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The Mathematics of Soap Films

The Mathematics of Soap Films
Author: John Oprea
Publisher: American Mathematical Soc.
Total Pages: 284
Release:
Genre: Mathematics
ISBN: 9780821884461

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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.


The Mathematics of Soap Films: Explorations with Maple

The Mathematics of Soap Films: Explorations with Maple
Author: John Oprea
Publisher: American Mathematical Soc.
Total Pages: 282
Release: 2000
Genre: Computers
ISBN: 0821821180

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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.


Demonstrating Science with Soap Films

Demonstrating Science with Soap Films
Author: Lovett
Publisher: CRC Press
Total Pages: 216
Release: 2017-11-22
Genre: Science
ISBN: 1351456202

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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


Demonstrating Science with Soap Films

Demonstrating Science with Soap Films
Author: D. R. Lovett
Publisher: Institute of Physics Publishing (GB)
Total Pages: 226
Release: 1994
Genre: Science
ISBN:

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Many of us have been fascinated as children by soap bubbles and soap films. Scientists and mathematicians have been interested in the properties of bubbles and films throughout scientific history. In Demonstrating Science with Soap Films David Lovett describes how the properties of soap films and bubbles can illustrate and elucidate a wide range of physical principles and scientific phenomena. Whilst much of the mathematics employed to explain concepts is at high school level, the more advanced topics are boxed and so may be omitted by readers without the appropriate mathematical background.


The Science of Soap Films and Soap Bubbles

The Science of Soap Films and Soap Bubbles
Author: Cyril Isenberg
Publisher: Courier Dover Publications
Total Pages: 244
Release: 1992
Genre: Games & Activities
ISBN: 9780486269603

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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.


Geometric Measure Theory

Geometric Measure Theory
Author: Frank Morgan
Publisher: Elsevier
Total Pages: 154
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483277801

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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.


Soap Bubbles, Their Colours and the Forces which Mold Them

Soap Bubbles, Their Colours and the Forces which Mold Them
Author: Charles Vernon Boys
Publisher: Courier Corporation
Total Pages: 193
Release: 1959-01-01
Genre: Science
ISBN: 0486205428

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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.


A Further Study of Soap Films

A Further Study of Soap Films
Author: Alberta Ginstie Prather
Publisher:
Total Pages: 12
Release: 1937
Genre: Calculus of variations
ISBN:

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Touching Soap Films

Touching Soap Films
Author: Andreas Arnez
Publisher: Springer Verlag
Total Pages: 16
Release: 2007
Genre: Computers
ISBN: 9783540240938

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This video introduces the world of soap films via the story of a young boy exploring the palace of soap films. Under the guidance of an old professor, he witnesses never-before-seen shapes and animations of soap films, and gains fascinating insights.