A Mobius Strip


Book Description

“Möbius strip: a one-sided surface formed by holding one end of a rectangle fixed, rotating the opposite end through 180 degrees, and then applying it to the first end.”—Webster’s Third International Dictionary In this intriguing book, Francis Schiller describes the philosophy, life, and work of Paul Möbius, tracing through them the beginnings of modern neuropsychiatry. Freud called Möbius “a pioneer of psychotherapy.” The grandson of the inventor of the Möbius strip, he made important contributions to both neurology and psychiatry. The Leipzig physician had come to the study of medicine by way of philosophy. Consistent with his own “nonmaterialistic monism,” he sought a unifying solution to the age-old problem of the relationship between the mind and the brain. Schiller aptly uses the geometrical puzzle invented by Möbius’s grandfather to illustrate Möbius’s view of this relationship. A Möbius Strip is a unique exploration of nineteenth-century views of the “mind-body problem” and of the relationship between disorders of the brain and the psyche. It sheds light on the origins of modern psychotherapy and the concept of the unconscious, the formulation of hysteria as a psychogenic disorder, the localization of function in the brain, the relationship between neurology and psychiatry, and turn-of-the-century ideas about sex and behavior. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1982.




Introduction to Möbius Differential Geometry


Book Description

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.




The Möbius Strip Topology


Book Description

In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777–1855) was an epochal example. August Ferdinand Möbius (1790–1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the “golden age” of pure mathematics and fundamental theory in physical sciences. Möbius’ legacy reaches far into today’s sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.




Mobius Inversion in Physics


Book Description

This book attempts to bridge the gap between the principles of pure mathematics and the applications in physical science. After the Mobius inversion formula had been considered as purely academic, or beyond what was useful in the physics community for more than 150 years, the apparently obscure result in classical mathematics suddenly appears to be connected to a variety of important inverse problems in physical science. This book only requires readers to have some background in elementary calculus and general physics, and prerequisite knowledge of number theory is not needed. It will be attractive to our multidisciplinary readers interested in the Mobius technique, which is a tiny but important part of the number-theoretic methods. It will inspire many students and researchers in both physics and mathematics. In a practical problem, continuity and discreteness are often correlated, and few textbook have given attention to this wide and important field as this book. Clearly, this book will be an essential supplement for many existing courses such as mathematical physics, elementary number theory and discrete mathematics.




Mobius Invariant QK Spaces


Book Description

This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.




The Trans Möbius Strip


Book Description




The Mechanics of Ribbons and Möbius Bands


Book Description

Recent developments in biology and nanotechnology have stimulated a rapidly growing interest in the mechanics of thin, flexible ribbons and Mobius bands. This edited volume contains English translations of four seminal papers on this topic, all originally written in German; of these, Michael A. Sadowsky published the first in 1929, followed by two others in 1930, and Walter Wunderlich published the last in 1962. The volume also contains invited, peer-reviewed, original research articles on related topics. Previously published in the Journal of Elasticity, Volume 119, Issue 1-2, 2015.




Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli


Book Description

"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. In this accessible book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including a valuable selection of exercises.







Mobius


Book Description