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.
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 books approach is the analysis of art from a geometric point of viewlooking 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
Section I. Introduction.
1. Introduction. 1.1. Overview. 1.2. Ways to
Analyze Art. 1.3. How to use this Book. Section II. Symmetry.
2. Symmetry.
2.1. The Nature of Symmetry. 2.2. Overview of Symmetry.
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. Leonardos 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.
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.
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.
6. Tilings. 6.1. Overview. 6.2. Tilings without RotationsFour
Tilings. 6.3. Tilings with Gyrations OnlySix Tilings. 6.4. Tilings with
KaleidoscopesFive New Tilings Plus Two Regular Tilings. 6.5. Tips For
Determining the Signature of a Tiling Pattern. 6.6. Summary of Tilings.
7.
Symmetry in The Work of MC Escher. 7.1. MC Eschers Tilings. 7.2. How to
Create Escher-Type Tilings. 7.3. Day and Night. 7.4. Cycle. Section III.
Perspective.
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.
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.
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.
11. Two-Point and Three-Point
Perspective. 11.1. Overview. 11.2. Two-Point Perspective. 11.3. Eshers
CycleAn Example of Two-Point Perspective. 11.4. Three-Point Perspective.
11.5. Using Two-Point and Three-Point Perspective.
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.
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.
14. Fractals. 14.1. Overview. 14.2. Constructing
Geometric Fractals. 14.3. Natural Fractals. 14.4. Fractal Dimension. 14.5.
Applications OF Fractals.
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.
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.
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.
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.
19. Euclidean and
Non-Euclidean Geometries. 19.1. Overview. 19.2. Euclids Postulates. 19.3.
The Validity of Non-Euclidean Geometries.
20. Topology. 20.1. Overview. 20.2.
The Konigsberg Bridge Problem. 20.3. Topology. 20.4. Topology in Art.
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 Composition. 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.
Catherine A. Gorini is a professor of mathematics at Maharishi International University (MIU) in Fairfield, Iowa, where she has taught for over forty years and served as dean of the faculty and dean of the College of Arts and Sciences. Her interests include geometry and connections between geometry and art, as well as mathematics education, connections between mathematics and consciousness, and liberal arts education. She started developing a geometry course for art majors over thirty years ago. This course is now popular with students of all majors. Her numerous teaching awards include the Outstanding Teacher of the Year award by MIU students in 2021 and the Award for Distinguished College or University Teaching of Mathematics given by the Mathematical Association of America in 2001. She received the 2019 Wege Award for Research from MIU.
Gorini edited Geometry at Work, published by the Mathematical Association of America, wrote the Facts on File Geometry Handbook, and has published journal articles in geometry, mathematics education, connections between mathematics and art, and the relationship between consciousness and mathematics. She is the executive editor of the International Journal of Mathematics and Consciousness and holds a PhD in mathematics from the University of Virginia in algebraic topology.
