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The Mathematics Of Soap Films
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Book Synopsis The Mathematics of Soap Films: Explorations with Maple by : John Oprea
Download or read book The Mathematics of Soap Films: Explorations with Maple written by John Oprea and published by American Mathematical Soc.. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.
Book Synopsis Demonstrating Science with Soap Films by : Lovett
Download or read book Demonstrating Science with Soap Films written by Lovett and published by CRC Press. This book was released on 2017-11-22 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of us have been fascinated as children by soap bubbles and soap films. Their shapes and colours are beautiful and they are great fun to pay with. With no les intensity, scientists and mathematicians have been interested in the properties of bubbles and films throughout scientific history. In this book David Lovett describes the properties of soap films and soap bubbles. He then uses their properties to illustrate and elucidate a wide range of physical principles and scientific phenomena in a way that unifies different concepts. The book will appeal not only to students and teachers at school and university but also to readers with a general scientific interest and to researchers studying soap films. For the most part simple school mathematics is used. Sections containing more advanced mathematics have been placed in boxes or appendices and can be omitted by readers without the appropriate mathematical background. The text is supported with * Over 100 diagrams and photgraphs. * Details of practical experiments that can be performed using simple household materials. * Computer programs that draw some of the more complicated figures or animate sequences of soap film configurations. * A bibliography for readers wishing to delve further into the subject. David Lovett is a lecturer in physics at the University of Essex. His research interests include Langmiur-Blodgett thin films and the use of models as teaching aids in physics. He has been interested in soap films since 1978 and has made a number of original contributions to the subject, particularly in the use of models which change their dimensions and their analogy with phase transitions. He has published three other books including ITensor Properties of Crystals (Institute of Physics Publishing 1989). John Tilley is also a lecturer in physics at the University of Essex with research interests in theoretical solid-state physics and soap films. He is coauthor of Superfluidity and Superc
Book Synopsis The Mathematics of Soap Films by : John Oprea
Download or read book The Mathematics of Soap Films written by John Oprea and published by American Mathematical Soc.. This book was released on with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.
Book Synopsis Geometric Measure Theory by : Frank Morgan
Download or read book Geometric Measure Theory written by Frank Morgan and published by Elsevier. This book was released on 2014-05-10 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.
Book Synopsis The Science of Soap Films and Soap Bubbles by : Cyril Isenberg
Download or read book The Science of Soap Films and Soap Bubbles written by Cyril Isenberg and published by Courier Dover Publications. This book was released on 1992 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb treatment of molecular and macroscopic properties of soap films and bubbles, emphasizing solutions of physical problems. Over 120 black-and-white illustrations, 41 color photographs.
Book Synopsis Visualizing Mathematics with 3D Printing by : Henry Segerman
Download or read book Visualizing Mathematics with 3D Printing written by Henry Segerman and published by JHU Press. This book was released on 2016-10-04 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Minimal Surfaces and Functions of Bounded Variation by : Giusti
Download or read book Minimal Surfaces and Functions of Bounded Variation written by Giusti and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Book Synopsis Soap Bubbles, Their Colours and the Forces which Mold Them by : Charles Vernon Boys
Download or read book Soap Bubbles, Their Colours and the Forces which Mold Them written by Charles Vernon Boys and published by Courier Corporation. This book was released on 1959-01-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent primer and classic work on the topic of soap bubbles and films employs simple experiments to establish a practical basis for the existence and function of surface tension and energy minimization. Experiments require only soap, straws, and bits of rubber to impart profound fundamental concepts related to fluids. 83 illustrations. 1911 edition.
Book Synopsis The Mathematical Mechanic by : Mark Levi
Download or read book The Mathematical Mechanic written by Mark Levi and published by Princeton University Press. This book was released on 2009-07-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.
Book Synopsis Variational Problems in Topology by : A.T. Fomenko
Download or read book Variational Problems in Topology written by A.T. Fomenko and published by Routledge. This book was released on 2019-06-21 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
Book Synopsis The Mathematical Tourist by : Ivars Peterson
Download or read book The Mathematical Tourist written by Ivars Peterson and published by Holt Paperbacks. This book was released on 1998-04-15 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first edition of The Mathematical Tourist, renowned science journalist Ivars Peterson took readers on an unforgettable tour through the sometimes bizarre, but always fascinating, landscape of modern mathematics. Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on * the relationship between mathematical knots and DNA * how computers based on quantum logic can significantly speed up the factoring of large composite numbers * the relationship between four-dimensional geometry and physical theories of the nature of matter * the application of cellular automata models to social questions and the peregrinations of virtual ants * a novel mathematical model of quasicrystals based on decagon-shaped tiles Blazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.
Download or read book Imagine Math 7 written by Michele Emmer and published by Springer Nature. This book was released on 2020-10-07 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine combining music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. This seventh volume starts with a homage to the Italian artist Mimmo Paladino who created exclusively for the Venice Conference 2019 ten original and unique works of art paper dedicated to the themes of the meeting. A large section is dedicated to the most recent Fields Medals including a Homage to Maryam Mirzakhani including a presentation of the exhibition on soap bubbles in art and science that took place in 2019. A section is dedicated to cinema and theatre including the performances by Claire Bardainne & Adrien Mondot. A part of the conference focused on the community of mathematicians, their role in literature and even in politics with the extraordinary example of Antanas Mockus Major of Bogotá. Mathematics in the constructions of bridges, in particular in Italy in the Sixties was presented by Tullia Iori. A very particular contribution on Origami by a mathematician, Marco Abate and an artist, Alessandro Beber. And many other topics. As usual the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture. The world, life, culture, everything has changed in a few weeks with the Coronavirus. Culture, science are the main ways to safeguard people's physical and social life. Trust in humanity's creativity and ability. The motto today in Italy is Everything will be fine. This work is addressed to all those who have an interest in Mathematics.
Book Synopsis An Aristotelian Realist Philosophy of Mathematics by : J. Franklin
Download or read book An Aristotelian Realist Philosophy of Mathematics written by J. Franklin and published by Springer. This book was released on 2014-04-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Book Synopsis The Use of Soap Films in Solving Torsion Problems by : Alan Arnold Griffith
Download or read book The Use of Soap Films in Solving Torsion Problems written by Alan Arnold Griffith and published by . This book was released on 1917 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Architecture and Mathematics from Antiquity to the Future by : Kim Williams
Download or read book Architecture and Mathematics from Antiquity to the Future written by Kim Williams and published by Birkhäuser. This book was released on 2015-02-11 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals. Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.
Download or read book How to Cut a Cake written by Ian Stewart and published by OUP Oxford. This book was released on 2006-10-12 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Welcome back to Ian Stewart's magical world of mathematics! This is a strange world of never-ending chess games, empires on the moon, furious fireflies, and, of course, disputes over how best to cut a cake. Each quirky tale presents a fascinating mathematical puzzle — challenging, fun, and also introducing the reader to a significant mathematical problem in an engaging and witty way.
Book Synopsis Multimedia Tools for Communicating Mathematics by : Jonathan Borwein
Download or read book Multimedia Tools for Communicating Mathematics written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on multimedia tools for communicating mathematics arose from presentations at an international workshop organized by the Centro de Matemtica e Aplicacoes Fundamentais at the University of Lisbon, in November 2000, with the collaboration of the Sonderforschungsbereich 288 at the University of Technology in Berlin, and of the Centre for Experimental and Constructive Mathematics at Simon Fraser University in Burnaby, Canada. The MTCM2000 meeting aimed at the scientific methods and algorithms at work inside multimedia tools, and it provided an overview of the range of present multimedia projects, of their limitations and the underlying mathematical problems. This book presents some of the tools and algorithms currently being used to create new ways of making enhanced interactive presentations and multimedia courses. It is an invaluable and up-to-date reference book on multimedia tools presently available for mathematics and related subjects.
