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.
Download or read book Geometry of Construction For Builders Architects Engineers written by T.B. Nichols and published by Routledge. This book was released on 2015-09-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ruler and Compass written by Andrew Sutton and published by Bloomsbury Publishing USA. This book was released on 2009-11-03 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the origins and principles of geometry, describing geometric constructions that can be achieved through the use of rulers and compasses.
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.
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.
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.
Download or read book Hands On Geometry written by Christopher M. Freeman and published by Taylor & Francis. This book was released on 2021-09-09 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Construction Geometry written by Brian Walmsley and published by CC Press. This book was released on 1999-03 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Hands On Geometry written by Christopher M. Freeman and published by Routledge. This book was released on 2021-09-09 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Linguistic Geometry written by Boris Stilman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stereotomy written by José Calvo-López and published by Springer Nature. This book was released on 2020-08-08 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the general concepts in stereotomy and its connection with descriptive geometry, the social background of its practitioners and theoreticians, the general methods and tools of this technology, and the specific procedures for the members built in hewn stone, including arches, squinches, stairs and vaults, ending with a chapter discussing the open problems in this field. Thus, it can be used as a reference book in the subject, but it can also read as a compelling narrative on this subject, one of the main branches of pre-industrial technology. Construction in hewn stone requires the use of geometrical methods and tools to assure that individual stones, either blocks or voussoirs, fit with one another and conform to the general shape of walls, arches or vaults. During the Late Middle Ages and the Renaissance, such techniques and instruments were developed empirically by masons and architects. Later on, learned mathematicians and engineers introduced refinements in these procedures and this branch of knowledge, known as stereotomy, furnished much material to descriptive geometry, a science born with the French Revolution which provided the foundation for projective geometry.
Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 1997-02-28 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Islamic Geometric Patterns written by Jay Bonner and published by Springer. This book was released on 2017-08-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this unique book is an in-depth examination of the polygonal technique; the primary method used by master artists of the past in creating Islamic geometric patterns. The author details the design methodology responsible for this all-but-lost art form and presents evidence for its use from the historical record, both of which are vital contributions to the understanding of this ornamental tradition. Additionally, the author examines the historical development of Islamic geometric patterns, the significance of geometric design within the broader context of Islamic ornament as a whole, the formative role that geometry plays throughout the Islamic ornamental arts (including calligraphy, the floral idiom, dome decoration, geometric patterns, and more), and the underexamined question of pattern classification. Featuring over 600 beautiful color images, Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Con struction is a valuable addition to the literature of Islamic art, architecture and geometric patterns. This book is ideal for students and scholars of geometry, the history of mathematics, and the history of Islamic art, architecture, and culture. In addition, artists, designers, craftspeople, and architects will all find this book an exceptionally informative and useful asset in their fields. Jay Bonner is an architectural ornamentalist and unaffiliated scholar of Islamic geometric design. He received his MDes from the Royal College of Art in London (1983). He has contributed ornamental designs for many international architectural projects, including the expansion of both the al-Masjid al-Haram (Grand Mosque) in Mecca, and the al-Masjid an Nawabi (Prophet’s Mosque) in Medina, as well the Tomb of Sheikh Hujwiri in Lahore, and the Ismaili Centre in London – to name but a few. He is committed to the revitalization of Islamic geometric design through the teaching of traditional methodological practices. To this end, in addition to publishing, Jay Bonner has lectured and taught design seminars at many universities and conferences in North America, Europe, North Africa and Asia.
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.
Download or read book A Beginner s Guide to Constructing the Universe written by Michael S. Schneider and published by Harper Collins. This book was released on 2014-04-01 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it. Contains numerous b&w photos and illustrations.
Download or read book Ruler and the Round written by Nicholas D. Kazarinoff and published by Courier Corporation. This book was released on 2012-09-11 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intriguing look at the "impossible" geometric constructions (those that defy completion with just a ruler and a compass), this book covers angle trisection and circle division. 1970 edition.
