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Author : Iris Mack Dayoub
Publisher :
ISBN 13 : 9780884881759
Total Pages : 172 pages
Book Rating : 4.8/5 (817 download)
Download or read book Geometry, Constructions and Transformations written by Iris Mack Dayoub and published by . This book was released on 1977 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henk J.M. Bos
Publisher : Springer Science & Business Media
ISBN 13 : 1461300878
Total Pages : 472 pages
Book Rating : 4.4/5 (613 download)
Download or read book Redefining Geometrical Exactness written by Henk J.M. Bos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. He then analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness.
Author : Ronald N. Umble
Publisher : CRC Press
ISBN 13 : 1482234726
Total Pages : 235 pages
Book Rating : 4.4/5 (822 download)
Download or read book Transformational Plane Geometry written by Ronald N. Umble and published by CRC Press. This book was released on 2014-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein's Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer's Sketchpad. Each concept is introduced synthetically (without coordinates) and analytically (with coordinates). Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA. After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane.
Author : Jorge Angeles
Publisher : Springer Nature
ISBN 13 : 3030431312
Total Pages : 182 pages
Book Rating : 4.0/5 (34 download)
Download or read book Fundamentals of Geometry Construction written by Jorge Angeles and published by Springer Nature. This book was released on 2020-04-18 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The textbook provides both beginner and experienced CAD users with the math behind the CAD. The geometry tools introduced here help the reader exploit commercial CAD software to its fullest extent. In fact, the book enables the reader to go beyond what CAD software packages offer in their menus. Chapter 1 summarizes the basic Linear and Vector Algebra pertinent to vectors in 3D, with some novelties: the 2D form of the vector product and the manipulation of “larger" matrices and vectors by means of block-partitioning of larger arrays. In chapter 2 the relations among points, lines and curves in the plane are revised accordingly; the difference between curves representing functions and their geometric counterparts is emphasized. Geometric objects in 3D, namely, points, planes, lines and surfaces are the subject of chapter 3; of the latter, only quadrics are studied, to keep the discussion at an elementary level, but the interested reader is guided to the literature on splines. The concept of affine transformations, at the core of CAD software, is introduced in chapter 4, which includes applications of these transformations to the synthesis of curves and surfaces that would be extremely cumbersome to produce otherwise. The book, catering to various disciplines such as engineering, graphic design, animation and architecture, is kept discipline-independent, while including examples of interest to the various disciplines. Furthermore, the book can be an invaluable complement to undergraduate lectures on CAD.
Author : Michael E. Mortenson
Publisher :
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geometric Transformations for 3D Modeling written by Michael E. Mortenson and published by . This book was released on 2007 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition is a comprehensive introduction to the theory and application of transformations. Presenting the more abstract foundation material in the first three chapters, Geometric Transformations in 3D Modeling reduces the clutter of theoretical derivation and development in the remainder of the text and introduces the operational and more application-oriented tools and concepts as the need arises. It assumes the reader has already taken analytic geometry and first-year calculus and has a working knowledge of basic matrix and vector algebra. This self-contained resource is sure to appeal to those working in 3D modeling, geometric modeling, computer graphics, animation, robotics, and kinematics. Features Explores and develops the subject in much greater breadth and depth than other books, offering readers a better understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relations between transformations. Describes how geometric objects may change position, orientation, or even shape when subjected to mathematical operations, while properties characterizing their geometric identity and integrity remain unchanged. Presents eigenvalues, eigenvectors, and tensors in a way that makes it easier for readers to understand. Contains revised and improved figures, with many in color to highlight important features. Provides exercises throughout nearly all of the chapters whose answers are found at the end of the book.
Author : Isaak Moiseevich I︠A︡glom
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geometric Transformations written by Isaak Moiseevich I︠A︡glom and published by . This book was released on 1962 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George E. Martin
Publisher : Springer Science & Business Media
ISBN 13 : 1461206294
Total Pages : 210 pages
Book Rating : 4.4/5 (612 download)
Download or read book Geometric Constructions written by George E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
Author : Alfred S. Posamentier
Publisher : Dale Seymour Publication
ISBN 13 : 9780866514293
Total Pages : 102 pages
Book Rating : 4.5/5 (142 download)
Download or read book Advanced Geometric Constructions written by Alfred S. Posamentier and published by Dale Seymour Publication. This book was released on 1988 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 19 basic straightedge and compass constructions and construction solutions to algebraic equations. Also explores triangle, circle, and non-compass constructions. Many proofs, exercises and problems.
Author : Исаак Моисеевич Яглом
Publisher : MAA Press
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.0/5 ( download)
Download or read book Geometric Transformations written by Исаак Моисеевич Яглом and published by MAA Press. This book was released on 1962 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost everyone is acquainted with plane Euclidean geometry as it is usually taught in high school. This book introduces the reader to a completely different way of looking at familiar geometrical facts. It is concerned with transformations of the plane that do not alter the shapes and sizes of geometric figures. Such transformations play a fundamental role in the group theoretic approach to geometry. The treatment is direct and simple. The reader is introduced to new ideas and then is urged to solve problems using these ideas. The problems form an essential part of this book and the solutions are given in detail in the second half of the book.
Author : A. M. Yaglom
Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.F/5 ( download)
Download or read book Geometric Transformations written by A. M. Yaglom and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Julius Petersen
Publisher :
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4.:/5 (319 download)
Download or read book Methods and Theories for the Solution of Problems of Geometrical Constructions Applied to 410 Problems written by Julius Petersen and published by . This book was released on 1879 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael McDaniel
Publisher : Universal-Publishers
ISBN 13 : 1627340289
Total Pages : 149 pages
Book Rating : 4.6/5 (273 download)
Download or read book Geometry by Construction written by Michael McDaniel and published by Universal-Publishers. This book was released on 2015-02-05 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: "'Geometry by construction' challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newly published research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material"--Back cover.
Author : Max Jeger
Publisher :
ISBN 13 :
Total Pages : 143 pages
Book Rating : 4.:/5 (636 download)
Download or read book Transformation Geometry written by Max Jeger and published by . This book was released on 1964 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ali R. Amir-Moéz
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.3/5 (91 download)
Download or read book Notes on Geometric Transformations written by Ali R. Amir-Moéz and published by . This book was released on 1998 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tammy Pelli
Publisher :
ISBN 13 : 9781930820432
Total Pages : 0 pages
Book Rating : 4.8/5 (24 download)
Download or read book Constructions written by Tammy Pelli and published by . This book was released on 2004-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics include: Segment Constructions; Angles Constructions; Constructions Based on Congruent Triangle Theorems; Special Segments in Triangles; Circle Constructions.
Author : Isaak Moiseevich I︠A︡glom
Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geometric Transformations written by Isaak Moiseevich I︠A︡glom and published by . This book was released on 1962 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : National Research Council (U.S.). Committee on Rational Transformations
Publisher :
ISBN 13 :
Total Pages : 412 pages
Book Rating : 4.3/5 (91 download)
Download or read book Selected Topics in Alegbraic Geometry written by National Research Council (U.S.). Committee on Rational Transformations and published by . This book was released on 1928 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
