#I have forgotten how to draw semi accurate anatomy

[palettepainter]

If Cementoss is marketable plushie shaped then why no marketable plushie??

[integrated-jebculus]

quarter 3

I have noticed a pattern in the last two quarters so far. The first half of each quarter, usually, is easier to grasp. The second half... is not. This quarter is no exception.[a]

I have also noticed that this quarter's lessons actually relied a lot on being able to picture things in your head. Because we don't exactly have a 3D modelling software to do the work for you (the applets on the GeoGebra website come close), you have to imagine that this line on a 2D space rotates this way and forms either a disk or a washer depending on how the rectangle is oriented or where it ends according to the bounds. This came as no challenge to me, as an artist who is actively working with 3D shapes to be able to draw human and animal anatomy accurately. Actually calculating their volume is the new part.[c] But even that I managed to grasp in the end, perhaps even more so than all the others--it was the first lesson I actually had a full understanding of, because it actually is simple. Does the rectangle hit the axis? You have a disk, and you only need one integral for this. Does the rectangle stop just units above or before the axis? You have a washer, and you have to take into account the radius of the hole too. It uses pretty much the same principle as calculating the area of a certain region within a bigger plane, or something of the sort.[f]

I still find it incredibly funny that finding the arc length and finding the centroid of a plane are placed right next to each other. I found the first absolute hell because I actually had to harken back to integration techniques I had long forgotten[e,g]. and I found a semi-practical use for the second in a Minecraft server of all places[d]. For context, a standard 2D map of a Minecraft world uses the x-z coordinate plane to denote coordinates, in which a single point is defined as a "block". This is how I found out that the designated center of this certain build in the Minecraft server is not the center; rather, it has been placed one block off the true center. This is a detail that will possibly haunt me forever, but this does not change the fact that somehow, this goofy little activity I did while I was incredibly bored drilled the practicality of the lesson into my brain. Sure, it may not be a real-life application, but I enjoyed it nonetheless. I appreciated it nonetheless. I learned that I can drive myself to learn a lesson back from scratch if I can apply to something tangible, like one of my favorite pastimes in this case[b].

Clockwise from top: my solution, the corresponding graph superimposed on the map, and an in-game screenshot of the true center (469, 81, -1581). Note that the block behind my character is the supposed center.

How can I be able to apply all of these lessons outside of the Cartesian plane? It is already a given in finding the volume of a cylinder, but with a lesson that requires the use of coordinates (e.g. finding the centroid of a plane), is there a certain way to write the "coordinates" of the true center of an object in the real world[h]?

Get through it. That is the goal I want to set for myself in the coming quarter. Get through it, and promise yourself to make things better[i]. Get through it, and it'll be over soon[j].