Metric Affine Geometry

Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers. Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric.

This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated.

The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group.

This monograph is suitable for students and aspiring geometry high school teachers. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Pages xv-xvii SYMBOLS, Pages xix-xx chapter 1 - affine geometry, Pages 1-111 chapter 2 - metric vector spaces, Pages 113-369 chapter 3 - metric affine spaces, Pages 371-426 epilogue, Pages 427-428 bibliography, Page 429 INDEX, Pages 431-435 Affine Geometry -- Metric Vector Spaces -- Metric Affine Spaces. [by] Ernst Snapper [and] Robert J. Troyer. Bibliography: P. [429]