Starting with your cylinders around arbitrary minor axes, by and large you've done the work fairly well, although there are a couple things I want to call to your attention:

• When drawing your ellipses, you're clearly aware of the importance of drawing through them two full times as mentioned in Lesson 1, but you do have a tendency to stop after one and a half turns of the ellipse, rather than completing the full two. I suspect you're not entirely aware of this, so I wanted to call it out so you could address the issue going forward. It's easy to fall into habits, but throughout our work for this course, it is important that we push ourselves to be especially aware of the choices we're making (whether consciously or unconsciously), and whether they line up with the instructions.

• I had noticed that for the majority of your pages, your red minor axis lines were very similar to the intended alignment you were hoping for (suggesting that you were either really good at aligning your ellipses, or that you may have not always been as fastidious as you could have been when identifying the correct minor axis line afterwards). I ended up grabbing one page where I could see at least one strong case for the latter - this page where the far end of 129's red line is definitely not correct, and went over to check each ellipse digitally. As shown here, the results showed that you are generally pretty good at estimating those alignments, although there are a couple cases there where the alignment is further off than it should be from the minor axis line you added in red. That said, as we can see here and here there are definitely cases where you're a bit careless in identifying the correct minor axis line after the fact, so be sure to keep a closer eye out.

Continuing onto your cylinders in boxes, your work here is fairly solid. This exercise is really all about helping develop students' understanding of how to construct boxes which feature two opposite faces which are proportionally square, regardless of how the form is oriented in space. We do this not by memorizing every possible configuration, but rather by continuing to develop your subconscious understanding of space through repetition, and through analysis (by way of the line extensions).

Where the box challenge's line extensions helped to develop a stronger sense of how to achieve more consistent convergences in our lines, here we add three more lines for each ellipse: the minor axis, and the two contact point lines. In checking how far off these are from converging towards the box's own vanishing points, we can see how far off we were from having the ellipse represent a circle in 3D space, and in turn how far off we were from having the plane that encloses it from representing a square.

By being as fastidious as you were here in ensuring you were applying the line extensions correctly, you were armed with ample information with which to judge how you could adjust your approach to bring those convergences together more consistently, and ultimately achieve ends that were closer to square in proportion.

I have just two things to call out, for you to keep in mind when leveraging this exercise in the future:

• While this was somewhat lessened towards the end, much of the time you did end up keeping your boxes' quite shallow in their foreshortening, at times getting very close to having those side edges running parallel on the page. For the reasons explained here in these reminders, I would recommend incorporating more convergence when practicing this exercise.

• Additionally, note that you have a tendency as your boxes get longer to have the edges in a given set converge in pairs, rather than all four together. This is basically because as that box gets longer, we have to actively force our convergences to be more rapid to make up the greater distance, and if we're already prone to keeping our edges fairly parallel, it can cause us to misjudge how much more they need to be angled in order to meet at the far-off vanishing point.

So, be sure to keep that in mind. I'll go ahead and mark this challenge as complete.