Mathematical Design
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A Mathematical Theory Of Design Foundations Algorithms And Applications
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Author : D. Braha
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Mathematical Theory Of Design Foundations Algorithms And Applications written by D. Braha 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 Technology & Engineering categories.
Formal Design Theory (PDT) is a mathematical theory of design. The main goal of PDT is to develop a domain independent core model of the design process. The book focuses the reader's attention on the process by which ideas originate and are developed into workable products. In developing PDT, we have been striving toward what has been expressed by the distinguished scholar Simon (1969): that "the science of design is possible and some day we will be able to talk in terms of well-established theories and practices. " The book is divided into five interrelated parts. The conceptual approach is presented first (Part I); followed by the theoretical foundations of PDT (Part II), and from which the algorithmic and pragmatic implications are deduced (Part III). Finally, detailed case-studies illustrate the theory and the methods of the design process (Part IV), and additional practical considerations are evaluated (Part V). The generic nature of the concepts, theory and methods are validated by examples from a variety of disciplines. FDT explores issues such as: algebraic representation of design artifacts, idealized design process cycle, and computational analysis and measurement of design process complexity and quality. FDT's axioms convey the assumptions of the theory about the nature of artifacts, and potential modifications of the artifacts in achieving desired goals or functionality. By being able to state these axioms explicitly, it is possible to derive theorems and corollaries, as well as to develop specific analytical and constructive methodologies.
Designs From Mathematical Patterns
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Author : Stanley Bezuszka
language : en
Publisher:
Release Date : 1978
Designs From Mathematical Patterns written by Stanley Bezuszka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Mathematical Methods In Computer Aided Geometric Design
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Author : Tom Lyche
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Mathematical Methods In Computer Aided Geometric Design written by Tom Lyche and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Mathematical Methods in Computer Aided Geometric Design covers the proceedings of the 1988 International Conference by the same title, held at the University of Oslo, Norway. This text contains papers based on the survey lectures, along with 33 full-length research papers. This book is composed of 39 chapters and begins with surveys of scattered data interpolation, spline elastic manifolds, geometry processing, the properties of Bézier curves, and Gröbner basis methods for multivariate splines. The next chapters deal with the principles of box splines, smooth piecewise quadric surfaces, some applications of hierarchical segmentations of algebraic curves, nonlinear parameters of splines, and algebraic aspects of geometric continuity. These topics are followed by discussions of shape preserving representations, box-spline surfaces, subdivision algorithm parallelization, interpolation systems, and the finite element method. Other chapters explore the concept and applications of uniform bivariate hermite interpolation, an algorithm for smooth interpolation, and the three B-spline constructions. The concluding chapters consider the three B-spline constructions, design tools for shaping spline models, approximation of surfaces constrained by a differential equation, and a general subdivision theorem for Bézier triangles. This book will prove useful to mathematicians and advance mathematics students.
A Mathematical Theory Of Design Foundations Algorithms And Applications
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Author : D. Braha
language : en
Publisher: Springer
Release Date : 2010-12-06
A Mathematical Theory Of Design Foundations Algorithms And Applications written by D. Braha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-06 with Technology & Engineering categories.
Formal Design Theory (PDT) is a mathematical theory of design. The main goal of PDT is to develop a domain independent core model of the design process. The book focuses the reader's attention on the process by which ideas originate and are developed into workable products. In developing PDT, we have been striving toward what has been expressed by the distinguished scholar Simon (1969): that "the science of design is possible and some day we will be able to talk in terms of well-established theories and practices. " The book is divided into five interrelated parts. The conceptual approach is presented first (Part I); followed by the theoretical foundations of PDT (Part II), and from which the algorithmic and pragmatic implications are deduced (Part III). Finally, detailed case-studies illustrate the theory and the methods of the design process (Part IV), and additional practical considerations are evaluated (Part V). The generic nature of the concepts, theory and methods are validated by examples from a variety of disciplines. FDT explores issues such as: algebraic representation of design artifacts, idealized design process cycle, and computational analysis and measurement of design process complexity and quality. FDT's axioms convey the assumptions of the theory about the nature of artifacts, and potential modifications of the artifacts in achieving desired goals or functionality. By being able to state these axioms explicitly, it is possible to derive theorems and corollaries, as well as to develop specific analytical and constructive methodologies.
Mathematical Design Of Wing Sections Second Edition
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Author : Boris Dolomanov
language : en
Publisher: Xlibris Corporation
Release Date : 2014-02-24
Mathematical Design Of Wing Sections Second Edition written by Boris Dolomanov and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-24 with Science categories.
From 1980 I was lead expert of Scientific Product Association ?Shipbuilding?, where I performed the works of creation the CAD System of vessels.1985 finished study the computer systems in Advanced Training Institute for Engineers. This period of life determined my scientific interest and purpose. The subject of researches becomes the problems of mathematical designing. I always combined the main work and the teaching of mathematics. In the dim time ?Perestroika? I and my family (wife and daughter) lived in Germany. I worked on ?Ponnath GmbH & Co?. From 1999 we are in USA. It?s very good new time in our life. In USA I continue the researched work in area of mathematical modeling. Result of this activity is decision the series of tasks and creation of Method for calculation of wings geometry. Boris Dolomanov
Morphing
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Author : Joseph Choma
language : en
Publisher: Hachette UK
Release Date : 2015-01-19
Morphing written by Joseph Choma and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Architecture categories.
Cylinders, spheres and cubes are a small handful of shapes that can be defined by a single word. However, most shapes cannot be found in a dictionary. They belong to an alternative plastic world defined by trigonometry: a mathematical world where all shapes can be described under one systematic language and where any shape can transform into another. This visually striking guidebook clearly and systematically lays out the basic foundation for using these mathematical transformations as design tools. It is intended for architects, designers, and anyone with the curiosity to understand the link between shapes and the equations behind them.
Opt Art
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Author : Robert Bosch
language : en
Publisher: Princeton University Press
Release Date : 2019-11-12
Opt Art written by Robert Bosch 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 2019-11-12 with Art categories.
Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art--opt art. art.
Opt Art
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Author : Robert Bosch
language : en
Publisher: Princeton University Press
Release Date : 2019-11-12
Opt Art written by Robert Bosch 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 2019-11-12 with Mathematics categories.
A fun and stunningly illustrated introduction to the art of linear optimization Linear optimization is a powerful modeling method for discovering the best solution to a problem among a set of available alternatives. It is one of today’s most important branches of mathematics and computer science—and also a surprisingly rich medium for creating breathtaking works of art. Opt Art takes readers on an entertaining tour of linear optimization and its applications, showing along the way how it can be used to design visual art. Robert Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art—opt art. Each chapter in this marvelously illustrated book begins with a problem or puzzle and demonstrates how the solution can be derived using a host of artistic methods and media, including 3D printing, laser cutting, and computer-controlled machining. Bosch focuses on mathematical modeling throughout—converting a problem into a workable mathematical form, solving it using optimization techniques, and examining the results, which can take the form of mosaics, line drawings, and even sculpture. All you need is some high-school algebra, geometry, and calculus to follow along. Featuring more than a hundred illustrations and photos of Bosch’s own art, Opt Art demonstrates how mathematics and computing can be used to create beauty and express emotion through amazing works of art.
Mathematical Design
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Author : Alan Wiltshire
language : en
Publisher:
Release Date : 1995
Mathematical Design written by Alan Wiltshire and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Geometrical drawing categories.
Task Design In Mathematics Education
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Author : Anne Watson
language : en
Publisher: Springer
Release Date : 2015-10-26
Task Design In Mathematics Education written by Anne Watson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-26 with Education categories.
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* This open access book is the product of ICMI Study 22 Task Design in Mathematics Education. The study offers a state-of-the-art summary of relevant research and goes beyond that to develop new insights and new areas of knowledge and study about task design. The authors represent a wide range of countries and cultures and are leading researchers, teachers and designers. In particular, the authors develop explicit understandings of the opportunities and difficulties involved in designing and implementing tasks and of the interfaces between the teaching, researching and designing roles – recognising that these might be undertaken by the same person or by completely separate teams. Tasks generate the activity through which learners meet mathematical concepts, ideas, strategies and learn to use and develop mathematical thinking and modes of enquiry. Teaching includes the selection, modification, design, sequencing, installation, observation and evaluation of tasks. The book illustrates how task design is core to effective teaching, whether the task is a complex, extended, investigation or a small part of a lesson; whether it is part of a curriculum system, such as a textbook, or promotes free standing activity; whether the task comes from published source or is devised by the teacher or the student.