Geometry in Schools

Robert W. Morris (editor)

Studies in Mathematics Education, Volume 5

UNESCO | 1986 | 197 páginas

online: unesdoc.unesco.org

Descrição: This is the fifth volume in a series designed to improve mathematics instruction by providing resource materials for those responsible for mathematics teaching. Focused on geometry in schools, it presents a panorama of current practices around the world and suggests future trends. The 14 chapters consider: "Developments in Geometry Teaching in Three Arab States" (Bannout and Hussain); "Geometry for 13-year-olds in Canada and the United States" (Robitaille and Travers); "Geometry Teaching in Latin America" (Lluis); "Geometry in Southeast Asia" (Peng-yee and Chong-keang); "Transformation Geometry in Retrospect" (Sinha); "Geometry at Secondary School Level in Sierra Leone" (Labor); "Geometry in the Primary School: What is Possible and Desirable" (Jzn); "Some Problems Concerning Teaching Geometry to Pupils Aged 10 to 14" (Koman, Kurina, and Ticha); "Teaching Geometry in the USSR" (Chernysheva, Firsov, and Teljakovskii); "The Crisis of Geometry Teaching" (Glaeser); "An Analysis of Geometry Teaching in the United Kingdom" (Fielker); "What are Some Obstacles to Learning Geometry?" (Bishop); "Teacher Education and the Teaching of Geometry" (Meserve and Meserve); and "Microcomputer-based Courses for Secondary School Plane. Geometry

Famous geometrical theorems and problems, with their history

William Whitehead Rupert

Boston, D.C. Heath & Co. | 1900

online: 
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The author, having derived much pleasure and inspiration from the brief historical notes in some of the mathematical text-books that he studied when a student in college, has thought that, by giving the history of a few of the most celebrated geometrical theorems and problems, he might place a light in the window which may throw a cheerful ray adown the long and sometimes dusty pathway that leads to geometrical truth. In the preparation of this little book most valuable assistance has been derived from Florian Cajori sHistory of Mathematics, James Gows History of Greek Mathematics, and G, J. Allmans Greek Geometry from Thales to Euclid, It is, however, toW. W.Rourse Balls reniarkably interesting Short History of Mathematics that Famous Geometrical Theorems and Problems owes the largest debt. To Professor A, D. Eisenhower, Principal of the Norristown High School, George Q.Sheppard, Professor of Mathematics, Hill School, Pottstown, Pa., Dr. George M.Philips, Principal West Chester State Normal School, and Daniel Carhart, Ce., Dean and Professor of Civil Engineering, Western University of Pennsylvania, who have read this book in manuscript, the author is indebted for valuable, suggestions and many kind words of encouragement.

Eli Maor

Beautiful geometry por Eli Maor; Eugen Jost Idioma: Inglês   Editora: Princeton, New Jersey : Princeton University Press, 2014.

The Pythagorean theorem : a 4,000-year history por Eli Maor Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©2007.

The Facts on File calculus handbook por Eli Maor Idioma: Inglês   Editora: New York : Facts on File, ©2003.

To infinity and beyond : a cultural history of the infinite. por Eli Maor Idioma: Inglês   Editora: Princeton : Princeton University Press, 1991.

Trigonometric delights por Eli Maor Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©1998.

E : the story of a number por Eli Maor Idioma: Inglês   Editora: Princeton, N.J. : Princeton University Press, ©1994.

Geometric Exercises in Paper Folding

Sundara T. Row 

Chicago, The Open Court pub. co | 1917

online: archive.org

online: chestofbooks.com (html)

PDF

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The idea of this book was suggested to me by Kindergarten Gift No. VIII. - Paper-folding. The gift consists of two hundred variously colored squares of paper, a folder, and diagrams and instructions for folding. The paper is colored and glazed on one side. The paper may, however, be of self-color, alike on both sides. In fact, any paper of moderate thickness will answer the purpose, but colored paper shows the creases better, and is more attractive. The kindergarten gift is sold by any dealers in school supplies ; but colored paper of both sorts can be had from stationery dealers. Any sheet of paper can be cut into a square as explained in the opening articles of this book, but it is neat and convenient to have the squares ready cut.

Geometry, Relativity and the Fourth Dimension

Rudolf v.B. Rucker

Dover Publications | 1977

online: archive.org

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Exposition of 4th dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Accessible to lay readers but also of interest to specialists. Includes 141 illustrations

Plane Geometry

Edward Rutledge Robbins

New York ; Cincinnati : American Book Company | 1915

online:  archive.org

Geometry have been :(a) To present a book that has been written for the pupil. The object sought in the study of Geometry is not solely to train the mind to accept only those statements as truth for which convincing reasons can be provided, but to cultivate a foresight that will appreciate both the purpose in making a statement and the process of reasoning by which the ultimate truth is established. Thus, the study of this formal science should develop in the pupil the ability to pursue argument coherently, and to establish one truth by the aid of other known truths, in logical order. The more mature members of a class do not require that the reason for every declaration be given in full in the text; still, to omit it altogether, wrongs those pupils who do not know and cannot perceive the correct reason. But to ask for the reason and to print the paragraph reference meets the requirements of the various degrees of intellectual capacity and maturity in every class. The pupil who knows and knows that he knows need not consult the paragraph cited ;the pupil who does not know may learn for himself the correct reason by the reference. It is obvious that the greater progress an individual makes in assimilating the subject and in entering into its spirit, the less need there will be for the printed reference.

Coordinate Geometry

Luther Pfahler Eisenhart 

Dover Publishing Inc. | 1939 |

online: archive.org

A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises.

College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle

Nathan Altshiller-Court

New York : Barnes & Noble | 1952

online: archive.org

Preface -- To the instructor -- To the student -- Geometric constructions -- Similitude and homothecy -- Properties of the triangle -- The quadrilateral -- The Simson line -- Transversals -- Harmonic division -- Circles -- Recent geometry of the triangle

Dover Publications | 2009 | 336 páginas | PDF | 31 Mb

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Translated into many languages, this book has been the standard university-level text for decades. Revised and enlarged by the author in 1952, it offers today's students exercises in construction problems, similitude, and homothecy, properties of the triangle and the quadrilateral, harmonic division, and circle and triangle geometry. 

The Elements Of Non Euclidean Geometry

Julian Lowell Coolidge

OXFORD AT THE CLARENDON PRESS | 1909

online: archive.org

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Chapters Include: Foundation For Metrical Geometry In A Limited Region; Congruent Transformations; The Three Hypotheses; The Introduction Of Trigonometric Formulae; Analytic Formulae; Consistency And Significance Of The Axioms; The Geometric And Analytic Extension Of Space; The Groups Of Congruent Transformations; Point, Line, And Plane Treated Analytically; The Higher Line Geometry; The Circle And The Sphere; Conic Sections; Quadric Surfaces; Areas And Volumes; Introduction To Differential Geometry; etc.

Introduction To Non Euclidean Geometry

Harold E. Wolfe

The Dryden Press | 1945

online: archive.org

PDF - 8,11 Mb

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Introduction to NON-EUCLIDEAN GEOMETRY by HAROLD E. WOLFE . PREFACE This book has been written in an attempt to provide a satisfactory textbook to be used as a basis for elementary courses in Non-Euclid ean Geometry. The need for such a volume, definitely intended for classroom use and containing substantial lists of exercises, has been evident for some time. It is hoped that this one will meet the re quirements of those instructors who have been teaching the subject tegularly, and also that its appearance will encourage others to institute such courses. x The benefits and amenities of a formal study of Non-Euclidean Geometry are generally recognized. Not only is the subject matter itself valuable and intensely fascinating, well worth the time of any student of mathematics, but there is probably no elementary course which exhibits so clearly the nature and significance of geometry and, indeed, of mathematics in general. However, a mere cursory acquaintance with the subject will not do. One must follow its development at least a little way to see how things come out, and try his hand at demonstrating propositions under circumstances such that intuition no longer serves as a guide. For teachers and prospective teachers of geometry in the secondary schools the study of Non-Euclidean Geometry is invaluable. With out it there is strong likelihood that they will not understand the real nature of the subject they are teaching and the import of its applications to the interpretation of physical space. Among the first books on Non-Euclidean Geometry to appear in English was one, scarcely more than a pamphlet, written in 1880 by G. Chrystal. Even at that early date the value of this study for those preparing to teach was recognized. In the preface to this little brochure, Chrystal expressed his desire to bring pangeometrical speculations under the notice of those engaged in the teaching of geometry He wrote It will not be supposed that I advocate the introduction of pan geometry as a school subject it is for the teacher that I advocate vi PREFACE such a study. It is a great mistake to suppose that it is sufficient for the teacher of an elementary subject to be just ahead of his pupils. No one can be a good elementary teacher who cannot handle his subject with the grasp of a master. Geometrical insight and wealth of geometrical ideas, either natural or acquired, are essential to a good teacher of geometry and I know of no better way of cultivat ing them than by studying pan geometry. Within recent years the number of American colleges and uni versities which offer courses in advanced Euclidean Geometry has increased rapidly. There is evidence that the quality of the teaching of geometry in our secondary schools has, accordingly, greatly improved. But advanced study in Euclidean Geometry is not the only requisite for the good teaching of Euclid. The study of Non-Euclidean Geometry takes its place beside it as an indispensable part of the training of a well-prepared teacher of high school geometry. This book has been prepared primarily for students who have completed a course in calculus. However, although some mathe matical maturity will be found helpful, much of it can be read profitably and with understanding by one who has completed a secondary school course in Euclidean Geometry. He need only omit Chapters V and VI, which make use of trigonometry and calcu lus, and the latter part of Chapter VII. In Chapters II and III, the historical background of the subject has been treated quite fully. It has been said that no subject, when separated from its history, loses more than mathematics. This is particularly true of Non-Euclidean Geometry...

Non-Euclidean Geometry: A Critical And Historical Study Of Its Development

Roberto Bonola

Chicago Open Court Pub. Co | 1912

online: archive.org

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Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky. Includes 181 diagrams.

Table of Contents

Chapter I. The Attempts to prove Euclid's Parallel Postulate.

1-5. The Greek Geometers and the Parallel Postulate

6. The Arabs and the Parallel Postulate

7-10. The Parallel Postulate during the Renaissance and the 17th Century

Chapter II. The Forerunners on Non-Euclidean Geometry.

11-17. GEROLAMO SACCHERI (1667-1733)

18-22. JOHANN HEINRICH LAMBERT (1728-1777)

23-26. The French Geometers towards the End of the 18th Century

27-28. ADRIEN MARIE LEGENDRE (1752-1833)

29. WOLFGANG BOLYAI (1775-1856)

30. FRIEDRICH LUDWIG WACHTER (1792-1817)

30. (bis) BERNHARD FRIEDRICH THIBAUT (1776-1832)

Chapter III. The Founders of Non-Euclidean Geometry.

31-34. KARL FRIEDRICH GAUSS (1777-1855)

35. FERDINAND KARL SCHWEIKART (1780-1859)

36-38. FRANZ ADOLF TAURINUS (1794-1874)

Chapter IV. The Founders of Non-Euclidean Geometry (Cont.).

39-45. NICOLAI IVANOVITSCH LOBATSCHEWSKY (1793-1856)

46-55. JOHANN BOLYAI (1802-1860)

56-58. The Absolute Trigonometry

59. Hypotheses equivalent to Euclid's Postulate

60-65. The Spread of Non-Euclidean Geometry

Chapter V. The Later Development of Non-Euclidean Geometry.

66. Introduction

Differential Geometry and Non-Euclidean Geometry

67-69. Geometry upon a Surface

70-76. Principles of Plane Geometry on the Ideas of RIEMANN

77. Principles of RIEMANN'S Solid Geometry

78. The Work of HELMHOLTZ and the Investigations of LIE

Projective Geometry and Non-Euclidean Geometry

79-83. Subordination of Metrical Geometry to Projective Geometry

84-91. Representation of the Geometry of LOBATSCHEWSKY-BOLYAI on the Euclidean Plane

92. Representation of RIEMANN'S Elliptic Geometry in Euclidean Space

93. Foundation of Geometry upon Descriptive Properties

94. The Impossibility of proving Euclid's Postulate

Appendix I. The Fundamental Principles of Statistics and Euclid's Postulate.

1-3. On the Principle of the Lever

4-8. On the Composition of Forces acting at a Point

9-10. Non-Euclidean Statics

11-12. Deduction of Plane Trigonometry from Statics

Appendix II. CLIFFORD'S Parallels and Surface. Sketch of CLIFFFORD-KLEIN'S Problems.

1-4. CLIFFORD'S Parallels

5-8. CLIFFORD'S Surface

9-11. Sketch of CLIFFORD-KLEIN'S Problem

Appendix III. The Non-Euclidean Parallel Construction and other Allied Constructions.

1-3. The Non-Euclidean Parallel Construction

4. Construction of the Common Perpendicular to two non-intersecting Straight Lines

5. Construction of the Common Parallel to the Straight Lines which bound an Angle

6. Construction of the Straight Line which is perpendicular to one of the lines bounding an acute Angle and Parallel to the other

7. The Absolute and the Parallel Construction

Appendix IV. The Independence of Projective Geometry from Euclid's Postu

1. Statement of the Problem

2. Improper Points and the Complete Projective Plane

3. The Complete Projective Line

4. Combination of Elements

5. Improper Lines

6. Complete Projective Space

7. Indirect Proof of the Independence of Projective Geometry from the Fifth Postulate

8. BELTRAMI'S Direct Proof of this Independence

Appendix V. The Impossibility of proving Euclid's Postulate. An Elementary Demonstration of this Impossibility founded upon the Properties of the System of Circles orthogonal to a Fixed Circle.

1. Introduction

2-7. The System of Circles passing through a Fixed Point

8-12. The System of Circles orthogonal to a Fixed Circle

Index of Authors

The Science of Absolute Space and the Theory of Parallels

A Long Way from Euclid

Constance Reid

 Thomas Y. Crowell Company | 1834

online: archive.org

Dover Publications | 2004 | 304 páginas

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This lively guide by a prominent historian focuses on the role of Euclid's Elements in mathematical developments of the last 2,000 years. No mathematical background beyond elementary algebra and plane geometry is necessary to appreciate the clear and simple explanations, which are augmented by more than 80 drawings. 1963 edition. 

Boxes, Squares and Other Things

A Teacher's Guide for a Unit in Informal Geometry

Marion I. Walter

National Council of Teachers of Mathematics | 1970 | pdf | 2,6 Mb

on-line: eric.ed.gov

Descrição: This unit describes an experience in informal geometry that is based on work with construction paper and milk cartons. The description is mostly of work actually carried out by children in the elementary grades involving such mathematical concepts as congruence, symmetry, the idea of a geometric transformation, and some basic notions of elementary group theory. The purposes of the unit are (1) to give students experience in visualizing two and three dimensional objects, and (2) to give students opportunity to learn to raise questions, pose problems, and learn to solve them.

Foundations of Geometry

David Hilbert

Open Court Publishing Company | 1971 | 226 páginas


on-line: gutenberg.org
on-line: archive.org

Geometry and Billiards

(Student Mathematical Library)
Serge Tabachnikov

American Mathematical Society | 2005 | 176 páginas | pdf | 1,1 Mb

math.psu.edu (link direto - versão draft)

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincaré recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State. 

Famous problems of elementary geometry : the duplication of the cube, the trisection of an angle, the quadrature of the circle

Felix Klein
Hard Press | 2007 | 92 páginas | DjVu

online: archive.org

mediafire.com (2,42 MB)
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Symmetry

Hermann Weyl

Princeton University Press | 1952 | pdf | 21,6 Mb

online: archive.org

Defines symmetry through a discussion of its many uses in a wide variety of fields both academic and natural.

How to Draw a Straight Line: A Lecture on Linkages

(NCTM Classics in Mathematics Education, Volume 6)


Alfred Bray Kempe

National Council of Teachers of Mathematics | 1977 (reimpressão de 1877) | 55 páginas | 1,6 Mb


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edição de 1877
online:
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País plano

Flatland: A Romance of Many Dimensions
(Oxford World's Classics)
Edwin A. Abbott
Oxford University Press, USA | 2006 | 176 páginas | PDF | 740 KB

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Flatland: A Parable of Spiritual Dimensions
(Oneworld Spiritual Classics)
Edwin A. Abbott

Oneworld Publications | 1995 | 160 páginas | 928 KB



on-line: geom.uiuc.edu

mat.ufmg.br (linkdireto)
online: .gutenberg.org
online: gutenberg.org

audio:archive.org

Planolândia: um romance de muitas dimensões
Edwin A. Abbott
(versão brasileira)

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Versão em espanhol, on-line: sectormatematica.cl