Minimal Surfaces Part 1 The Art

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Minimal Surfaces Part 1 The Art

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Author : Jean Constant
language : en
Publisher: Hermay NM
Release Date : 2022-06-16

Minimal Surfaces Part 1 The Art written by Jean Constant and has been published by Hermay NM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-16 with Art categories.

A two-part book on the exploration of minimal surfaces. In mathematics, a minimal surface is a surface for which the mean curvature H is zero at all points. These elegant and complex shapes found in Nature from butterflies, beetles, or black holes are studied today in statistics, material sciences, and architecture. I explored this singular shape from the perspective of a visual artist for 52 weeks, January-December 2021. Inspiring in many ways, the esthetics of these complex equations borne in the minds of brilliant scientists add a unique all-encompassing perspective to shapes and objects also found in Nature. I structured the project into part 1 – the art inspired by the shape- and part 2 - the plain visualization of the equations that stand in their own right as a beautiful expression of a mathematical mind at work. I included the informal log I kept throughout the journey in both parts. In part 2, I added the mathematical background that helped me understand the particular shape I was working on. Both sides complement each other in helping us appreciate these unrivaled original expressions of our environment.

Minimal Surfaces

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Author : Jean Constant
language : en
Publisher: Hermay NM
Release Date : 2022-08-09

Minimal Surfaces written by Jean Constant and has been published by Hermay NM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-09 with Mathematics categories.

A 52 illustration two-part book on the exploration of minimal surfaces. Part 1 explores the surface from an artistic perspective, and part 2 visually reproduces the equations that stand in their own right as a beautiful expression of pure geometry. Each book includes notes from an informal work-in-progress diary and references directing the reader to the images’ original mathematical source. Both sides complement each other in helping us appreciate better these unrivaled expressions of our environment found in nature, from butterflies to black holes, and studied in statistics, material sciences, and architecture.

Prime Number Geometry

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Author : Jean Constant
language : en
Publisher: Hermay NM
Release Date : 2024-08-01

Prime Number Geometry written by Jean Constant and has been published by Hermay NM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-01 with Art categories.

The 52 Illustration Prime Number series is a new chapter in the ongoing Math-Art collection exploring the world of mathematics and art. Inspired by the research of mathematicians from yesterday and today, this project aims to explore the visual aspect of numbers and highlight the unexpected connections between the challenging world of calculus, geometry, and art. Some will find references to ethnomathematics or a reflection on the universal cross-cultural appeal of mathematics; others will find a relation with the world we’re mapping for tomorrow, and hopefully, all will enjoy this unexpected interpretation of numbers from an artistic standpoint.

Minimal Surfaces

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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16

Minimal Surfaces written by Ulrich Dierkes 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 2010-08-16 with Mathematics categories.

Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Björling ́s initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau ́s problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche ́s uniqueness theorem and Tomi ́s finiteness result. In addition, a theory of unstable solutions of Plateau ́s problems is developed which is based on Courant ́s mountain pass lemma. Furthermore, Dirichlet ́s problem for nonparametric H-surfaces is solved, using the solution of Plateau ́s problem for H-surfaces and the pertinent estimates.

Minimal Surfaces I

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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27

Minimal Surfaces I written by Ulrich Dierkes 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 2013-11-27 with Mathematics categories.

Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.

Boy Singular Surfaces

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Author : Jean Constant
language : en
Publisher: Hermay NM
Release Date : 2018-06-17

Boy Singular Surfaces written by Jean Constant and has been published by Hermay NM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-17 with Art categories.

A Course In Minimal Surfaces

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Author : Tobias Holck Colding
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-18

A Course In Minimal Surfaces written by Tobias Holck Colding and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-18 with Mathematics categories.

Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

A Survey Of Minimal Surfaces

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Author : Robert Osserman
language : en
Publisher: Courier Corporation
Release Date : 2013-12-10

A Survey Of Minimal Surfaces written by Robert Osserman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-10 with Mathematics categories.

Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.

Lectures On Minimal Surfaces

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Author : Johannes C. C. Nitsche
language : en
Publisher:
Release Date : 1989

Lectures On Minimal Surfaces written by Johannes C. C. Nitsche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

Mathematics And Modern Art

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Author : Claude Bruter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23

Mathematics And Modern Art written by Claude Bruter 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 2012-04-23 with Mathematics categories.

The link between mathematics and art remains as strong today as it was in the earliest instances of decorative and ritual art. Arts, architecture, music and painting have for a long time been sources of new developments in mathematics, and vice versa. Many great painters have seen no contradiction between artistic and mathematical endeavors, contributing to the progress of both, using mathematical principles to guide their visual creativity, enriching their visual environment with the new objects created by the mathematical science. Owing to the recent development of the so nice techniques for visualization, while mathematicians can better explore these new mathematical objects, artists can use them to emphasize their intrinsic beauty, and create quite new sceneries. This volume, the content of the first conference of the European Society for Mathematics and the Arts (ESMA), held in Paris in 2010, gives an overview on some significant and beautiful recent works where maths and art, including architecture and music, are interwoven. The book includes a wealth of mathematical illustrations from several basic mathematical fields including classical geometry, topology, differential geometry, dynamical systems. Here, artists and mathematicians alike elucidate the thought processes and the tools used to create their work