Starting with your cylinders around arbitrary minor axes, unfortunately it appears that you have missed some important instructions here, and as a result, did not complete this part of the challenge correctly. There are two main issues:

• Firstly, you appear to be drawing the majority of your cylinders with no foreshortening at all - keeping the side edges parallel to one another (or in other words, pushing the vanishing point that governs them to infinity. This is a specific issue that is addressed at length in this section of reminders. It explains both why forcing the vanishing point to infinity is incorrect in this situation, as well as calls further attention to the part of the homework/assignment section which specifically asks students to vary their rates of foreshortening across this part of the challenge.

• Secondly, when going through the error analysis step (where we identify the true minor axes of our ellipses), you appear to be drawing a single red line for each cylinder, cutting through both ellipses. The instructions shows that you need to do this separately for each ellipse. Since there's a significant likelihood that the ellipses are not aligned perfectly to one another, drawing a single minor axis line is unlikely to correctly identify the minor axis line of both, and so it would not provide useful information to help you adjust your approach into the next page of cylinders.

It is extremely important that you ensure you follow the instructions to the best of your ability, and when embarking on longer challenges like this one, that will likely require you to revisit those instructions periodically in order to keep them fresh in your mind. Unfortunately it does seem that ball was dropped here, but you will have the opportunity to correct this.

Fortunately, your cylinders in boxes were by and large done well, and do apply the instructions correctly for the most part. 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 applying those line extensions correctly throughout the set, you continually armed yourself with an accurate analysis of where your lines were converging correctly, and where they were off. You were then able to apply this going forward into your next page, gradually developing your overall sense of proportion in 3D space.

There are two main things I want you to keep an eye on for this exercise in the future:

• Like in the previous section, be sure not to force any vanishing points to infinity. For example, number 172 appears to have been drawn without convergences. My assumption there could be wrong, as this could just be the result of things going awry - what you intended to do is what matters most, and the fact that this is one instance amongst many others that did feature convergence suggests that this may have merely been a slip-up, whereas with the cylinders around arbitrary minor axes it was frequent enough to be obviously intentional. Still, in the case that 172's considerably more parallel lines, I just wanted to shine some light on this as something to avoid, as outside of simply being incorrect, it also would make the line extensions considerably less useful.

• I was going to call out instances of your sets of edges converging in pairs (rather than all four together), but upon looking more closely at your work, I think this is an issue that happened quite infrequently, and moreover it appears to be something you're showing clear signs of being aware of and attempting to address directly. So instead of calling this out as an issue, I will instead commend you on addressing it as purposely and intentionally as I can clearly see in your work.

So! You dropped the ball with the cylinders around arbitrary minor axes, but did a great job with the cylinders in boxes. I will need to assign revisions for the first part, but where my intent was to assign a full 150, I think we'll cut that in half instead.