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Mathematical World

Liberal Arts Mathematics with an Art Emphasis

Patricia OakleyGoshen College

Mathematical World

A survey of selected content chosen to help build basic number sense, develop skills in pattern recognition, use mathematical modeling to represent and investigate practical problems.

Topics: Shapes

• Shapes and Proportions: The Human Figure

• Shapes and Patterns: Pythagoras and Fibonacci

Jacques-Louis David

Le Corbusier: Le ModulorJohn Tenniel

Topics: Symmetry

• Rigid Motions

• Composition of Rigid Motions

• Symmetry

• Symmetry Groups

• Border Patterns

• Wallpaper Patterns

• Tilings

Pompeii

Lakota Blanket

Topics: Perspective

• Vanishing Points

• Geometry of Perspective Drawing

• Viewing Distance and the Picture Plane

• Coordinate Systems

• Anamorphic Art

Albrecht Altdorfer

Albrecht Durer

John Singer Sargent Kelly HouleLimbourg Brothers

Topics: Dimension

• Contour Drawings

• Flatland

• Cubes

• Shape of Space

• Fractals

Salvador Dali

Mark Townsend

Portfolio: 2000

• Create a portfolio that contains images that illustrate the topics that we studied in class.

• Images can be original drawings, photos, clips from magazines.

• The portfolio should demonstrate your understanding of the mathematics behind the topics.

Final Project: 2006

• Topic that connects math and art.

• Include portfolio of images that illustrate the topic.

• Paper that shows the connections between mathematics and art in the chosen topic.

Student Work: Final Project

• Escher

• Pablo Picasso

• Dick Termes

• Border Patterns in Costa Rican Ceramics

• Amish Quilts

• Origami

• Photoshop

• Lissajous Curves

Conclusion

A survey of selected content chosen to help build basic number sense, develop skills in pattern recognition, use mathematical modeling to represent and investigate practical problems.

Quotes

• (This class) helped me to see a completely different side of mathematics. It helped me to see how math appears in nature, and how it can be used in everyday life, as well as in art.

• I had always thought of myself as a person who would never be “good” at math. This class has showed me how math is in everything we do and see. It is not all just crunching numbers and coming out with a figure. It is more, it is the world we live in. I drive my fîancê crazy because I am constantly points out great circles, trinagles, symmetries, and patterns. For me this is wonderful. I have conquered my insecurity in the math world.

References

• Viewpointshttp://mypage.iu.edu/~mathart/viewpoints/

• MATC: Patternhttp://www.dartmouth.edu/~matc/math5.pattern/syllabus.htmlhttp://www.math.dartmouth.edu/~matc/math5.pattern/syllabus01.htmlhttp://www.math.dartmouth.edu/~matc/math5.pattern/index.html

• MATC: Geometry in Art and Architecturehttp://math.dartmouth.edu/~matc/math5.geometry/

• Mathematics in Art and Architecturehttp://www.math.nus.edu.sg/aslaksen/teaching/math-art-arch.shtml

References

• J. Kappraff, Connections: The Geometric Bridge between Art and Science.

• Johathan Choate, Robert L. Devaney, Alice Foster, Fractals: A Toolkit of Dynamics Activities

• Jeffrey Weeks, Exploring the Shape of Space

• Edwin Abbot, Flatland

• Rudolf B. Rucker, Geometry, Relativity, and the Fourth Dimension

• Edward B. Burger and Michael Starbird, The Heart of Mathematics

• Peter Tannenbaum and Robert Arnold, Excursions in Modern Mathematics

• For All Practical Purposes

• L. Christine Kinsey and Teresa E. Moore, Symmetry, Shape, and Space: An Introduction to Mathematics Through Geometry

• Paul Calter, Squaring the Circle: Geometry in Art and Architecture

Student Work: Names

Student Work: Names

Student Work: Border Patterns

Student Work: Border Patterns

Student Work: Border Patterns

Student Work: Border Patterns

Student Work: Tilings

Student Work: Tilings

Part of final portfolio project

Student Work: Perspective

NotesGeometry of One Point

Perspective

Student Work: Contours

Contours of a Cat

Student Work: Portfolio

Student Work: Portfolio

Student Work: Final Project (Photoshop)

Student Work: Final Project (Costa Rican Ceramics)