Plane and Solid Geometry
Nature and the world around us that we ourselves design, furnish, and build contain many geometric patterns and structures. This is one of the reasons that geometry should be studied at school. At first, the study of geometry is experimental. Results are taught and used in numerous examples. Only later do proofs come into play. But are these proofs truly necessary, or can we do without them? A natural answer is that every statement must be provided with a proof, because we want to know whether it is true. However, it is clear that the less experienced student may become frustrated by the pr- ence of too many proofs. Only later will the student understand that proofs not only show the correctness of a statement, but also provide better insight into the relationsamong various propertiesof the objects that arebeing st- ied. Learning statements without proofs, you risk not being able to see the forest for the trees. For this reason, we will pay much attention to a careful presentation of proofs in this book. In the development of the theory of plane geometry there are, however, many tricky questions, especially at the beg- ning. The presentation of proofs at that stage is in general more concealing than revealing. My first objective in writing this book has been to give an accessible - position of the most common notions and properties of elementary Euclidean geometry in dimensions two and three.
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Plane and Solid Geometry
Nature and the world around us that we ourselves design, furnish, and build contain many geometric patterns and structures. This is one of the reasons that geometry should be studied at school. At first, the study of geometry is experimental. Results are taught and used in numerous examples. Only later do proofs come into play. But are these proofs truly necessary, or can we do without them? A natural answer is that every statement must be provided with a proof, because we want to know whether it is true. However, it is clear that the less experienced student may become frustrated by the pr- ence of too many proofs. Only later will the student understand that proofs not only show the correctness of a statement, but also provide better insight into the relationsamong various propertiesof the objects that arebeing st- ied. Learning statements without proofs, you risk not being able to see the forest for the trees. For this reason, we will pay much attention to a careful presentation of proofs in this book. In the development of the theory of plane geometry there are, however, many tricky questions, especially at the beg- ning. The presentation of proofs at that stage is in general more concealing than revealing. My first objective in writing this book has been to give an accessible - position of the most common notions and properties of elementary Euclidean geometry in dimensions two and three.
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Plane and Solid Geometry

Plane and Solid Geometry

Plane and Solid Geometry

Plane and Solid Geometry

Overview

Nature and the world around us that we ourselves design, furnish, and build contain many geometric patterns and structures. This is one of the reasons that geometry should be studied at school. At first, the study of geometry is experimental. Results are taught and used in numerous examples. Only later do proofs come into play. But are these proofs truly necessary, or can we do without them? A natural answer is that every statement must be provided with a proof, because we want to know whether it is true. However, it is clear that the less experienced student may become frustrated by the pr- ence of too many proofs. Only later will the student understand that proofs not only show the correctness of a statement, but also provide better insight into the relationsamong various propertiesof the objects that arebeing st- ied. Learning statements without proofs, you risk not being able to see the forest for the trees. For this reason, we will pay much attention to a careful presentation of proofs in this book. In the development of the theory of plane geometry there are, however, many tricky questions, especially at the beg- ning. The presentation of proofs at that stage is in general more concealing than revealing. My first objective in writing this book has been to give an accessible - position of the most common notions and properties of elementary Euclidean geometry in dimensions two and three.

Product Details

ISBN-13: 9780387782409
Publisher: Springer New York
Publication date: 10/08/2008
Series: Universitext
Edition description: 2008
Pages: 349
Product dimensions: 6.00(w) x 9.20(h) x 0.90(d)

Table of Contents

Plane Geometry.- Transformations.- Symmetry.- Curves.- Solid Geometry.
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