Geometry for the Artist is based on a course of the same name which started in the 1980s at Maharishi International University. It is aimed both at artists willing to dive deeper into geometry and at mathematicians open to learning about applications of mathematics in art. The book includes topics such as perspective, symmetry, topology, fractals, curves, surfaces, and more. A key part of the book’s approach is the analysis of art from a geometric point of view—looking at examples of how artists use each new topic. In addition, exercises encourage students to experiment in their own work with the new ideas presented in each chapter.
This book is an exceptional resource for students in a general-education mathematics course or teacher-education geometry course, and since many assignments involve writing about art, this text is ideal for a writing-intensive course. Moreover, this book will be enjoyed by anyone with an interest in connections between mathematics and art.
Features
Abundant examples of artwork displayed in full color
Suitable as a textbook for a general-education mathematics course or teacher-education geometry course
Designed to be enjoyed by both artists and mathematicians
Author(s): Catherine A. Gorini
Publisher: CRC Press/Chapman & Hall
Year: 2023
Language: English
Pages: 254
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
SECTION I: Introduction
CHAPTER 1: Introduction
1.1. OVERVIEW
1.2. WAYS TO ANALYZE ART
1.3. HOW TO USE THIS BOOK
SECTION II: Symmetry
CHAPTER 2: Symmetry
2.1. THE NATURE OF SYMMETRY
2.2. OVERVIEW OF SYMMETRY
CHAPTER 3: Finite Designs
3.1. SYMMETRIC DESIGNS
3.2. SYMMETRY TRANSFORMATIONS
3.3. SYMMETRIES OF A SQUARE
3.4. SYMMETRIES OF A PINWHEEL
3.5. LEONARDO’S THEOREM
3.6. SIGNATURE OF A SYMMETRIC DESIGN
3.7. IMPORTANT EXAMPLES OF SYMMETRIC DESIGNS
3.8. COMPOUND OR LAYERED DESIGNS
3.9. SYMBOLS AND LOGOS
3.10. SACRED GEOMETRY
3.11. TIPS FOR DETERMINING THE SYMMETRIES OF A DESIGN
3.12. CREATING SYMMETRIC DESIGNS
CHAPTER 4: Band Ornaments
4.1. OVERVIEW
4.2. SYMMETRIES OF A BAND
4.3. THE SEVEN TYPES OF BAND ORNAMENTS
4.4. THE SEVEN TYPES OF SYMMETRIES OF BAND ORNAMENTS
4.5. MAKING A BAND ORNAMENT OF YOUR OWN
CHAPTER 5: The Regular Tilings
5.1. OVERVIEW
5.2. TRANSLATIONS OF A TILING
5.3. A TILING BY SQUARES
5.4. A TILING BY EQUILATERAL TRIANGLES
5.5. A TILING BY REGULAR HEXAGONS
5.6. WHAT WE HAVE LEARNED ABOUT REGULAR TILINGS
5.7. NEW TILINGS FROM OLD
CHAPTER 6: Tilings
6.1. OVERVIEW
6.2. TILINGS WITHOUT ROTATIONS—FOUR TILINGS
6.3. TILINGS WITH GYRATIONS ONLY—SIX TILINGS
6.4. TILINGS WITH KALEIDOSCOPES—FIVE NEW TILINGS PLUS TWO REGULAR TILINGS
6.5. TIPS FOR DETERMINING THE SIGNATURE OF A TILING PATTERN
6.6. SUMMARY OF TILINGS
CHAPTER 7: Symmetry in the Work of MC Escher
7.1. MC ESCHER’S TILINGS
7.2. HOW TO CREATE ESCHER-TYPE TILINGS
7.3. DAY AND NIGHT
7.4. CYCLE
SECTION III: Perspective
CHAPTER 8: Introduction to Linear Perspective
8.1. OVERVIEW
8.2. INTRODUCTION TO LINEAR PERSPECTIVE
8.3. THE GEOMETRY OF LINEAR PERSPECTIVE
8.4. THE CENTRAL VANISHING POINT
8.5. ANALYSIS OF A PERSPECTIVE PICTURE
8.6. HOW TO DRAW A PICTURE IN ONE-POINT PERSPECTIVE
8.7. AERIAL OR ATMOSPHERIC PERSPECTIVE
CHAPTER 9: Drawing Grids in Perspective
9.1. OVERVIEW
9.2. DRAWING A SQUARE GRID IN PERSPECTIVE
9.3. WHERE IS THE DIAGONAL VANISHING POINT?
9.4. FINDING THE DIAGONAL VANISHING POINT IN A PAINTING
9.5. FORESHORTENING DISTANCES IN A PERSPECTIVE PAINTING
9.6. USING GRIDS TO DRAW SHAPES IN PERSPECTIVE
CHAPTER 10: The Conic Sections
10.1. OVERVIEW
10.2. THE CONIC SECTIONS
10.3. THE CIRCLE
10.4. THE ELLIPSE: A CIRCLE IN PERSPECTIVE
10.5. THE PARABOLA: A FOUNTAIN OF WATER
10.6. THE HYPERBOLA: A SHADOW ON A WALL
10.7. DRAWING A CIRCLE IN PERSPECTIVE
CHAPTER 11: Two-Point and Three-Point Perspective
11.1. OVERVIEW
11.2. TWO-POINT PERSPECTIVE
11.3. ESHER’S CYCLE—AN EXAMPLE OF TWO-POINT PERSPECTIVE
11.4. THREE-POINT PERSPECTIVE
11.5. USING TWO-POINT AND THREE-POINT PERSPECTIVE
CHAPTER 12: Perspective in the Work of MC Escher
12.1. OVERVIEW
12.2. RELATIVITY
12.3. BELVEDERE
12.4. ASCENDING AND DESCENDING
SECTION IV: Fractals
CHAPTER 13: Proportion and Similarity
13.1. OVERVIEW
13.2. CONGRUENT FIGURES
13.3. SIMILAR FIGURES
13.4. CONGRUENCE AND SIMILARITY IN ART
13.5. IMPORTANT EXAMPLES OF CONGRUENCE AND SIMILARITY
CHAPTER 14: Fractals
14.1. OVERVIEW
14.2. CONSTRUCTING GEOMETRIC FRACTALS
14.3. NATURAL FRACTALS
14.4. FRACTAL DIMENSION
14.5. APPLICATIONS OF FRACTALS
CHAPTER 15: Dynamical Systems and Chaos
15.1. OVERVIEW
15.2. DYNAMICAL SYSTEMS
15.3. MATHEMATICAL DYNAMICAL SYSTEMS
15.4. CHAOS
15.5. DYNAMICAL SYSTEMS AND CHAOS IN ART
15.6. CHAOS AND CHANCE
CHAPTER 16: The Mandelbrot Set
16.1. OVERVIEW
16.2. THE COMPLEX NUMBERS
16.3. GRAPHING COMPLEX NUMBERS
16.4. CONSTRUCTING THE MANDELBROT SET
16.5. PROPERTIES OF THE MANDELBROT SET
SECTION V: Curves, Spaces, and Geometries
CHAPTER 17: Lines and Curves
17.1. OVERVIEW
17.2. STRAIGHT LINES AND THEIR SLOPES
17.3. CURVES AND CURVATURE
17.4. SPECIAL CURVES
17.5. HOW ARTISTS USE LINES AND CURVES
CHAPTER 18: Surfaces
18.1. OVERVIEW
18.2. SURFACES
18.3. EUCLIDEAN GEOMETRY
18.4. ELLIPTIC GEOMETRY
18.5. HYPERBOLIC GEOMETRY
18.6. THE THREE GEOMETRIES AND CURVATURE
18.7. THE THREE GEOMETRIES AROUND YOU
CHAPTER 19: Euclidean and Non-Euclidean Geometries
19.1. OVERVIEW
19.2. EUCLID’S POSTULATES
19.3. THE VALIDITY OF NON-EUCLIDEAN GEOMETRIES
CHAPTER 20: Topology
20.1. OVERVIEW
20.2. THE KÖNIGSBERG BRIDGE PROBLEM
20.3. TOPOLOGY
20.4. TOPOLOGY IN ART
CHAPTER 21: Pictorial Composition
21.1. OVERVIEW
21.2. GEOMETRIC PRINCIPLES OF PICTORIAL COMPOSITION
21.3. PORTRAITS
21.4. HOW THE EYE MOVES AROUND A PICTURE
21.5. UNDERSTANDING PICTORIAL COMPOSTION
Bibliography
APPENDIX A: Suggestions for Final Projects
A.1. ART RESEARCH PROJECT
A.2. ART RESEARCH TEAM PROJECT
A.3. CREATIVE PROJECT
APPENDIX B: Answers to Selected Exercises
Index
