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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.

...® About this Title. John Oprea, Cleveland State University, Cleveland, OH ... Wikizero - Richmond surface ... . Publication: The Student Mathematical Library Publication Year 2000: Volume 10 ISBNs: 978--8218-2118-3 (print); 978-1-4704-2127-4 (online) The Mathematics of Soap Films book. Read reviews from world's largest community for readers. Nature tries to minimize the surface area of a soap film thr... John Oprea's "The Mathematics of Soap Films: Explorations with Maple" has five chapters and about 250 pages. The book "is about the mathematics which describes the geometric proper ... The mathematics of soap films (2000 edition) | Open Library ... . The book "is about the mathematics which describes the geometric properties of soap films. Using...plane geometry, differential geometry, complex analysis and the calculus of variations, we...understand why soap films take the shapes they do..." Chapter one, surface tension, has 30 ... Find helpful customer reviews and review ratings for The Mathematics of Soap Films: Explorations With Maple (Student Mathematical Library, Vol. 10) (Student Mathematical Library, V. 10) at Amazon.com. Read honest and unbiased product reviews from our users. The Mathematics of Soap Films: Explorations with Maple est un excellent livre. Ce livre a Ã©tÃ© Ã©crit par l'auteur John Oprea. Sur notre site smartmobilitybelgium.be, vous pouvez lire le livre The Mathematics of Soap Films: Explorations with Maple en ligne. In differential geometry, a Richmond surface is a minimal surface first described by Herbert William Richmond in 1904. It is a family of surfaces with one planar end and one Enneper surface-like self-intersecting end.. It has Weierstrass-Enneper parameterization = /, =.This allows a parametrization based on a complex parameter as = [(âˆ’ /) âˆ’ + / (+)] = [(âˆ’ /) + + / (+)] = [/] 3. References J. Oprea, The Mathematics of Soap Films: Explorations with Maple c, Student Mathematical Library 10, American Mathematical Society, Providence, 2000. R ... Mathematics. Soap bubbles are physical examples of the complex mathematical problem of minimal surface.They will assume the shape of least surface area possible containing a given volume. A true minimal surface is more properly illustrated by a soap film, which has equal pressure on inside as outside, hence is a surface with zero mean curvature.A soap bubble is a closed soap film: due to the ... The Mathe...