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The book contains a survey of research on non-regular Riemannian geome try, carried out mainly by Soviet authors. The beginning of this direction oc curred in the works of A. D. Aleksandrov on the intrinsic geometry of convex surfaces. For an arbitrary surface F, as is known, all those concepts that can be defined and facts that can be established by measuring the lengths of curves on the surface relate to intrinsic geometry. In the case considered in differential is defined by specifying its first geometry the intrinsic geometry of a surface fundamental form. If the surface F is non-regular, then instead of this form it is convenient to use the metric PF' defined as follows. For arbitrary points X, Y E F, PF(X, Y) is the greatest lower bound of the lengths of curves on the surface F joining the points X and Y. Specification of the metric PF uniquely determines the lengths of curves on the surface, and hence its intrinsic geometry. According to what we have said, the main object of research then appears as a metric space such that any two points of it can be joined by a curve of finite length, and the distance between them is equal to the greatest lower bound of the lengths of such curves. Spaces satisfying this condition are called spaces with intrinsic metric. Next we introduce metric spaces with intrinsic metric satisfying in one form or another the condition that the curvature is bounded.

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Genre Book : Mathematics
Author Book : V.N. Berestovskij
Publisher : Springer Science & Business Media
Release Book : 1993-10-14
Download Book : 250 Pages
ISBN-10 : 3540547010


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A complete overview of the geometry associated with computer graphics that provides everything a reader needs to understand the topic. Includes a summary hundreds of formulae used to solve 2D and 3D geometric problems; worked examples; proofs; mathematical strategies for solving geometric problems; a glossary of terms used in geometry.

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Genre Book : Computers
Author Book : John Vince
Publisher : Springer
Release Book : 2006-01-16
Download Book : 342 Pages
ISBN-10 : 1846281164


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If your child is struggling with math, then this book is for you; the short book covers the topic and also contains 30 practice problems to work with. This subject comes from the book “Fourth Grade Math (For Home School or Extra Practice)”; it more thoroughly covers more fifth grade topics to help your child get a better understanding of fourth grade math. If you purchased that book, or plan to purchase that book, do not purchase this, as the problems are the same.

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Genre Book : Study Aids
Author Book : Greg Sherman
Publisher : Home School Brew Press
Release Book : 2013-11-26
Download Book : 40 Pages
ISBN-10 : 9781629171500


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Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

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Genre Book : Mathematics
Author Book : A.N. Parshin
Publisher : Springer Science & Business Media
Release Book : 1994-04-25
Download Book : 286 Pages
ISBN-10 : 3540546820


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Genre Book :
Author Book :
Publisher : Rex Bookstore, Inc.
Release Book :
Download Book : Pages
ISBN-10 : 9712302334


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Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and useful links.

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Genre Book : Computers
Author Book : Duncan Marsh
Publisher : Springer
Release Book : 2006-03-30
Download Book : 350 Pages
ISBN-10 : 9781846281099


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One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics. The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.

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Genre Book : Mathematics
Author Book : I. Martin Isaacs
Publisher : American Mathematical Soc.
Release Book : 2009
Download Book : 222 Pages
ISBN-10 : 0821847945


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Analyse wireless network performance and improve design choices for future architectures and protocols with this rigorous introduction to stochastic geometry.

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Genre Book : Computers
Author Book : Martin Haenggi
Publisher : Cambridge University Press
Release Book : 2012-10-18
Download Book : 284 Pages
ISBN-10 : 9781107014695


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Genre Book :
Author Book :
Publisher : CUP Archive
Release Book :
Download Book : Pages
ISBN-10 : 1001368940


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This book constitutes the thoroughly refereed proceedings of the 18th International Conference on Discrete Geometry for Computer Imagery, DGCI 2014, held in Siena, Italy, September 2014. The 34 revised full papers presented were carefully selected from 60 submissions. The papers are organized in topical sections on Models for Discrete Geometry, Discrete and Combinatorial Topology, Geometric Transforms, Discrete Shape Representation, Recognition and Analysis, Discrete Tomography, Morphological Analysis, Discrete Modelling and Visualization, Discrete and Combinatorial Tools for Image Segmentation and Analysis.

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Genre Book : Computers
Author Book : Elena Barcucci
Publisher : Springer
Release Book : 2014-09-03
Download Book : 423 Pages
ISBN-10 : 9783319099552