One advantage to waiting a little before responding to a chapter is that you have a chance to see how other classmates have answered and you can react to them. The Golden Section is a good example. You can raise the question about the part it plays in nature to others interested in that topic and we should be able to get something going.
In a sense computers are more open-minded than we are, but only because we told them to be and they are also more compliant than we are. It is true that we are drawn again and again to the familiar, usually the second or possibly the third dimension. We can prefer the representations that reduce higher-dimensional phenomena to places where we have a lot of first-hand experience, but ultimately we have to face the fact that not all problems can be treated directly this way.
Algebra and geometry can be complementary all right, but sometimes they seem to have little to do with one another. Algebraists often are quite willing to go off on some formal investigation with little regard for anyone's ability to create illustrations. There are even some geometers like that, some of whom call themselves "algebraic geometers". Within that field there are some who still like to visualize but a great many avoid that exercise.
By the way, I find that if I retype your apostrophes and quotation marks on my Power PC, then the funny symbols tend to go away. I wonder what causes that problem?