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Mathematics and Art


Left: Katsushika Hokusai, "In the Hollow of a Wave off the Coast of Kanagawa," woodblock ca. 18305.
Right: Fractal curve generated by three similarity transformations.

Who could use this material?

  • Instructors teaching geometry, algebra, vectors, 3-space coordinates, fractal geometry
  • Art Instructors teaching perspective or art history

Target Audience

  • Undergraduates with at least finite math or college algebra/trig

Course Descripton

Perspective is presented in seven different settings:
  1. Experiment. Real world scenes are outlined with masking tape on windows and digitally photographed for later analysis, reproducing classic Renaissance investigations.

  2. Abstraction. Appropriate mathematics is introduced to describe the window experiments.

  3. Spreadsheet. Using the new mathematics and an ordinary spreadsheet program, true perspective drawings are made with scatter plots and traditional or spreadsheet drawing tools.

  4. Generalization. Phenomena observed in window experiments and spreadsheet drawings are validated as theorems on vanishing points, vanishing lines, rendering of regularly spaced objects, and various other drawing techniques valuable to the artist.

  5. Studio. Pencil drawings are executed using the new theorems.

  6. Seminar. A professional artist visits the class to show and discuss her work, which includes solutions of more advanced perspective problems.

  7. Museum/Analysis. On a field trip to an art museum, students view pre- and post-Renaissance attempts at perspective, and analyze true perspective works by determining the unique correct viewpoint for each piece. Also, students analyze photographs of the classroom building to determine the approximate location of the camera.

Fractal geometry is introduced in the form of a geometric modeling problem (modeling the Wabash River using box counting dimension) and then a fractal drawing program is used to illustrate the use of fractal forms in 19th century Japanese woodblock prints. Students also use the program to create free-form art, and in more technical final projects if they choose.

Components of the course

  • Experiments
  • Field Trip
  • Guest Artist
  • Studio Sessions
  • Computer Lab
  • Lectures, Quizzes
  • Projects

Course "Mathematics and Art" Web Page

Mathematics and Art workshops: Viewpoints

For more information, contact ...

  • Marc Frantz, Department of Mathematical Sciences, Indiana University at Bloomington
  • Annalisa Crannell, Department of Mathematics, Franklin and Marshall College,

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