Mathematics of Art
Fall 2008

Professor Annalisa Crannell
Office Hours: by appointment and whenever my door is open
Office: Bonchek College House and 220 Stager
E-mail: annalisa.crannell@fandm.edu
Web Page: www.fandm.edu/people/a_crannell    
Telephone: 717-291-4222


Preceptors: Dierdre Kelly and Craig Harris


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!  

 

Course Materials (What You’ll Need)
from the bookstore:
    • A copy of Flatland, by E. A. Abbott.
    • Rules for Writers, by Diana Hacker
from the Math Office
    • Viewpoints:  Mathematical Perspective and Fractal Geometry in Art
            miscellaneous
                • Access to a word-processor and to an e-mail account.
                • A stapler.    
                • A brain.
            from the art store (see the attached list)


Grading/Calendar
eight 1-page papers    (20%, or 2% each)    almost every Thursday, 3 p.m.
first 4-page paper    (10%)    early October
second 4-page page    (20%)    November
final paper    (20%)    December 16
Math/Art homeworks    (20%)    weekly
final art project    (10%)    December 16


Attendance
You will be learning a lot from your classmates and they will be learning a lot from you, so I expect that you come prepared, with proper materials, and that you participate fully.  Please be advised that Math Department and F&M policy state that penalties (including grade reduction and/or dismissal from the course) may be assessed for excessive, unexcused absences.

 
Weekly Writing Assignments
With a few exceptions, you will have a 1-page paper due every Thursday at 3 p.m., and I will count the best eight of these papers toward your final grade. There are 14 weeks in the class, and you will have two 5-page papers due (see below).  This means you may choose to skip writing a paper twice during the semester without any serious danger to your grade.  I will usually announce the topic of these papers one week in advance, so that you may begin writing during the weekend and revise your paper over the course of the following week.

These papers should be written in  a nice 12-point font (Times is nice, but Optima is like shouting); the margins should be no narrower than 0.75 inches; the lines should be 1.5 spaced, and there should be a title, the due-date, and your name at the top of the page.  You may NOT hand in more than one page, despite various temptations to do so.  I want you to think hard about making your writing as concise and forceful as possible.  


 
Weekly Math /Art Assignments
Every week, you will have assignments that involve drawing.  You will be learning to draw by using math (or perhaps you will be learning to solve mathematics problems by drawing).  A good drawing takes time; I expect that you will spend at least 2 hours on your sketches, so make sure you carve out time for this.  Most students tell me that these sketches (a) take longer than they would have expected and (b) give them a real sense of accomplishment.  

 
The long papers
Over the course of the semester, you will “adopt” a piece of art that uses (or perhaps deliberately misuses) perspective to create an illusion—I will say more about this assignment once class begins.  During the first few weeks of class, you will choose the piece of art and make sure that I approve of your choice.  In October, you will write a paper describing the piece and placing it in an artistic context.  In November, you will write a paper describing the mathematics of the perspective in this piece.  Each of these two papers will become part of the reading assignments for the entire class.  For this reason, each of these papers will have 3 different deadlines: one for one-third of the class; another for another third of the class; and a third for the last five students.

The class times on the Tuesdays after these assignments are due will be devoted to discussing and critiquing the papers that your peers have written.  All students will be expected to participate in these discussions.

On December 16, the final ten-page paper will be due (your final art project will be due the same day).  This paper will describe both the artistic and mathematical aspects of your work . . . that is, it will combine and improve upon the ideas and prose of the previous two papers.


 
Reading Assignments
I expect you to read your text, your classmates’ papers, and (eventually) Flatland and to be prepared to discuss these assignments.  In addition, you will be reading scholarly work related to your “adopted” piece of art.





 
Help
I love to talk about math, art, or life in general.  Please feel free to ask me questions both in and out of class; I've got a lot of office hours and am around a good deal of the time.  I’m even more congenial if you bring me chocolate.  

Your preceptors, Dierdre and Craig, are brilliant and creative.  In addition, they write prose that is specific and evocative.  May you do the same.

The Writing Center (717-291-3866) is available for those who want help with their written projects, and there are also several undergraduate mathematics teaching assistants who hold regular hours (their schedules will be announced shortly).



 

A Supplies List

A pad (or several different-sized pads) of drawing paper.  
Graph paper (optional)
A way to carry your pad of paper and other supplies.
A selection of drawing pencils.
A selection of colored pencils (optional)
A portable pencil sharpener.
A Pink-Pearl or White Eraser
Straightedges (also called ``rulers’’): 12’’ and 18”
A calculator that can do logarithms
Access to computer spreadsheet software.
 “Windows” and washable markers (optional)
An Annotated Supplies List
What you’ll definitely need, what you might want, and why

A pad (or several different-sized pads) of drawing paper.  
You won’t make drawings you’re proud of on lined, 3-hole punch paper.  White, smooth-surface, medium weight paper is best.  Small sketchbooks (4”x 6”) can go with you everywhere and are good for jotting down quick ideas or doing practice sketches; larger sizes (even as large as 18”x24”) give you more space to work on a more detailed drawing.  Newsprint is low-quality and should be used only for exercises that are not meant to be saved or shown; I don’t recommend it for this course.  

Graph paper (optional)
There are many exercises in which you will be drawing vertical and horizontal lines.  You might want to do some of the rough drafts on graph paper, or use a sheet of graph paper with dark lines underneath your white paper for your more formal drawings.  But many people are happy to “wing it” without graph paper, and that’s fine, too.

A way to carry your pad of paper and other supplies.
You don’t want the drawings you work so hard on to be damaged by the rain or to get stepped on just because you can’t carry everything easily.  Art stores sell “portfolios” that can hold large paper.  Large garbage bags can help protect your pad in a downpour.

A selection of drawing pencils.
At the bare minimum, you will need a medium-weight pencil (for example, a # 2 pencil).  Mechanical pencils don’t give you the same flexibility as wooden pencils.  

For even more options while drawing, artists use pencils with a variety of hardnesses.  A “B” or “F” pencil is about the same as a #2 pencil.  To get softer pencils (which make darker lines), choose 2B, 4B and the very soft 6B.  To get harder pencils (which make lighter lines), choose 2H, 4H, and the very hard 6H.  One of the reasons you might want a variety of pencils in this course is that they can help you distinguish between guide lines you’ll be drawing (which you’ll want to erase when the drawing is done) and more permanent lines.  

A selection of colored pencils (optional)
This book doesn’t deal directly with color, but sometimes color gets the creative juices flowing.  If you don’t know much color theory, your pictures of scenes (hallways, rooms, buildings, etc) are actually likely to look better if you do them in black-and-white, but you might want to play with colored pencils when you’re sketching cubes, blocky letters, and other geometric objects.

A portable pencil sharpener.
Since you are likely to use this a LOT in this course, it makes sense to buy a fairly sturdy one.  If you buy a 50-cent sharpener that drops the shavings on your desk and doesn’t get the pencils sharp anyway, you’ll soon wish you had gotten a nicer model.

A Pink-Pearl or White Eraser
You will use your eraser almost as much as you use your pencils.  Good artists know that erasing is an important part of drawing.  In fact, many artists will cover a section of the paper with their pencil and then use an eraser to ``draw’’ the light parts of the scene.  You don’t want to rely on the little eraser on the end of your pencil, or on the whims of a novelty eraser shaped like a smiley face.  And when you’ve almost completed a drawing and want to erase the guidelines, you’ll get sick at heart if your old, hard eraser leaves ugly smudge marks on your paper.  

Straightedges (also called ``rulers’’): 12’’ and 18”
There are two important qualities to straightedges.  One is that they can help you make very straight lines:  avoid bumpy wooden rulers, but plastic or metal rulers are usually fine.  The other is that they help you make long lines (the 6-inch ruler that comes in your daily planner won’t work).  A 12” ruler is probably good enough for most in-class work; for your homework sketches you will probably find yourself wishing for a longer straightedge so that you can comfortably draw lines to vanishing points that are off the edges of your sketchpad.  

A calculator that can do logarithms (optional)
It doesn’t have to be a fancy graphing calculator.  Any calculator that has a button saying “ln” or “log” will be fine.

Access to computer spreadsheet software.
When we do perspective drawing via spreadsheets, we will primarily use Microsoft Excel, but the ideas behind these instructions ought to work with other brands of spreadsheet software, as well.

“Windows” and washable markers (optional)
The early exercises in this book emphasize looking at the world through a window; if you  like these activities you can recreate them anywhere you like by using sheets of Plexiglas, or clear transparencies that you can put into a sturdy (cardboard?) frame.