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Author : Beauregard Stubblefield
Publisher : Unknown
Page : 280 pages
File Size : 46,9 Mb
Release : 1969
Category : Geometry
ISBN : PSU:000027307458
Author : Meridon Vestal Garner,B. G. Nunley
Publisher : Unknown
Page : 186 pages
File Size : 40,6 Mb
Release : 1971
Category : Geometria
ISBN : 0876203500
Here, explored in an intuitive manner, are the basic concepts of geometry required for effective teaching of elementary school mathematics. The text investigates the metric and non-metric properties of both plane and three-dimensional geometric figures. Also included is a study of plane coordinate geometry. Very precise mathematically, this text will serve as the basis for a more rigorous study of geometry. Answers to selected problems are also provided.
Author : Margaret Wiscamb Hutchinson
Publisher : Merrill Publishing Company
Page : 324 pages
File Size : 49,8 Mb
Release : 1972-01-01
Category : Geometry
ISBN : 0675094275
Author : Alfred Tarski
Publisher : Univ of California Press
Page : 70 pages
File Size : 48,7 Mb
Release : 2023-11-15
Category : Mathematics
ISBN : 9780520348097
Author : Melvin Hausner
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 44,6 Mb
Release : 2018-10-17
Category : Mathematics
ISBN : 9780486835396
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Author : the late Richard Courant,Herbert Robbins
Publisher : Oxford University Press
Page : 592 pages
File Size : 41,9 Mb
Release : 1996-07-18
Category : Mathematics
ISBN : 019975487X
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.
Author : Daniel C. Alexander,Geralyn M. Koeberlein
Publisher : Unknown
Page : 624 pages
File Size : 45,5 Mb
Release : 2019
Category : Electronic
ISBN : 1337614084
ELEMENTARY GEOMETRY FOR COLLEGE STUDENTS, 7th Edition, is designed to help students develop a comprehensive vocabulary of geometry, an intuitive and inductive approach to the development of principles, and strong deductive skills to solve geometry-based real-world applications. Over 150 new exercises provide additional practice in writing proofs. Available with access to WebAssign, an online study tool that helps students master the course concepts.
Author : Strassburg
Publisher : Unknown
Page : 118 pages
File Size : 50,5 Mb
Release : 2021-12-17
Category : Electronic
ISBN : 1928538983
The Intuitive Geometry method is a basic set of principles for using overlapping circles to create and design anything. The method includes the circle, square, triangle, hexagon, pentagon, spirals, waves, and scaling. The book includes the method with step by step instructions, step by step examples and artwork to showcase the method.
Author : Israel M. Gelfand,Tatiana Alekseyevskaya (Gelfand)
Publisher : Springer Nature
Page : 420 pages
File Size : 55,5 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9781071602997
This text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format – the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class. Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject. Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and “move” them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certain operations and the instruments to perform these operations are available for drawing objects and figures on the plane. This structure corresponds to presenting, sequentially, projective, affine, symplectic, and Euclidean geometries, all the while ensuring students have the necessary tools to follow along. Geometry is suitable for a large audience, which includes not only high school geometry students, but also teachers and anyone else interested in improving their geometrical vision and intuition, skills useful in many professions. Similarly, experienced mathematicians can appreciate the book’s unique way of presenting plane geometry in a simple form while adhering to its depth and rigor. “Gelfand was a great mathematician and also a great teacher. The book provides an atypical view of geometry. Gelfand gets to the intuitive core of geometry, to the phenomena of shapes and how they move in the plane, leading us to a better understanding of what coordinate geometry and axiomatic geometry seek to describe.” - Mark Saul, PhD, Executive Director, Julia Robinson Mathematics Festival “The subject matter is presented as intuitive, interesting and fun. No previous knowledge of the subject is required. Starting from the simplest concepts and by inculcating in the reader the use of visualization skills, [and] after reading the explanations and working through the examples, you will be able to confidently tackle the interesting problems posed. I highly recommend the book to any person interested in this fascinating branch of mathematics.” - Ricardo Gorrin, a student of the Extended Gelfand Correspondence Program in Mathematics (EGCPM)
Author : K. Böröczky,G. Fejes Tóth
Publisher : North Holland
Page : 528 pages
File Size : 41,6 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015033998355
Author : Zalman Usiskin
Publisher : IAP
Page : 125 pages
File Size : 49,5 Mb
Release : 2008-01-01
Category : Education
ISBN : 9781607526001
This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published. Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are “natural number,” “parallel lines” and “congruent triangles,” “trapezoid” and “isosceles trapezoid,” the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division. Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed. As a result, many students misuse and otherwise do not understand the role of definition in mathematics. We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated. The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.
Author : Gail S. Konkle
Publisher : Unknown
Page : 268 pages
File Size : 40,9 Mb
Release : 1974
Category : Geometry
ISBN : UOM:49015000689126
Author : Emily Carson,Renate Huber
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 52,8 Mb
Release : 2006-01-24
Category : Mathematics
ISBN : 1402040393
Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.
Author : Paul Alexandroff
Publisher : Courier Corporation
Page : 68 pages
File Size : 52,6 Mb
Release : 1961-06-01
Category : Mathematics
ISBN : 9780486607474
Alexandroff's beautiful and elegant introduction to topology was originally published in 1932 as an extension of certain aspects of Hilbert's Anschauliche Geometrie. The text has long been recognized as one of the finest presentations of the fundamental concepts, vital for mathematicians who haven't time for extensive study and for beginning investigators. The book is not a substitute for a systematic text, but an unusually useful intuitive approach to the basic concepts. Its aim is to present these concepts in a clear, elementary fashion without sacrificing their profundity or exactness and to give some indication of how they are useful in increasingly more areas of mathematics. The author proceeds from the basics of set-theoretic topology, through those topological theorems and questions which are based upon the concept of the algebraic complex, to the concept of Betti groups which binds together central topological theories in a whole and upon which applications of topology largely rest. Wholly consistent with current investigations, in which a larger and larger part of topology is governed by the concept of homology, the book deals primarily with the concepts of complex, cycle, and homology. It points the way toward a systematic and entirely geometrically oriented theory of the most general structures of space. First English translation, prepared for Dover by Alan E. Farley. Preface by David Hilbert. Author's Foreword. Index. 25 figures.
Author : Grant W. Reid
Publisher : John Wiley & Sons
Page : 192 pages
File Size : 55,7 Mb
Release : 2007-06-29
Category : Architecture
ISBN : 9780470112311
One of the most difficult tasks for a designer is to translate concepts into specific and detailed organizations of space. From Concept to Form in Landscape Design, Second Edition provides vital, functional techniques that make the transformation easier and more effective. This perceptive resource examines both traditional and nontraditional methods of landscape design, providing the conceptual and philosophical foundations for ideas and their visual expression. The revised and expanded Second Edition includes: * A new chapter dealing with the creative thought process for generating ideas * Precise case studies showing sequential form evolution * Hundreds of detailed photographs to assist in visualizing various techniques * Inspiring images from nature for naturalistic form development * Atypical design examples as impetus for innovation * Accompanying web site with projects for classroom students and self-learners alike From Concept to Form in Landscape Design, Second Edition presents the landscape transformation process in a highly visual manner, creating both a vivid learning experience for students and a useful toolbox for working designers. Replete with compelling, valuable, and accessible insights for designing outdoor spaces, Reid's book is an ideal blend of inspiration and application.