A Book Of Curves
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A Book Of Curves
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Author : Edward Harrington Lockwood
language : en
Publisher: Cambridge University Press
Release Date : 1967
A Book Of Curves written by Edward Harrington Lockwood and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Curves categories.
Describes the drawing of plane curves, cycloidal curves, spirals, glissettes and others.
A Book Of Curves
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Author : E.D. Lockwood
language : en
Publisher:
Release Date : 1961
A Book Of Curves written by E.D. Lockwood and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
A Book Of Curves
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Author : E. H. Lockwood
language : de
Publisher:
Release Date : 1967
A Book Of Curves written by E. H. Lockwood and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
The Seduction Of Curves
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Author : Allan McRobie
language : en
Publisher: Princeton University Press
Release Date : 2017-09-19
The Seduction Of Curves written by Allan McRobie and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Art categories.
In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world--from our bodies to Salvador Dalí's paintings and the space-time fabric of the universe itself. The book focuses on seven curves--the fold, cusp, swallowtail, and butterfly, plus the hyperbolic, elliptical, and parabolic "umbilics"--and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician René Thom.
The Advanced Geometry Of Plane Curves And Their Applications
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Author : C. Zwikker
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
The Advanced Geometry Of Plane Curves And Their Applications written by C. Zwikker and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.
Curves And Surfaces
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Author : M. Abate
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-11
Curves And Surfaces written by M. Abate 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 2012-06-11 with Mathematics categories.
The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.
A Catalog Of Special Plane Curves
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Author : J. Dennis Lawrence
language : en
Publisher: Courier Corporation
Release Date : 2013-12-31
A Catalog Of Special Plane Curves written by J. Dennis Lawrence and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
DIVOne of the most beautiful aspects of geometry. Information on general properties, derived curves, geometric and analytic properties of each curve. 89 illus. /div
Space Filling Curves
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Author : Hans Sagan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Space Filling Curves written by Hans Sagan 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 2012-12-06 with Mathematics categories.
The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis.
Complex Algebraic Curves
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Author : Frances Clare Kirwan
language : en
Publisher: Cambridge University Press
Release Date : 1992-02-20
Complex Algebraic Curves written by Frances Clare Kirwan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-20 with Mathematics categories.
This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.
Curves
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Author : Victoria Janashvili
language : en
Publisher:
Release Date : 2015-07-15
Curves written by Victoria Janashvili and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with categories.