Note the little headings on your amended week 10 document that get rid of those annoying extra characters.
This chapter is more difficult, I agree. We are stretching the notion of dimension to cover positions of an object rather than just the object itself, and this makes a difference. Almost always we have to simplify the situation by ignoring many of the possibly relevant variables so we can be left with something tractable.
Your question about the screen saver, and your answer to your question, are good ones. It turns out that there is a bit more dimensionality to the problem you stated in that the four lengths do not tell you exactly what kind of a quadrilateral you have. Three lengths will determine a triangle all right, but you have some flexibility for quadrilateral, one dimension more (= one more degree of freedom).
Can you locate a DeChirico painting to put into your document to show what you are experiencing? Your roommate can help you scan it it.