Mathematics of Art:  One-page papers

Socrates Paper Socrates, in the Allegory of the Cave, claims,
 
“Some persons fancy that instruction is like giving eyes to the blind, but we say that the faculty of sight was always there, and that the soul only requires to be turned round towards the light.”
 
Do you agree?  Give me an example of a time you learned something important to you.  Was it more like “getting eyes” where you had been blind, or more like discovering something you already somehow knew?
Taping Exercise In a one-page paper, describe what we did in the taping exercise on the first Friday of class.  Include not only the details of what we did, but also some of the lessons that you learned from the exercise.   If there are confusions or questions that you have, feel free to include those, too.

I am interested in this paper partly for feedback reasons (that is, I want to see if what you learned is what I thought you learned).  I also want you to practice using correct, descriptive terminology (distinguishing between objects and their images).
How to succeed in your classes Over the course of the first week of class, I want you to interview your professors; ask each of them what is the best way to study for their class. You will write an essay based on what they tell you, so take good notes as you interview them.  For this paper, describe something worth noting that you learned from talking to your professors.  Perhaps you discovered that they all emphasized the same idea; perhaps they were wildly different in their approach.  Perhaps you heard just what you expected to hear (and that surprised you), or perhaps you learned something new by talking to them.  

In this paper, I want you to pay careful attention to developing a thesis (an interesting sentence with an interesting verb) and to supporting that thesis with specific, relevant details.
Blind Copying Exercise Blind Copying Exercise
Vignette Summary Choose one of the artist vignettes from our textbook, “Viewpoints: Mathematical Perspective and Fractal Geometry in Art”.  What is the main point the artist is trying to make in his or her essay?  Summarize the parts of the essay that support this point (or if you think the artist did not support that point well, say so).

What these 1-page papers (Socrates redux and Vignette Summary) have in common is this:  I want you to commit to a thesis, and then use judicious and accurate evidence from a text to support your argument.  Do you understand what your author is actually saying?  Can you paraphrase accurately?  Do you include relevant quotations correctly?  Can you construct an argument in support of your own thesis, even though other people could reasonable argue a different thesis?
Active/Passive paper Write one page with two paragraphs about your art project.  (The two paragraphs can be two different topics, or the second paragraph might continue the topic that the first paragraph starts.)
 
    You should write one of these paragraphs entirely in the active voice.  
    The other paragraph should be written (by you) entirely in the passive voice.  
    There should be no neutral verbs anywhere on the page.
What kinds of math are in your piece of art? I have put you into groups based on mathematical similarities in your artwork. You should meet with your groups and figure out what it is about your pieces that are mathematically similar. Since each of your artworks are different, your analyses will be different, too, and so I can't tell you in general terms what you ought to include.  But I have strong opinions about each of your pieces individually!   To help you think about your paper, I want you to meet in these groups and work together before your 1-page paper is due.

You should jointly think out loud about good approaches to take.  In this paper, you will tell me what kinds of mathematical aspects you intend to explore in your next 4-page paper.  Being specific about how this relates to your piece of art will help.  For example, saying "I will draw a plan view" isn't specific.  Saying, "I will probably have to draw 3 different plan views, so that my readers can see the top of the building, the side of the building that they think they see, and the side of the building that they actually see," is much better.

What am I looking for as I grade this?  
 • Content:  I am looking to see that you've thought seriously about several things: your piece, what we've learned in this class, and how those two things do (or even cooler, don't) fit together.  
• Honesty.  If you have questions about what you're going to say in your 4-page paper, bring those up!  If you're uncertain about which of two approaches you might take, say so.  I want to use this paper to guide you.  I don't want Serious Baloney (BS).
• Good exposition.  As always.
Viewing Distance Paper In this one-page paper, you will choose a painting that uses correct perspective, and you will describe, step-by-step, how to determine the viewing position.  This means that you will need to find a fairly decent image of the painting and also to know its original size, so you will need to include the citation for the book/website/museum where you found your figure you use as well as for the information about its size.  It also means that I expect you to give me an actual number for the viewing distance (with units and everything)!
 
I expect you to use the mathematicians’ “we” together with vigorous, active voice, as in,
 
            To locate the primary vanishing point, we can extend
             the red lines along the left and right sides of the desk.  We
            see that these points meet at the saint’s right eyebrow.”
Plan View Paper Create one plan view diagram that explains an aspect of perspective in your adopted art work.  (Your 5-page paper might have more than one; for this paper, use just one diagram).  In this one-page paper, you will describe this plan view and also use it to explain one or more aspects of your artwork.    You will therefore hand in two pages: the diagram and the essay.
Flatland/Allegory Paper Both Abbott (in Flatland) and Plato (in the Allegory of the Cave) describe a character who sees only two dimensions for the greater part of his life, who suddenly encounters a 3-dimensional world, and who returns to his original 2-d world with a knowledge that none of his compatriots can share.  Each story ends with questions about the obligation of a person who has knowledge and the effect that new knowledge can have for a society that is comfortable in the lack of that knowledge.  

In this essay, I want you to focus not on knowing the world in a new way, but in seeing the world in a new way.  Compare (or contrast) the kind of sight that Plato’s returned cave dweller gains with the sight that Abbott’s Mr. Square gains.