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Overview
Foundations of Three-Dimensional Euclidean Geometry provides a modern axiomatic construction of three-dimensional geometry, in an accessible form. The method of this book is a graduated formulation of axioms, such that, by determining all the geometric spaces which satisfy the considered axioms, one may characterize the Euclidean space up to an isomorphism. A special feature of Foundations of Three-Dimensional Euclidean Geometry is the introduction of the parallel axiom at an early stage of the discussion, so that the reader can see what results may be obtained both with and without this important axiom. The many theorems, drawings, exercises, and problems richly enhance the presentation of material. Foundations of Three-Dimensional Euclidean Geometry is suitable as a textbook for a one- or two-semester course on geometry or foundations of geometry for undergraduate and beginning graduate students. Mathematics majors in M.A.T. programs will find that this exposition of a classical subject will contribute greatly to their ability to teach geometry at all levels; and logicians, philosophers, and engineers will benefit from this book's applications to their own interests.Synopsis
Foundations of Three-Dimensional Euclidean Geometry provides a modern axiomatic construction of three-dimensional geometry, in an accessible form. The method of this book is a graduated formulation of axioms, such that, by determining all the geometric spaces which satisfy the considered axioms, one may characterize the Euclidean space up to an isomorphism. A special feature of Foundations of Three-Dimensional Euclidean Geometry is the introduction of the parallel axiom at an early stage of the discussion, so that the reader can see what results may be obtained both with and without this important axiom. The many theorems, drawings, exercises, and problems richly enhance the presentation of material. Foundations of Three-Dimensional Euclidean Geometry is suitable as a textbook for a one- or two-semester course on geometry or foundations of geometry for undergraduate and beginning graduate students. Mathematics majors in M.A.T. programs will find that this exposition of a classical subject will contribute greatly to their ability to teach geometry at all levels; and logicians, philosophers, and engineers will benefit from this book's applications to their own interests.