Self Intersection Properties Of Dragon Curves
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Self Intersection Properties Of Dragon Curves
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Author : W.R. Richardson
language : en
Publisher:
Release Date : 1970
Self Intersection Properties Of Dragon Curves written by W.R. Richardson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Geometry Of Curves And Surfaces With Maple
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Author : Vladimir Rovenski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Geometry Of Curves And Surfaces With Maple written by Vladimir Rovenski 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 2013-12-01 with Mathematics categories.
This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.
Canadian Theses
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Author : National Library of Canada
language : en
Publisher:
Release Date : 1974
Canadian Theses written by National Library of Canada and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Dissertations, Academic categories.
Calculating The Self Intersections Of Bezier Curves
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Author : Dieter Lasser
language : en
Publisher:
Release Date : 1988
Calculating The Self Intersections Of Bezier Curves written by Dieter Lasser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
A user-friendly divide-and-conquer algorithm is presented for finding all the self intersection points of a parametric curve in the Bernstein-Bezier representation. The underlying idea of the algorithm is to deal with the Bexier polygon instead of the curve description itself. By alternately subdividing the Bezier polygon and estimating the self intersection regions the self intersection points are finally approximated by straight line intersections of the refined Bezier polygons. The algorithm also calculates the parameter values of the self intersection points. In addition to the convex hull and the approximation property of the Bezier polygon the working of the algorithm is based on a very intuitive angle criterion. Keywords: Bezier curves; Spline curves; Intersection.
Self Intersections Of Curves On Surfaces
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Author : S. P. Tan
language : en
Publisher:
Release Date : 1995
Self Intersections Of Curves On Surfaces written by S. P. Tan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
The Family Tree Of Fractal Curves
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Author : Jeffrey Ventrella
language : en
Publisher: Eyebrain Books
Release Date : 2019-07
The Family Tree Of Fractal Curves written by Jeffrey Ventrella and has been published by Eyebrain Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07 with Computers categories.
This book explains a taxonomy of plane-filling curves (fractal curves with a fractal dimension of 2). it includes the classic fractal curves described in Mandelbrot's original book. Many new fractal curves are introduced. The taxonomy is based upon the Gaussian integers and the Eisenstein integers - each forming a lattice (square and triangular). These lattices have algebraic properties, which allows number theory to be used in describing and classifying these curves. This work has been under development for over 30 years. An earlier version of this taxonomy is described in the book ""Brain-filling Curves"", also by Jeffrey Ventrella. More on plane-filling curves can be found at fractalcurves.com
Introduction To Probability
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Author : Joseph K. Blitzstein
language : en
Publisher: CRC Press
Release Date : 2014-07-24
Introduction To Probability written by Joseph K. Blitzstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
Self Similar Groups
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Author : Volodymyr Nekrashevych
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-05
Self Similar Groups written by Volodymyr Nekrashevych and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-05 with Mathematics categories.
Self-similar groups (groups generated by automata) appeared initially as examples of groups that are easy to define but that enjoy exotic properties like nontrivial torsion, intermediate growth, etc. The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible to a wide mathematical readership, including graduate students interested in group theory and dynamical systems.
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.
Measure Topology And Fractal Geometry
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Author : Gerald A. Edgar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Measure Topology And Fractal Geometry written by Gerald A. Edgar 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 2013-04-17 with Mathematics categories.
From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1