Starting with your cylinders around arbitrary minor axes, your work here is by and large done fairly well. I have a couple suggestions to offer, although as a whole you're taking care with executing your marks and applying the principles of the ghosting method, and you're quite fastidious in checking the alignment of those ellipses afterwards when marking in your red minor axes. You're catching both more obvious issues, as well as the minor ones that can easily be overlooked and cause us to plateau in our growth.

So there's two main things I want you to keep in mind going forward.

• Firstly, you have a tendency here to draw your cylinders quite small, with a fair bit of space around them left free, to the point that you could probably draw those cylinders twice as big without them touching or overlapping. When it comes to the spatial reasoning we're continually exploring throughout this course, drawing bigger helps a lot, so be sure to make full use of the space available to you.

• The other point is that it helps to keep in mind that the "shifts" from one ellipse to the other - both in its overall scale as the cylinder's side edges converge more dramatically, and in its shift in degree, getting wider as we move farther back along the cylinder's length, are both manifestations of foreshortening. In other words, they convey the same information - just how much of the cylinder's length can be measured directly on the page, and how much is hidden in the "unseen" dimension of depth. Because they're conveying the same thing, they do have to work somewhat in tandem. This means that as the convergence of your side edges gets more dramatic, forcing the scale of the far end down, it would also be making it proportionally wider so the shift in degree is also made to match. You don't have to worry about just how much wider you have to make it, just be sure to match extreme scale shifts with more extreme degree shifts.

Continuing onto your cylinders in boxes, your work here is progressing pretty well, and a lot of that comes down to your effective use of the line extensions. 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.

There's one thing I noticed on occasion though that you'll want to keep an eye on. When you're drawing your ellipses, always ensure that they're touching all four edges of the plane enclosing them first and foremost. That's your main priority, and then a close second is aiming to align to the correct minor axis direction. That ensures that the ellipse "describes" the plane, and that your minor axis is likely to be closer to correct. From there, that leaves only the degree to carry the bulk of any mistakes or issues that may result, which is closely related to the proportions of the plane itself.

Overall, you are mindful of this, but towards the end of the set I caught a number of cases - like 235, 236, 237, where this was slipping. 247 and 249 are also examples of this, but I think that they're more likely to have just been errors in execution, rather than in your actual intent, which is normal.

Anyway, all in all, solid work. I'll go ahead and mark this challenge as complete.