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Author: George E. Martin Publisher: Springer Science & Business Media ISBN: 1461206294 Category : Mathematics Languages : en Pages : 210
Book Description
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: George E. Martin Publisher: Springer Science & Business Media ISBN: 1461206294 Category : Mathematics Languages : en Pages : 210
Book Description
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: Jorge Angeles Publisher: Springer Nature ISBN: 3030431312 Category : Technology & Engineering Languages : en Pages : 182
Book Description
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: T.B. Nichols Publisher: Routledge ISBN: 1317742826 Category : Architecture Languages : en Pages : 241
Book Description
Geometry of Construction has long been acknowledged as the most concise and instructive guide to the technical geometry of the construction industry, and a vital resource for students in architecture, carpentry, stonemasonry and engineering. Beginning with the very basics of technical drawing, it provides a series of increasingly complex exercises to clearly explain all that the reader needs to know about geometry. Each topic is covered with a detailed diagram and carefully written instructions, enabling the student to progress from basics such as the circle and construction of scales, to some of the most complex challenges including the entasis of a column, an ionic volute, the hemispherical dome and the setting out of barrel vaulting. The authors, T. B. Nichols and N. P. Keep, both worked extensively in the construction industry before moving into teaching, so they were ideally suited to produce this highly practical guide. First published in 1947, a revised edition, incorporating numerous suggestions from students and lecturers on Raking Sections, the Projection of Points, of Lines, and of Planes, the True Lengths of Lines, the Oblique Plane and on Roof Surfaces, was produced in 1954. Last published in 1966, it has been unobtainable since then. It remains one of the most useful books for any student in the construction industry.
Author: Michael McDaniel Publisher: Universal-Publishers ISBN: 1627340289 Category : Education Languages : en Pages : 149
Book Description
"'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: Tammy Pelli Publisher: ISBN: 9781930820432 Category : Geometry concept Languages : en Pages : 0
Book Description
Topics include: Segment Constructions; Angles Constructions; Constructions Based on Congruent Triangle Theorems; Special Segments in Triangles; Circle Constructions.
Author: Boris Stilman Publisher: Springer Science & Business Media ISBN: 1461544394 Category : Computers Languages : en Pages : 403
Book Description
Linguistic Geometry: From Search to Construction is the first book of its kind. Linguistic Geometry (LG) is an approach to the construction of mathematical models for large-scale multi-agent systems. A number of such systems, including air/space combat, robotic manufacturing, software re-engineering and Internet cyberwar, can be modeled as abstract board games. These are games with moves that can be represented by the movement of abstract pieces over locations on an abstract board. The purpose of LG is to provide strategies to guide the games' participants to their goals. Traditionally, discovering such strategies required searches in giant game trees. These searches are often beyond the capacity of modern and even conceivable future computers. LG dramatically reduces the size of the search trees, making the problems computationally tractable. LG provides a formalization and abstraction of search heuristics used by advanced experts including chess grandmasters. Essentially, these heuristics replace search with the construction of strategies. To formalize the heuristics, LG employs the theory of formal languages (i.e. formal linguistics), as well as certain geometric structures over an abstract board. The new formal strategies solve problems from different domains far beyond the areas envisioned by the experts. For a number of these domains, Linguistic Geometry yields optimal solutions.
Author: Brian Walmsley Publisher: CC Press ISBN: 9780919852198 Category : Technology & Engineering Languages : en Pages : 170
Book Description
This textbook is designed to develop an understanding of geometrical applications for students in carpentry, millwork, building, and drafting courses. Each unit starts with simple exercises and moves to more complex assignments.
Author: Christopher M. Freeman Publisher: Taylor & Francis ISBN: 1000500276 Category : Education Languages : en Pages : 84
Book Description
Put compasses into your students' hands and behold the results! Hands-On Geometry teaches students to draw accurate constructions of equilateral triangles, squares, and regular hexagons, octagons, and dodecagons; to construct kites and use their diagonals to construct altitudes, angle bisectors, perpendicular bisectors, and the inscribed and circumscribed circles of any triangle; to construct perpendicular lines and rectangles, parallel lines, and parallelograms; and to construct a regular pentagon and a golden rectangle. Students will enjoy fulfilling high standards of precision with these hands-on activities. Hands-On Geometry provides the background students need to become exceptionally well prepared for a formal geometry class. The book provides an easy way to differentiate instruction: Because the lessons are self-explanatory, students can proceed at their own pace, and the finished constructions can be assessed at a glance. Grades 4-6
Author: B. Rosenfeld Publisher: Springer Science & Business Media ISBN: 9780792343905 Category : Mathematics Languages : ja Pages : 424
Book Description
This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
Author: Hans Freudenthal Publisher: Elsevier ISBN: 1483184641 Category : Mathematics Languages : en Pages : 217
Book Description
Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications to closed geodesies; groups of homeomorphisms; complemented modular lattices; and topological descriptive planes. Subsequent chapters focus on collineation groups; exceptional algebras and exceptional groups; the connection between algebra and constructions with ruler and compasses; and the use of differential geometry and analytic group theory methods in foundations of geometry. Von Staudt projectivities of Moufang planes are also considered, and an axiomatic treatment of polar geometry is presented. This monograph will be of interest to students of mathematics.
Author: George E. Martin
Author: George E. Martin
Author: Jorge Angeles
Author: T.B. Nichols
Author: Michael McDaniel
Author: Tammy Pelli
Author: Boris Stilman
Author: Brian Walmsley
Author: Christopher M. Freeman
Author: B. Rosenfeld
Author: Hans Freudenthal