Geometric Constructions

Author : George E. Martin
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206293

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Geometric Constructions by George E. Martin Pdf

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 : Andrew Sutton
Publisher : Wooden Books Us
Page : 64 pages
File Size : 40,7 Mb
Release : 2022-03-15
Category : Mathematics
ISBN : 1952178096

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Ruler and Compass by Andrew Sutton Pdf

How do you draw a heptagon? What about a heptakaidecagon? How do you fit circles perfectly into triangles? And around them? If the computer is down - could you do it with ruler and compass? In this unique little book, Andrew Sutton guides you through the once treasured principles of ruler and compass constructions, used for centuries by architects, carpenters, stonemasons and master craftsmen. Designed to last until the lights go out, this is a timeless book. WOODEN BOOKS USA. Small books, BIG ideas. Tiny but packed with information. "Stunning" NEW YORK TIMES. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST.

Author : Deane Arganbright
Publisher : CRC Press
Page : 218 pages
File Size : 42,7 Mb
Release : 1993-08-03
Category : Mathematics
ISBN : 0849389380

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Practical Handbook of Spreadsheet Curves and Geometric Constructions by Deane Arganbright Pdf

Practical Handbook of Spreadsheet Curves and Geometric Constructions presents a compelling description of how to use commercially available spreadsheets to design and create high-quality graphs of a variety of curves, including classical curves in mathematics. The book contains more than 65 models for the geometric construction of families of curves such as strophoids, pedals, involutes, and others. Models in the book are designed to be interactive so that users can experiment with them to produce eye-catching curves, designs, and patterns. Examples come from calculus, parametric equations, constructions of classical families, and graphs of conformal mappings of a complex variable. The author, a leading authority on spreadsheets, presents innovative techniques for using spreadsheet graphing to generate large families of lines and circles that describe various curves as envelopes of the families. The final chapter of the book discusses the use of commercial spreadsheets to create animation effects. The book is heavily illustrated, with more than 200 graphs and 60 tables. An accompanying 3.5" disk provides 25 selected examples written in Quattro Pro 2.0, Lotus 1-2-3 2.3, and Microsoft Excel 4.0. Designed for both experienced and novice spreadsheet users, Practical Handbook of Spreadsheet Curves and Geometric Constructions will be an invaluable resource for mathematicians, engineers, scientists, and computer scientists. The book will also benefit professional artists and designers interested in learning new techniques for producing mathematical curves using spreadsheet software.

Author : Wendy Conklin
Publisher : Teacher Created Materials
Page : 11 pages
File Size : 48,6 Mb
Release : 2014-02-01
Category : Electronic
ISBN : 9781425878603

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Geometry Learning Contracts--Understanding Geometric Constructions by Wendy Conklin Pdf

This learning contract lesson allows learners to work at their own paces in a flexible learning environment. Written specifically for mathematics teachers, this lesson helps facilitate the understanding and process of writing learning contracts.

Author : Nicholas D. Kazarinoff
Publisher : Courier Corporation
Page : 160 pages
File Size : 43,6 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486143613

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Ruler and the Round by Nicholas D. Kazarinoff Pdf

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.

Author : Michael McDaniel
Publisher : Universal-Publishers
Page : 150 pages
File Size : 46,8 Mb
Release : 2015-02-05
Category : Geometrical constructions
ISBN : 9781627340281

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Geometry by Construction by Michael McDaniel Pdf

"'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 : Elias C. Tonias,Constantine N. Tonias
Publisher : Springer
Page : 431 pages
File Size : 41,6 Mb
Release : 2016-04-28
Category : Mathematics
ISBN : 9783319242958

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Geometric Procedures for Civil Engineers by Elias C. Tonias,Constantine N. Tonias Pdf

This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.

Author : T.B. Nichols,Norman Keep
Publisher : Routledge
Page : 241 pages
File Size : 43,9 Mb
Release : 2015-09-30
Category : Architecture
ISBN : 9781317742821

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Geometry of Construction: For Builders, Architects, Engineers by T.B. Nichols,Norman Keep Pdf

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 : Roshdi Rashed
Publisher : Routledge
Page : 770 pages
File Size : 50,8 Mb
Release : 2013-06-26
Category : History
ISBN : 9781135072537

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Ibn al-Haytham's Theory of Conics, Geometrical Constructions and Practical Geometry by Roshdi Rashed Pdf

Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3, provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninth and tenth centuries, and the historical and epistemological development of ‘infinitesimal mathematics’ as it became clearly articulated in the oeuvre of Ibn al-Haytham. This volume examines the increasing tendency, after the ninth century, to explain mathematical problems inherited from Greek times using the theory of conics. Roshdi Rashed argues that Ibn al-Haytham completes the transformation of this ‘area of activity,’ into a part of geometry concerned with geometrical constructions, dealing not only with the metrical properties of conic sections but with ways of drawing them and properties of their position and shape. Including extensive commentary from one of world’s foremost authorities on the subject, this book contributes a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context. This fundamental text will appeal to historians of ideas, epistemologists and mathematicians at the most advanced levels of research.

Author : Jorge Angeles,Damiano Pasini
Publisher : Springer Nature
Page : 182 pages
File Size : 41,9 Mb
Release : 2020-04-18
Category : Technology & Engineering
ISBN : 9783030431310

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Fundamentals of Geometry Construction by Jorge Angeles,Damiano Pasini Pdf

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 : Christopher M. Freeman
Publisher : Taylor & Francis
Page : 84 pages
File Size : 46,8 Mb
Release : 2021-09-09
Category : Education
ISBN : 9781000500271

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Hands-On Geometry by Christopher M. Freeman Pdf

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 : Alfred S. Posamentier,William Wernick
Publisher : Unknown
Page : 106 pages
File Size : 41,9 Mb
Release : 1973
Category : Geometrical drawing
ISBN : PSU:000014560293

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Geometric Constructions by Alfred S. Posamentier,William Wernick Pdf

Author : Tammy Pelli,Tammy Pelli Leonard
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2004-02
Category : Geometry concept
ISBN : 1930820437

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Constructions by Tammy Pelli,Tammy Pelli Leonard Pdf

Topics include: Segment Constructions; Angles Constructions; Constructions Based on Congruent Triangle Theorems; Special Segments in Triangles; Circle Constructions.

Author : Сергей Петрович Новиков,Искандер Асанович Тайманов
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 41,6 Mb
Release : 2006
Category : Diffentiable manifolds
ISBN : 9780821839294

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Modern Geometric Structures and Fields by Сергей Петрович Новиков,Искандер Асанович Тайманов Pdf

Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.

Author : Alfred S. Posamentier
Publisher : Dale Seymour Publication
Page : 102 pages
File Size : 45,9 Mb
Release : 1988
Category : Geometrical constructions
ISBN : 0866514295

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Advanced Geometric Constructions by Alfred S. Posamentier Pdf

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.