Geometric Transformations III

New Mathematical Library

I. M. Yaglom

Mathematical Association of America | 1973 | 246 páginas | RAR - PDF | 7,29 Mb

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This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in this series, but can be studies independently. It is devoted to the treatment of affine and projective transformations of the plane these transformations include the congruencies and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the principles of affine and projective geometry may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.


Contents
Translator’s Preface
From the Author’s Preface
Introduction - What is Geometry? (Final Essay)
Chapter 1- Affinitie and Projective Transformations

(Affinities and Projectivities) 10

Parallel projection of a plane onto a plane. Affine transformations of the plane 10

Central projection of a plane onto a plane. Projective transformations of a plane

Central projections which carry a circle into a circle. Stereographic projections 54

Reciprocation (polarity) of the plane. Principle of duality 66

Projective transformation of a line and a circle. Straightedge construction 87

Non-Euclidean Geometry of Lobachevsky-Bolyai (Hyperbolic Geometry) 103

Supplement. Non-Euclidean Geometry of Lobachevsky-Bolyai

(Hyperbolic Geometry)

Livros da mesma série, disponíveis no blog:

Geometric Transformations I (1962)
Geometric Transformations II (1968)

Making Math Accessible for the At-Risk Student: Grades 7-12

Linda Lee Ptacek

Libraries Unlimited | 2011| 185 páginas | RAR - PDF | 11,47 Mb

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12102012ma

Every day, secondary math teachers face classrooms containing students with a wide range of abilities, yet each child is expected to meet the same testing standards. Special education teachers are often asked to collaborate in classrooms outside of their curricular areas providing accommodations and modifications. Both math teachers and special education instructors can benefit from effective, alternative-presentation strategies specifically designed for students struggling with math.

Making Math Accessible for the At-Risk Student comprises organizational, instructional, and motivational activities that are adaptable across grade levels. This cornucopia of best-practice strategies and resources is designed to help at-risk students achieve standards in math. The first six chapters discuss the most common reasons adolescent and preadolescent students struggle with math and present techniques to keep these students engaged in the classroom. The remainder of the book is a treasure trove of activities that utilize the instructional strategies with specific content to help all students succeed.