Transformational plane geometry
type: Item
instance of: scholarly article
zbMATH Open document ID: 1311.51001
author: Zhigang Han
author: Ronald N. Umble
publication date: 2014-11-10T00:00:00Z
Mathematics Subject Classification ID: 51-01
Mathematics Subject Classification ID: 51N10
Mathematics Subject Classification ID: 51N20
Mathematics Subject Classification ID: 97G40
Mathematics Subject Classification ID: 97G50
zbMATH DE Number: 6367311
zbMATH Keywords: Euclidean plane geometry
zbMATH Keywords: isometry
zbMATH Keywords: similarity
zbMATH Keywords: translation
zbMATH Keywords: rotation
zbMATH Keywords: reflection
zbMATH Keywords: rosette group
zbMATH Keywords: frieze group
zbMATH Keywords: wallpaper group
zbMATH Keywords: cristallographic restriction
zbMATH Keywords: edge tessellation
zbMATH Keywords: Penrose tiling
describes a project that uses: Geometer's Sketchpad
MaRDI profile type: Publication
title: Transformational plane geometry
published in: Textbooks in Mathematics
review text: This book is designed for a one semester course at the junior undergraduate level and turns especially to future educators in the USA. Before the authors address the reader in the Preface, surprisingly in the Foreword two graduate students in mathematics education present evidence that the content of the book relates directly to two national (US) standards for mathematics; furthermore, the Foreword contains valuable tips for prospective teachers anywhere. More than 100 very aesthetical figures catch the reader's eyes even when only browsing through the book. ``This text provides a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. Indeed, as indicated in the National Council of Teachers of Mathematics: Principles and Standards of School Mathematics\dots the transformational approach is the methodology of choice for teaching geometry in the secondary schools:\dots.'' Each new concept is introduced synthetically and analytically, and often consolidated by examples. For the plane Euclidean geometry the authors use 5 undefined terms and 10 postulates, that are more than necessary, in order to begin transformational geometry as soon as possible. Some of the chapters contain ``exploratory activities'' in order to motivate the subsequent ideas; hereto the authors use a software which performs geometrical constructions such as \texttt{Geometer's sketchpad}. The arrangement and clarity of the text meets the most demanding pedagogical and mathematical requirements. Highlights of the book are the classification of isometries and similarities of the Euclidean plane. Although the text offers a wonderful first step into transformational plane geometry, the title promises too much: affine and projective transformations of the plane are not even mentioned. In particular the reviewer appreciated the elaborations in Chapter 7 that are accompanied by numerous well-chosen figures.NEWLINENEWLINEThe text is divided into 8 chapters, each begins with an ov…
reviewed by: Rolf Riesinger
description: scientific article; zbMATH DE number 6367311