So, who’s ready for geometry!?
If this sentence is ever said aloud and seriously, it would be safe to wager that the vast response would not be one of enthusiasm. Yet, our geometry teachers were actually right. Geometry is important, it is very important. Geometry is also fun; And I’m not making a joke. The real joke is actually the one most of our school systems played on us. No shade to our every-day teachers trying to make an honest living, but it was the way that we were taught geomtry that was the failure. Yet, geometry is vital to how we see, understand, and thus experience our world visually.
So, today we’re going back, all the way back to the basics. We’re going to learn our shapes, and we’re going to do it the right way, without a single bit of math.
THE PIONEERS
So, who do we have to thank for Geometry? There are actually many contributions over history from countless people; Plato is one of the most popular of those names in the conversation, mainly because of his idea of the Platonic Solids. Now Plato was also an avid philospher, and as such had the idea that there was a reality, beyond the one we could see, that consisted of ideal forms, and that all 3-dimensional objects are manifestations of the forms of this realm that lie beyond. From this realm also, sprang his foundational solid forms. These foundational solid forms became known as The Five Platonic Solids for this reason. Each of these solids is a 3D object most people would be familiar with, even if not by name; they are the Hexahedron (the Cube), the Tetrahedron (the triangular pyramid), the Octahedron (3D rhombus, or jewel shape), The Icosahedron, and Dodecahedron.
Now obviously as time has moved on, so has this theory been used and changed in many ways, however, I believe that Plato was definitely onto something, if at the very least partly. I believe that our visual reality is based off of specific possibilities of form, against which light reacts and gives us the visual world we have before us daily. The foundational forms discussed here will be very different from Plato’s, but will have similar foundations.
One thing I want to make note of is this; In the context we will use here, Geometry is about space, not about mathematics – Mass, not Measure. Space is technically what makes up the three-dimensional reality we are a part of, therefore it is first experienced before it can be calculated. That experiential aspect is what we need to gain a firm hold of. Again, using the analogy of light as language from a previous post; we do not count and calculate the number of words in our sentences, or the ratio of sentences per paragraph or thought, we simply speak. However, languages do still have alphabets, grammar, and rules to follow. Don’t worry though, there will be plenty of fun to have with those in our case.
THE SECOND DIMENSION
Now, let us begin, without any further delay. We’ll start with what I call the “fundamental shapes.” These are (or should be) the most recognizable 2D shapes that any of us will encounter in our everyday life. They are what most of us learned in our most elementary starts in schooling. The Triangle (equilateral, and right versions), Square, Rectangle, Circle, Ellipse, Trapezoid, Rhombus, Pentagon (5 points), Hexagon (6 points), and Octagon (8 points). You will also here me refer to these shapes and their variations as “Conceptual” in future lessons and posts, and we’ll get to that in proper time. Not only are these fundamental because they are most easily recognizeable, but also because they are the basis for most of the more complex forms we see in both the man-made and natural worlds.
Of the complex variations of these shapes, we’ll start with the basic 3D versions. The simplest way to start this 3D perception is in recognizing these as “planes” of 3 dimensions, or as I like to call them, the “faces” of these shapes. For example, with the Cube, the basic equal-sided Square can be seen as the front “face” (or plane) of the Cube. The same applies to each of the other 2D shapes listed above. But, just like with a face, in 3 dimensions, planes have to ability to turn toward or away form us, also known as rotation. We won’t dive straight into the concept of rotation just yet, but to dip our toes in the water, we will next approach slants and angles. I know, it’s sounding more and more like math, but stay with me, it will not be.
FUNDAMENTAL AWARENESS
Take a look at the key terms described of above, if you haven’t already. These are the very first step to perspectival awareness. The ability to perceive is most important here on our path, it is an essential part of experience and memory, and precedes each; and as I mentioned not long ago, it is experience which precedes measurement. So, when we add a slant to these faces, decreasing their corners and angles, we must also recognize that we are also developing an aspect of our 3 dimensional awareness. The face of these shapes is turning away from us, up, down, side-to-side, and diagonally. Just like a human face does, for example. As it turns away, the aspects of it “shrink” closer together in our view, decreasing the angles between its ends and corners. This is rotation at its most basic level of understanding.
Just like that, we’ve already gone over our next essential method of practice. Remember, this is NOT an art philosophy page, it is practical one. I want the most important take away from this site to be METHODS OF PRACTICE, as it is how we practice which will not just determine our skill level on this journey, but the skill-ceiling as well. Our philosophy is only as useful as it can be applied to our everyday living. Just as in the second-to-last example, let’s use this slant creation exercise as just that, exercise. Just as we do with the body, we need reps, and sets, done consistently to improve here. Just as shown, up, down, side-to-side, and diagonally, every direction, every fundemental 2D shape. Below is a brief example of my own, done in Procreate on iPad.
This specific exercise will not, and should not, be difficult. Don’t try to overthink it, or make it more challenging than it is at face value. The point is not challenge, it is memorization. These are shapes we all know and remember from our youngest days of schooling, as such you should not have to really think. We simply want to be reflexively accustomed to knowing these shapes from every slant and angle. Put on relaxing or engaging music, and let yourself do a few sets of reptitions with these, 5 to 10 minutes maybe, multiple times as week. If you’re a more experienced artist, and simply are trying to solidify your fundamentals, use this as a warmup for your hands/brain before starting some of your own more engaging drawing and practice. Eventually, perhaps as soon as a couple weeks of doing this, you might notice you can naturally remember what these different shapes look like, and have a kind of “sense” of how they would look if moving in front of you. You’ll be able to draw them at these various slants and angles without using any reference at all. This is a genuine sign; you are flexing those visualization muscles. Now, all we have to do is make them much, much stronger.
THE ANSWER IS NOT WITHIN YOU, THE ANSWER IS YOU