Mathematics of Art
Fall 2011

General Remarks on the Course    
Welcome to Franklin & Marshall College!  The aim of this course is to do just that—to welcome you into a community of scholars.  At the heart of our community lies a dedication to writing and scholarship, and during the semester you will get a chance to partake in both of these activities.

The two main questions that we will be asking this semester are these:  How do we fit a 3-dimensional world on a 2-dimensional canvas?  and How do we look at a piece of perspective art?  Toward the end of the semester, we will build on these concepts to explore other kinds of dimensions (we’ll tour 4-dimensional space and draw several fractional-dimensional objects).   You will learn to answer our two main questions by asking and solving geometric problems, by drawing your answers to these questions, by reading, and--of course--by communicating your answers to others both orally and in writing.

In addition, you will become the class expert on one piece of art.  You will first explore the history and artistic significance of this piece by doing research in the library--that is, you will learn what other scholars have said about this piece of art.  You will then apply what you have learned in the class to describe the mathematical basis of perspective of this piece of art--that is, you will BE the scholar on this aspect of this piece.

In the past, students have used the ideas they learned in this course as the basis for future projects at F&M and in graduate school:  studying architecture, creating mathematics education projects, doing research on tiling patterns in Spain and Italy, and more.   Let me know about your own interests and goals! 


The Summer Assignment

  Plato's Allegory of the Cave
   and climate change readings

 

Links to course resources   
The course syllabus
Supplies list
A weekly schedule

One-page paper assignments
Research paper assignment

Getting ready for the final paper and final art project

How to Format Figures
How to cite and format a bibliography

How I'll grade the final paper
How I'll grade your final art project


Examples of Math in the Art

Our course library page, put together by the amazing Louise Kulp

Upcoming open-office hours (just drop in)
Thursday, December 8
2 - 4 p.m.
Tuesday, December 13
9-noon, 3:30-5 p.m.


Some hyper-cube links, courtesy of Professor McCooey.

Stereoscopic hypercube viewer: pretty nifty -- it's not just hypercubes. You can build fancy polytopes via cartesian products, etc.
    http://dogfeathers.com/java/hypercube2.html
    It has non-stereo options, too.

    Related: http://dogfeathers.com/java/hyperstar.html#hyperplanes

    Cross-sections of the hyper-cube: .
    http://demonstrations.wolfram.com/SectionsOfTheFourCube/

    There is a difference between cross-sections and projections -- Flatland versus Plato's cave. And one of our projections is stereoscopic, so this comes up:
    http://torus.math.uiuc.edu/jms/java/stereop/



Professor Annalisa Crannell
Office Hours: by appointment and whenever my door is open
Office:  204 Stager
E-mail: annalisa.crannell@fandm.edu
Web Page: http://edisk.fandm.edu/annalisa.crannell    
Telephone: 717-291-4222