisher: Springer-Verlag

ISBN: 3322895696

Category: Technology & Engineering

Page: 156

View: 8408

In the present time, objects generated by computers are replacing models made from wood, wire, and plaster. It is interesting to see how computer graphics can help us to understand the geometry of surfaces and illustrate some recent results on representations of the real projective plane.

The Natural philosophy of Emanuel Swedenborg

A Study in the Conceptual Metaphors of the Mechanistic World-View


Author: David Duner

Publisher: Springer Science & Business Media

ISBN: 9400745605

Category: Philosophy

Page: 476

View: 4636

Although Emanuel Swedenborg (1688–1772) is commonly known for his spiritual philosophy, his early career was focused unnatural science. During this period, Swedenborg thought of the world was like a gigantic machine, following the laws of mechanics and geometry. This volume analyzes this mechanistic worldview from the cognitive perspective, by means of a study of the metaphors in Swedenborg’s texts. The author argues that these conceptual metaphors are vital skills of the creative mind and scientific thinking, used to create visual analogies and abstract ideas. This means that Swedenborg’s mechanistic and geometrical worldview, allowed him to perceive the world as mechanical and geometrical. Swedenborg thought ”with” books and pens. The reading gave him associations and clues, forced him to interpret, and gave him material for his intellectual development.

Classical Algebraic Geometry

A Modern View


Author: Igor V. Dolgachev

Publisher: Cambridge University Press

ISBN: 1107017653

Category: Mathematics

Page: 639

View: 509

Makes classical algebraic geometry accessible to the modern mathematician.

Some Adventures in Euclidean Geometry


Author: Michael de Villiers

Publisher: Dynamic Mathematics Learning

ISBN: 0557102952

Category: Euclid's Elements

Page: 219

View: 1644

This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.

2019 Monthly Planner

Schedule Organizer Beautiful Geometric Style Background Cover Monthly and Weekly Calendar to Do List Top Goal and Focus


Author: Victoria Mann

Publisher: Planner

ISBN: 9781728820309

Category: Cooking

Page: 200

View: 912

This 2019 Monthly Planner provides 12 months worth of weekly and daily calendars from January 2019 to December 2019, more space for Goal, Daily schedule, Appointment, To do list and notes. Created and printed in the USA, each book features premium grade interior paper that can stand up to any marker or pen. The elegant, modern cover will look lovely on top of your desk or in your backpack. Features: Stylish Beautiful Composition with geometric style cover Printed in the USA Perfectly sized at 8.5" x 11" 12 months: January-December 2019 You can use for personal, work, to do list, small diary for note of the day and all purposes. Monthly and Weekly Action plan One month per each two page spread with unruled daily blocks. Printed on quality paper. Light weight. Easy to carry around. Best for Black Friday, Cyber Monday, Thanksgiving, Christmas gift and New Year gift. Everyone need to have the best planner since the first of the year.Give it for yourself friends family and co-worker and Have a great year together.

Riemannian Geometry


Author: Sylvestre Gallot,Dominique Hulin,Jacques Lafontaine

Publisher: Springer Science & Business Media

ISBN: 9783540204930

Category: Mathematics

Page: 322

View: 9119

Many years have passed since the ?rst edition. However, the encouragements of various readers and friends have persuaded us to write this third edition. During these years, Riemannian Geometry has undergone many dramatic - velopments. Here is not the place to relate them. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However,R- mannian Geometry is not only a fascinating ?eld in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance [L2]). These have been followed, quite recently, by a possibly successful approach to the Poincar ́ e conjecture. In another direction, Geometric Group Theory, a very active ?eld nowadays (cf. [Gr6]), borrows many ideas from Riemannian or metric geometry. Butletusstophoggingthelimelight.Thisisjustatextbook.Wehopethatour point of view of working intrinsically with manifolds as early as possible, and testingeverynewnotiononaseriesofrecurrentexamples(seetheintroduction to the ?rst edition for a detailed description), can be useful both to beginners and to mathematicians from other ?elds, wanting to acquire some feeling for the subject.

Computer Graphics and Geometric Modelling



Author: Max K. Agoston

Publisher: Springer Science & Business Media

ISBN: 9781852338176

Category: Computers

Page: 959

View: 1616

The second book of a two-volume work in which the author presents an overview of computer graphics as seen in the context of geometric modeling and the mathematics required to understand the subject.

The Geometry of Syzygies

A Second Course in Algebraic Geometry and Commutative Algebra


Author: David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 0387264566

Category: Mathematics

Page: 246

View: 4167

First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.

Flavors of Geometry


Author: Silvio Levy

Publisher: Cambridge University Press

ISBN: 9780521629621

Category: Mathematics

Page: 194

View: 1720

Lectures on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation.

Advances in Analysis and Geometry

New Developments Using Clifford Algebras


Author: Tao Qian,Thomas Hempfling,Alan McIntosh,Frank Sommen

Publisher: Springer Science & Business Media

ISBN: 9783764366612

Category: Mathematics

Page: 376

View: 3990

At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. This book collects refereed papers from a satellite conference to the ICM 2002, plus invited contributions. All articles contain unpublished new results.


Kurven - Flächen - Mannigfaltigkeiten


Author: Wolfgang Kühnel

Publisher: Springer-Verlag

ISBN: 3658006153

Category: Mathematics

Page: 284

View: 9012

Dieses Buch ist eine Einführung in die Differentialgeometrie und ein passender Begleiter zum Differentialgeometrie-Modul (ein- und zweisemestrig). Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel "Die innere Geometrie von Flächen". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über "Einstein-Räume", die eine große Bedeutung sowohl in der "Reinen Mathematik" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, was durch zahlreiche Abbildungen unterstützt wird. Bei der Neuauflage wurden einige zusätzliche Lösungen zu den Übungsaufgaben ergänzt.

Non-Euclidean Geometries

János Bolyai Memorial Volume


Author: András Prékopa,Emil Molnár

Publisher: Springer Science & Business Media

ISBN: 0387295550

Category: Mathematics

Page: 506

View: 2793

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

Das BUCH der Beweise


Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662577674

Category: Mathematics

Page: 360

View: 9788

Diese fünfte deutsche Auflage enthält ein ganz neues Kapitel über van der Waerdens Permanenten-Vermutung, sowie weitere neue, originelle und elegante Beweise in anderen Kapiteln. Aus den Rezensionen: “... es ist fast unmöglich, ein Mathematikbuch zu schreiben, das von jedermann gelesen und genossen werden kann, aber Aigner und Ziegler gelingt diese Meisterleistung in virtuosem Stil. [...] Dieses Buch erweist der Mathematik einen unschätzbaren Dienst, indem es Nicht-Mathematikern vorführt, was Mathematiker meinen, wenn sie über Schönheit sprechen.” Aus der Laudatio für den “Steele Prize for Mathematical Exposition” 2018 "Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdös immer wieder zitierte BUCH gehören, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Sätze enthält. Manchmal lässt der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, überraschenden Zusammenhängen und unerwarteten Volten.", Mai 2002 "Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdös, verständlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Lösungen mit Aha-Effekt, auch für Nicht-Mathematiker." "Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999 "Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern.", Mai 2002

The Beautiful Necessity


Author: Claude Fayette Bragdon

Publisher: Simon and Schuster

ISBN: 1627936513

Category: Philosophy

Page: 64

View: 8559

Written in 1910, The Beautiful Necessity discusses architectural theory by American architect and writer, Claude Fayette Bragdon.