Exploring Discrete Geometry / Thomas Q. Sibley.

Format:

Book

Author/Creator:

Sibley, Thomas Q., author.

Series:

Annenberg communication series ; Volume 56.

Anneli Lax New Mathematical Library ; Volume 56

Language:

English

Subjects (All):

Discrete geometry--Textbooks.

Discrete geometry.

Physical Description:

1 online resource (170 pages)

Edition:

First edition.

Place of Publication:

Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society, [2024]

Summary:

Together with its clear mathematical exposition, the problems in this book take the reader from an introduction to discrete geometry all the way to its frontiers. Investigations start with easily drawn figures, such as dividing a polygon into triangles or finding the minimum number of "guards" for a polygon ("art gallery" problem). These early explorations build intuition and set the stage. Variations on the initial problems stretch this intuition in new directions. These variations on problems together with growing intuition and understanding illustrate the theme of this book: "When you have answered the question, it is time to question the answer." Numerous drawings, informal explanations, and careful reasoning build on high school algebra and geometry.

Contents:

Cover

Half-title page

Title page

Copyright

Dedication

Contents

Introduction

Acknowledgments

Chapter 1. Beginning Explorations

1.1. Lines and Regions

1.2. Diagonals and Triangulations

1.3. Distances and Points

1.4. The Art Gallery Problem

1.5. Geometric Patterns

1.6. Voronoi Diagrams

Appendix. What Is a Polygon?

Chapter 2. First Variations

2.1. Lines and Regions

2.2. Diagonals and Triangulations

2.3. Distances and Points

2.4. The Art Gallery Problem

2.5. Geometric Patterns

2.6. Voronoi Diagrams

Chapter 3. Further Variations

3.1. Lines and Regions

3.2. Diagonals and Triangulations

3.3. Distances and Points

3.4. The Art Gallery Problem

3.5. Geometric Patterns

3.6. Voronoi Diagrams

Chapter 4. Final Explorations and Connections

4.1. Lines and Regions

4.2. Diagonals and Triangulations

4.3. Distances and Points

4.4. Art Gallery Problems

4.5. Geometric Patterns

4.6. Voronoi Diagrams

Answers to Exercises

Suggested Reading

Bibliography

Index

Terms

People

Back Cover.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

ISBN:

1-4704-7808-0