MA398 -- Visualizing Mathematics
Description
This course will be an opportunity to explore how various aspects of
mathematics can be visualized by physical and virtual models, often in
quite beautiful ways, and conversely how mathematics can be used as a tool
in designing beautiful physical and virtual models.
Here are some examples that we may look at, but some choice of topics
will be guided by the interests of the class members.
- Symmetry: How many different kinds of wallpaper patterns are there?
How can we recognize them?
- Polyhedra: What are they, and what role do they play in art,
chemistry, etc.?
- Proofs without words: How can we "see" such formulas as the sum
of the first n odd integers is n squared?
- The fourth dimension: How can we visualize it?
- The Mandelbrot set: Some of us have seen it many times. What is it?
- Fractals: What are they, and how are some fractal images generated?
- Animations: What is some mathematics underlying animated films such
as those produced by Pixar?
We will construct both physical and virtual models, using some free
(but incredibly powerful) software, such as POV-Ray --
see http://www.povray.org.
The prerequisite for the course is facility with algebra and geometry,
and a willingness to learn more as needed. Calculus is not a
prerequisite, but if you know it, you will find use for it! Knowledge
of a particular computer programming language
is not a prerequisite, but we will be learning how to use
some computer programs that require some attention to logic and
detail, so patience in this regard is likely to be needed.
At the end of the course it would be nice to host an exhibition!
Course Information
Course Notes
Assignments
Some Interesting Websites
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Art and Music
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Beyond the Third Dimension
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Bridges The Bridges Organization focuses on
connections between art and mathematics
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Bridging the Gap Between Math and Art Bridges Festival:
Mathematical Connections in Art, Music and Science
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Discovering the Art of Mathematics
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Erik Demaine Computer scientist, mathematician and artist
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European Society for Mathematics and the Arts
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FlowingData "FlowingData explores how statisticians, designers, data scientists, and others use analysis, visualization, and exploration to understand data and ourselves."
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The International Society of the Arts, Mathematics, and Architecture
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Journal of Humanistic Mathematics
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Manny's Math Art "This FB page is for digital + conventional artwork of any kind that demonstrates mathematical and aesthetic qualities."
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Math and Art: The Good, the Bad, and the Pretty Course at Franklin and Marshall College
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Math and the Art of M.C. Escher
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Mathematical Imagery
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Mathematics and Art Wikipedia article
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Mathematics and Art Feature column of the American Mathematical Society
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Mathematics and Art -- So Many Connections Article by Doris Schattschneider
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Mathematics in Art and Architecture
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The Museum of Math New Museum of Mathematics in New York
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Topics in Mathematics: Art and Music Resource list from the Math Archives
- The University of Kentucky Center for Visualization and Virtual Environments
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Virtual Math Museum
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A Virtual Space-Time Travel Machine
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Visual Insight American Mathematical Society blog on visualizing mathematics
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Visualizing Math Tumblr
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Visual Mathematics
Elements and Principles of Design -- Documents by Daniel Lee
Software
- POV-Ray -- Raytracing software
- SketchUp Free 3D modeling software
- Blender Powerful modeling software
- OpenSCAD Free 3D modeling software
- Documentation. See also the examples available to you when you run the program.
- Some Examples
- Autodesk 123D Collection of apps for modeling, including:
- GeoGebra Algebra and geometry
- Sage General computation
- Wingeom Geometry (PC only)
Three-Dimensional Printing
Art
Dance
Fourth Dimension
Fractals
Games
Infinity
Non-Euclidean Geometry
Mechanisms
Music
Origami
Polyhedra
Puzzles
Sculpture
Spherical Geometry
Symmetry
Tensegrity
Videos
