Starting with your cylinders around arbitrary minor axes, I'm very pleased to see that you varied the rates of foreshortening quite a bit, as requested in the assignment section. Some students appear to miss this. I also noticed a number of other important points:

• You're executing your ellipses with confidence, maintaining even, consistent shapes

• Your ghosted lines are coming along quite well - there's always room for improvement, but the margins of error are quite small indeed

• You've been quite fastidious in checking the alignment of your ellipses, picking up even on fairly small deviations.

There's really just one thing I want to draw your attention here, and it's something that is easier to identify when a student varies their foreshortening as you have done here, giving me the opportunity to call it out in my critique. It's also an issue that is more prominent earlier on, and less so as you progress. Whether that speaks to a conscious understanding or just an instinctual development, I can't say - so I'll explain it anyway.

If you look at some cases like 29 and 31, you'll see examples of very rapid, dramatic foreshortening. That foreshortening manifests in two ways, each being a "shift" from one end to the other. We have the scale shift which naturally occurs as the side edges converge towards their vanishing point, resulting in the one closer to the viewer being larger, and the one farther away being smaller. Then there's the degree shift, where the farther end is generally wider than the closer one.

The issue occurs when these two "shifts" occur independently of one another - so in these two cases, we can see how the degree shift is more minimal, while the scale shift is more significant. We may pick up on this looking a little off, and the reason is that it implies a contradiction. One shift suggests a more dramatic foreshortening, and the other suggests a much shallower one. One tells the viewer that what they see of the cylinder's length is only a small part, with the rest being hidden in the "unseen dimension" of depth, whereas the other tells us that what we see is pretty much the full length of the form.

Always try to get those two shifts to occur roughly in tandem. No need for perfection here, just a general trend where either both are dramatic, or both are shallow.

Continuing onto your cylinders in boxes, you've done a great job here as well. 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.

To this point, I can see that you've made considerable progress, and that your estimation of those proportions has developed quite well, to the point that they should help quite a bit when you get into Lesson 6.

With that, I'll go ahead and mark this challenge as complete. Keep up the good work.