Tag Archives: Development

ARTithmetic: Geometry Ordered My Artistic World

Fine artists and math aren’t usually friends. Math is a necessary evil at times, but visual and wordy creative types generally avoid it. (And for those of you who know my fanaticism concerning grammar and spelling, yes, the title above was intentional, and no, I do not have a fever. I do however suffer from a fascination with terrible puns. And no, there isn’t any other kind of pun.)

However, math skills are incredibly useful in many areas of drawing, painting, printmaking, sculpture and more. Linear perspective is based on mathematical relationships, lending realistic proportions to depictions. It translates into sculpture getting anatomy in proportion; into fashion design measuring for pattern sizing. Ancient cultures, Michelangelo, and modern artists alike utilized measuring and drawing grids for enlarging paintings. Mathematical volume ratios are important in timing and recipes, from acids for etching printing plates, to mixing paints, to formulating ceramic glazes and kiln temperatures and firing times.

I didn’t like math much, except geometry. It actually has saved my art projects on many occasions. It isn’t just figuring square footage for a rectilinear wall (length x width) before you buy too much paint. It can be handy to figure out the perimeter of various shapes depending on a project’s needs, and you may not be able to predict all the needs you’ll have in future projects, so it’s good to already have a working knowledge of math embedded in your grey matter before a problem crops up (especially if you’re under a deadline).

The point is, for example, at this particular juncture you don’t know how big the circle is or the radius or diameter from the info you have right in front of you. This is how you find out. Once I had a project into which I had to figure out how to fit a circle exactly between random elements that were not making it easy to just measure a diameter; the three places crowding into the space formed a triangle. Using my existing knowledge of geometry, I could figure out the precise point at which I needed to place my compass point, based on a principle that didn’t even require actual measuring. No measuring? Cool. I did have a couple of extra steps because the space was already halfway enclosed and I did have to take measurements to recreate a triangle from those three points to get the angles right, but I’ll start by the main concept, which, barring such constraints, really requires no measuring.

Figure 1

First, some basic vocabulary, like you need to know that straight line segments connect singular points. Simple enough. Then you must understand what perpendicular means: that would be a line that is exactly 90 degrees difference from another line. Then you should know that “bisect” means to cut in half. Also know that the center point of a circle is theoretically where one could put a compass point to adjust the business end to scribe a circle around it, and the distance between the circle’s edge to the center point is called a radius, and the distance across the widest part of a circle from edge to edge is a diameter. Sorry if that seems a little too elementary, but I’m trying not to assume too much (I haven’t limited who visits here other than spammers and other mischief makers).

Figure 2

That introduction should prepare anyone for the following rule: the center point of a circle that will pass through all three of any three points (in any orientation to each other) may be found by determining the respective perpendicular bisectors of two line segments connecting any two pairs of the three points, and locating the intersection of these two bisectors. For example, on Figure 2 one line segment paired with its perpendicular bisector is in purple, and the other pair is in green; where the green and purple bisectors intersect is where you put your compass point; adjust it to the span between that point (the center point) and any one of the random three points, and you will see that the circle drawn with that radius will pass through all three of those points.

Figure 3

Now, your three points can be in any proportional orientation to each other; they needn’t be lined up anywhere close to a regular sequence as they nearly are in Figure 2 above. Alternatively, as in Figure 3 here, two points can be rather close to each other, while the third is relatively distant, yet you will find that the principle of the intersection of perpendicular bisectors functions every bit as accurately with any configuration for finding that common radius at that intersection point. You’ll notice that the intersection seems to be more “between” some of the points in this second example; whereas before, it seemed more “outside” of the area of the more lined up points. And that’s okay, either way.

Figure 4
Figure 5
Figure 6

So…how does one determine that perpendicular bisector? Well, there’s always measuring it out, which is a fat pain in the neck, but the easy way is with any straightedge and the compass with its pencil. Even if all you have is a piece of scrap paper, you can fold it over a few times and the fold will make a nice straightedge if you don’t abuse it too much. You don’t need a ruler with measuring marks, and you don’t actually have to calculate anything; the laws of physics do the heavy lifting, and you’re just an apparatus. So let’s try it:

1. Draw a line segment between any two of the three points.

2. Draw a second segment between (either) end of the first segment (since you only have the two choices left), and the third point.

3. The same procedure for finding the perpendicular bisector (steps 4 through 7) will be applied to each segment, so choose just one to perform it on first.

4. Stretch your compass just a little farther than the length of line segment #1. A distance that could produce a nearly equilateral triangle would be sufficient distance to get a good bisector length.

5. Place your compass point on one end of the segment.

6. Estimate about where you think a perpendicular line would pass on both sides of the segment and mark an arc (just part of a circle) lightly but generously in that vicinity, to be sure it crosses it on both sides fully. Do not readjust your compass after making these lines. Figure 6 may help you see what I mean on placement.

7. Repeat the arc process from the point on the other end of segment #1. Again, don’t readjust your compass by mistake; these arcs must be equal from either side to stay centered. This will produce a little “X” on either side of segment #1. Drawing a line that passes right through those two X’s will be the perpendicular bisector of that segment.

8. Now repeat steps 4 through 7, only for (whichever your choice is for:) segment #2.

Now if you have a physical project that you needed a circle shape for, you can cut out the circle you just made, and use the circle itself (either it, or use the hole it left in the paper or cardboard you cut it from) as a drawing template. Cut it out of chipboard or whatever and it’ll be a little sturdier than just on paper, but a little harder to cut out. Or match a circle template to it if you can…you may not be able to, though, since available sizes of templates are so limited. If you’re an adult, I suggest cutting it out carefully by hand with and X-Acto knife instead of scissors if you can (but kids, DO get help from an adult; X-Acto type art knives are notorious for slicing even adults if one isn’t very careful and steady), or if you’re lucky enough to have a circle cutter, go for that if you’re working in wood. (It bears mentioning that in every school, furniture, design or model building shop I ever worked in, these art knives had way more accident reports than any of the power tools! Don’t be overly confident; be extra careful!!)

My project for which I first had to use this knowledge had a key area that was very difficult to access, because other elements were already in the way to just being able to measure easily. Knowing the (perhaps obscure) three-point rule about circles was already in my brain, patiently waiting for a use when I found I needed it. It paid off!

But sometimes you’ll need actual measurements for a triangle. The thing one has to remember is that any 3 points (that can locate a circle) also makes a triangle, and all triangles have 3 sides. Those sides (like the segments we made in the last exercise) have center points, (and therefore, they have perpendicular bisectors). Triangles also have 3 vertices (vertexes if you prefer), or corners, and no matter what proportion the triangle is in (right, obtuse, scalene, equilateral, isosceles; whatever), those 3 vertices always total 180 degrees when you add their angle measurements together. Always! And that means that there is always a way to figure any single unknown measurement, so long as you have the degree measurements of at least 2 vertices, or of at least 2 sides. This is why the Pythagorean theorem works for right triangles; but I’ll explain that later. Don’t worry: the formula is almost easier than the pronunciation. (You can scroll down to Figures 8 and 10 for triangle references, where these two triangle paragraphs are expanded upon.)

What if you don’t have a right triangle? Well, how much info do we have? Is it enough? You pretty much need measurements of 2/3 of the sides or 2/3 of the vertices degrees to get that last third of either. There are ways to do combinations of a vertex and a couple of sides and things like that, but I have neither needed that combination nor have I any recollection of how to do it, and it’s late and I’m too tired to look any of this stuff up; I’m going purely on memory in this whole post…literally from decades past.

Practical Applications

You might wonder why we even want to know any stuff about sides. Well, if you’re edging a shape with some sort of trim, you’d need to figure out the perimeter measurement, or the distance around it, so you’d know how much yardage/board footage (or other type of length) of trim to buy. If you’re painting a big shape, you’d want to know how much paint you’ll need, and need to calculate the area of a shape. Most containers tell builders or DIY remodelers how many fluid ounces or gallons or whatever they contain; some will say how many square inches or feet or whatever that liquid volume will cover…but they may not. And having far too much or too little is often a problem if you fail to plan. Paint can get pricy, and it’s bad for the environment to waste it and many people don’t even bother to look at recycling. So waste not!

Area, a measure of the surface of a two-dimensional entity, is good knowledge for many things: ordering sod for your yard, or raw canvas to stretch z number of q sized stretched canvases plus their borders, or concrete for your patio, or to help calculate how much x number of cows will eat grazing a pasture in y amount of time before you have to rotate them to a different pasture and let the other pastures grow again for the next round. Cows? We’re talking about cows? Heck yeah! Math is super useful in almost any topic. So there are formulas to help us figure this stuff out for almost any shape, even if you have to take a big weird shape and break it up into smaller components that are easier to define and then add it all together.

Quadrilaterals, Triangles and Circles

I guess I’ll start with quadrilaterals, or four-sided figures; they’re the easiest. Perimeter for a square would be S x 4, where S stands for Side. For a rectangle it would be (length x 2) plus (width x 2), or L2+W2. For a parallelogram it would be the same as for a rectangle, and for a rhombus, perimeter formula would be the same as for a square…but not so for area.

Figure 7

The area (A) of a square or rectangle is simply A=L x W. For a rhombus, you measure the lines connecting the opposing corners and multiply those: A=D1 x D2 (D stands for diagonal). For a parallelogram it’s a liiiittle more complicated, because you kind of break it up into components, one of which is a triangle, so I’ll shelf the parallelogram and teach you about triangles first, with a quick detour to trapezoids in between.

Triangles are nearly their own field of study and I do believe that relates to the term “trigonometry”. All I remember from trig is how to figure the sine, cosine, and tangent, and I’ve not yet had practical cause to use it, so I’ll skip that for my audience. We’ll concentrate on perimeter and area.

Figure 8

The perimeter of any triangle is just derived by adding the sides’ values to each other. The area, however, is obtained by using the formula A=½ h(b); in other words, area equals ½ times the height, times the base (when you see parentheses in a formula, it means to multiply the value within and the values outside the parentheses…it saves confusion using the old-school multiplication symbol x alongside variables which also may look like x). It makes more sense when you look at a right triangle and notice that it’s like someone sliced a square (or a rectangle, or a rhombus) in half diagonally…base times height is a whole lot like length times width for a square…then you divide it in half, because it’s only half of the area of the quadrilateral it would fit in. ½ h(b). Picture that while looking at the different triangle types in Figure 8 above. So…what are height and base?

Well, you can take any triangle and assign one side (generally the bottom) as the base. From there, the top corner opposite that base is what determines height, but only if you measure on the perpendicular. It doesn’t matter if the height is directly over the base or hanging out in the “air”, as it might with an obtuse triangle. The height is always completely perpendicular to the base (see Figure 8 above, on far right; the obtuse triangle with the dotted lines; note how that also translates to the acute triangle in center).

Now I’m just going to give formulas for shapes, and if you have questions on how to execute them, please email me…or contact your local math teacher, who is probably (hopefully) far better at explaining this than I am.

Figure 9

A trapezoid at first seems like a Frankenstein’s monster of shapes, but its formula is pretty easy, kind of ripped off from the triangle, but it acknowledges measurements for a top AND a bottom base: A=1/2 h(b1+b2). You don’t double the height, because it’s still just one height. Note that the formula below the parallelogram in Figure 9 says “either base”, not “both”, because you only need ONE. Since they’re the same (they’re parallel and so are the sides that connect them), you can choose either one of them.

Figure 10

Right triangles of course have special rules all their own. In geometry they always have a little square in the corner reminding you that their angle is 90 degrees. The single side exactly opposite that right angle is called the hypotenuse. The example shown on the far left is actually an isosceles triangle (two 45-degree angles plus one 90-degree angle equals 180 degrees), but sides a and b could also be different lengths, and the other two angles can be different measurements as well (as they would necessarily be, what with having different length sides). For example, the triangle on the right has one 30-degree angle, one 60-degree angle, and the (right) 90-degree angle, again adding up to 180 degrees.

Right triangles are where the Pythagorean theorem comes in: a2 x b2 = c2. If a triangle with sides abc is a right triangle with c being the hypotenuse (the side opposite the right angle), where the number of length units a=3 and of b=4, and you don’t know c, you can calculate that using the theorem: a2 + b2 = c2,  and a=3 so 3×3=9, and b=4 so 4×4=16, so 32 + 42 = c2, then 9 +16 = c2, then c2 is obviously 25, and the square root of 25 is 5. So 5 is the measurement of that hypotenuse. Obviously, the measurements rarely calculate so they fall into such neat round numbers; this is just an easy example. You can figure other square roots manually, but it is admittedly tedious; I highly recommend using a calculator for this component. Similarly, if you change the same proportion around so that b is the value missing instead of c, you can just subtract a from c to get b, or: c2a2=b2, instead of adding like we just did.

Figure 11

Hmm…we’ve done quadrilaterals and triangles quite enough. So back to circles – let’s do some actual math. One of the most “famous” formulas in geometry is “Pi R squared“, or πr2. In truth, that’s not a complete formula; it’s only half! You need to know what that combination yields. In this case, it’s the Area, so A=πr2 is the whole (balanced) formula. The A again represents Area; the r represents the radius, or the distance from the center point to any edge of a circle (and it’s the same distance to any edge of the same circle). Another useful formula for circles is for the Circumference, or the distance around the outside – and yes, basically it’s the same thing as perimeter for other shapes; “circumference” is just a specialized term for the perimeter of a circle. The formula looks a tiny bit like the one for Area, but don’t confuse the two: C=2πr or in longhand: Circumference = 2 times pi times the radius. (It really is quite different in function.) Now, anyone who’s paying attention will notice that 2 times radius is the same thing as (one times) the diameter, since the diameter is the distance across a circle at its widest, which necessarily runs through the center point…essentially, 2 radiuses. So you could alternately say π(d) and be done with it. Except, of course, until you need to plug in a definition for π (pronounced pi like the Greek letter). Pi is a “magical” circle-specific value represented by 22/7 – which, since those numbers don’t ever make human sense together, have a decimal equivalent something like:

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230646…blah blah, random constant ad infinitum…but for most practical purposes, 3.14 is adequate. If you don’t dig doing immortal arithmetic using top-heavy improper fractions with anemic prime denominators, go for the decimal shorthand instead. I think I’ve done more with circles than with any other shape, save for squares…obviously.

Formulas For Forms

Artists also work with 3-D geometric forms as well as simply 2-D shapes. Remember from our art lessons on Forms that forms are essentially mere spatial extrusions or rotations of shapes, expanding 2-D to 3-D. Formulas abound for forms as well, but instead of needing formulas for area and circumference or perimeter, they need formulas for things like volume and surface area…things like for the sphere: V=4/3(π)r3. Prisms are easy; calculate the shape on the end and multiply by the height of the prism to get the volume of it. Surface area of those, you just calculate the areas of rectangular sides and add them all to the areas of each of the ends. Pyramids are 4 equilateral or isosceles triangles plus a square base for surface area. Volume for those is a little weirder. Cubes are made of 6 squares, so their surface area would be the area of one square times 6; its volume would be Length times Width times Height (LxWxH). Tetrahedrons are 4-sided forms with all equilateral sides. When you get into dodecahedrons, icosahedrons and the like, you’ve gone beyond what I’ve ever had use for personally, but there are mathematic resources on the web you can search for with any question – or, again, contact your local friendly math expert and he or she will likely be glad for the inquiry.

Grow Further from the Foundations

Of course, shapes and forms may not always conform to geometric proportions; sometimes they are organic shapes or forms (see lesson on Shape). But usually you can guesstimate parts based on similarity to a geometric counterpart…or five.

Now, you may be wondering…how on earth again can any of this be useful to an artist? I’m certainly not saying it comes up with every project. But when it does come up, it is good to be prepared, and know what you’re doing. I had to figure out how to draw proper gothic arches for my 3-tree triptych. I had to figure out perspective for Catreedral. I had to stay aware of paint to medium to water ratios in all of my acrylic mixtures so my paint didn’t lose adhesion viscosity effective in relation to the canvas or other substrates. I do commission work to fit in certain spaces in situ.

A lot of times it’s like my first example: you’re trying to fit an element into a composition with only part of the information you need to execute it, and you should know how to generate that missing information from what you do have. It can help you assemble 3-dimensional forms; it can help you understand proportion when drawing things either freehand or by perspective. It can help you organize radial or concentric arrays or grids in regular intervals to make patterns. It can be used in symbolic capacities. It can help you distribute elements on a certain shape and size of substrate. Perimeter and circumference are good for figuring minimum linear measurements for physical materials to wrap around the outside of a shape. Volume is good for figuring out how much resin you can fill a hollow form with, or how much airspace a solid one will take up, or how much water or glycerin it would displace if submerged; while area and surface area would let you know how much paint or flocking or whatever you would need to color or coat the thing with. When you get into large shapes or forms this sort of calculation takes on a more significant importance with budgeting supplies, as well as figuring sale price from a root of cost of materials, times your hourly rate, differentials, incidentals and whatever is relevant for your medium and project. It’s not always formulas; sometimes it’s understanding the theory and relationships behind the formula and applying it in a custom situation. I’ve gotten to the place where I know some of this stuff so well, I can visualize it accurately without doing computations, which saves lots of time with sometimes impatient or unrealistic clients.

Model of Ruvo Center for Brain Health in Symphony Park (formerly called Union Park as a project) in downtown Las Vegas NV; deduced from old 3D files that couldn’t translate to my laser cutting equipment; I utilized geometry and a torch to make it happen. Finished model for RNL (lower left) is less than 3″ in any dimension.

When I was an architectural model builder, I was given a rather challenging project: to produce a very quick small-scale context model of a building designed by a visionary architect named Frank Gehry…without any plans or elevations. I was to fabricate it from rigid, flat clear acrylic sheet, and manipulate it to match the feel of an existing context model. I had no access at the time to 3D printers, and clear media on those had not yet been developed. I had to figure out how to make a flat pattern, cut it on the laser cutter out of clear acrylic, and then carefully melt it into shape with a propane torch and tweezers to bend it into shape, but I needed a starting point that was viable, in a flat pattern I could cut out first on the laser cutter. I scrutinized a digital virtual model of this building, which looked, as some say, like a crumpled piece of paper, and then I noticed that the (thankfully ubiquitous) windows were of a certain ratio of proportion to themselves and between each other, and were laid out on a sort of grid, and I started twirling the camera angle in the file all around, (no idea who drafted it or how; stellar job though), counting in all the relevant directions, taking notes and creating a schematic. I ended up, using synthesized knowledge from my foundations in geometry, making a very faithful yet tiny model of that building that satisfied all requirements from my superiors and from the client. Geometry prowess made my deducing the pattern for it possible, and my job very well may have depended on it…I was after all running the model shop, and there was no one else to figure it out for me, or so I assumed; it was my job to do it. Math saved my proverbial posterior. Never underestimate the income value of the ability to analyze and solve.

If you prepare and have these geometric principles in your head already, you will be able to spontaneously formulate solutions to many future problems on the fly, without ever having anticipated this or that particular challenge prior to its presenting itself. In professional situations, clients are not willing to wait around for you to learn basic, practical information like math to finish their project; you should already know that stuff. That’s part of doing the job. A well-rounded artist is versatile – and by nature, a problem solver. Math, and particularly the user-friendly concrete geometry, is another essential tool in your utility belt.

It must be said that art should not be funneled down to graphic design applications, any more than math should be limited to what a calculator can do for you. What I mean is, get down in the muck (or paint or clay or hand ciphering) and do it manually; figure it out on your own, without a machine, because that is what it takes to get your brain to be really agile and useful in unpredictable situations. And hey, if an anti-tech dystopian society befalls us, you’ll have marketable skills that will fast earn your reputation as a person in great demand and of great success by default, since most dullards won’t be able to add two and two and come up with four without some microchip telling them so, or be able figure out how big a barrel to make to fit that low-tech washbasin in the corner of his hovel, let alone how much pitch to coat it with so it doesn’t turn his dirt floor to mud.

If you are frustrated with other academic subjects, and struggling to find relevance for them in your life, I do hope you take this post to heart as the first of many examples of how things are, in fact, connected, and how they can be made useful. Aspects and underlying concepts in different areas of knowledge can be synthesized quite usefully into other areas, informing your vocation in ways that are rich and multilayered, and propelling you (and your career) into deeper realms of excellence in your craft.

This sort of outside-the-box thinking is actually cultivated in studying the arts themselves, more than in other more common school subjects alone. This is also why I am more a proponent of STEAM schools over STEM (Science, Technology, Engineering and Math schools)…the “A” standing for “Arts”, of course…and that’s not just visual arts, but all arts, for they all stimulate and stretch the brain in unique ways: analysis, synthesis and evaluation over mere memorization, comprehension and simple applications. It’s the type of creative, often unstructured yet free and communicative thinking that fosters inventive minds and generates entrepreneurs, and that’s a pretty darn important bundle of skills these days. On that note, I encourage everyone to support arts education in all schools, because it enhances technology training in crucial ways that cannot be taught without the arts. Arts and the way they challenge our brain development will always be just as valuable to our culture as math, sciences and history, and as important as communication and social skills will always be, which we are relearning as a society, through recent backsliding and failures, that we still very much need to retain and sustain. Arts, in concert with technology and other sectors, will help us to preserve, portray and propel our culture.

Lines based on numerical proportions in space show off Vermeer’s linear onepoint perspective in “The Music Lesson”.
Look how real that space feels! Math is good, y’all.

Image (prior to my editing) courtesy of Google Art Project. Please email using contact form if issues with image.

All content on this site © 2013-2019/present L. Eilee S. George; all rights reserved.

Your Passion is Not an Island to Itself

I started drawing as soon as my dimpled little fist could grasp one of those big fat crayons. I’d been fascinated by the concept of art since I was two, when my mother explained, in simple terms, the idea of imagination and art looking like reality. I didn’t care how long it took…if someone else could do it, I wanted that magical power to create something from nothing and make people believe it. I wanted it more than anything–and it was not a passing fancy. Decades later, the fire hasn’t faded.

When my class hit second grade, we all had to take IQ tests. I scored within a couple points of genius and was placed in a “gifted” class the next year with other advanced students. We got extra projects to stimulate our nimble, hungry minds; we had an engaging teacher, and most of us were quite happy and productive. My artwork flourished, I had a diverse group of friends, and my life was very, very good.

Then my family had to move. My father’s job caused this occasionally, and it was always an upheaval. But in this particular timing, in the place we ended up, was to do nearly irreparable damage to my academic path. The new school district didn’t even have an accelerated program. I was placed in what would be my normal grade with no accommodation or interest in the level of study I had become accustomed to. My new teachers had no recourse provided them by the district; their classes were large, their syllabi were set and their hands proverbially tied. But I wasn’t privy to this fact.

I struggled in my new school, academically and socially. I was the “weird new kid”: hurting in the looks department, wearing outdated hand-me-downs and sporting a “funny accent” (Southern), and newly being forced into wearing thick brown ugly glasses. On top of that, I was presented with scholastic material I had mastered one to two years before. I found zero incentive to repeat studies with which I, by then, was bored. I made few friends, least of all my teacher, who (in my angry young eyes) bore almost as much blame for this torture as my parents. And my parents were absorbed with starting the new job, setting up the new household, getting acclimated to the town and its citizens, and dealing with my older siblings’ more rebellious growing pains to the disruption in their own lives as well. Lost in the shuffle, I felt like the invisible girl, and I naïvely began devising an outlandish plan to run away, convinced that no one would notice. Luckily, a sensible girl named Cheryl, in whom I had confided this boneheaded plan, talked me into waiting a while to see if things got better, pointing out that I had no money for a bus to California, and had no verified place to live if I could get there. She should have been in a “gifted” class! She had told me, that if I left…at least she’d notice. I had to admit, it was nice to hear this from somebody.

So, lacking any better plan, I stayed around, and went on strike and refused to do my homework. Rivers of notes were sent home from my fourth grade teacher, followed by visits to the principal’s office, parental lectures after PTA meetings, swats at school for repeated offenses with a thick oak board with holes drilled in it for better aerodynamics, and a fair number of swats at home with lesser tools of inspiration, yet none of this was provocative enough for me to mend my ways. All of this was for missing what I rightfully viewed as redundant homework assignments, mind you. Fifth grade came and my resentment festered, and my study habits grew more dismal; D’s and even occasional F’s became heavyweights on my report card, although I still got A’s in English and spelling because I actually liked them. At quarterly meetings, my fifth grade teacher spoke kindly of me to my parents, and he noted that I was still brilliant for my age, yet I wasn’t being challenged enough…. But he was simply fascinated by my early artistic prowess. He showed my folks the papers he had confiscated that I was doodling on, telling them how advanced I was, and he asked them on more than one occasion if he could keep some of the drawings to have as proof that he knew me “when” someday I would be a famous artist (so sorry to have disappointed him; he was a sweet old man). It’s very flattering, of course, but by this time my folks were not only tuned into the fact their littlest had a serious issue afoot, but they were also straining at any way to get through to me; I had shut them out along with everyone else and lived in a tormented fantasy world, trying to escape the ennui and frustration I felt toward the real one.

When you’re a kid you don’t necessarily understand that adults go where the work is and everything (and everyone) else kind of has to fall in line with that, no matter whether or not it’s ideal; meals have to come from somewhere. A kid just understands how he or she feels until something is explained, or better, demonstrated, to the end of changing that mindset with a convincing argument and fact. I still needed that presented to me in a way that I felt mattered. I held out stubbornly, and foolishly.

Changes at home continued and I still felt like a last priority. My social life was very limited by multiple factors beyond my control and I had a big chip on my shoulder. Moving had been hard on me, at (apparently) a key age. I had been very popular with many friends in my old town, where we had owned a nicer house in a neighborhood full of kids, where there were things to do and fun to be had, and I had enjoyed a bigger room, and now this still-new place I hated for more reasons than I could count. I liked my fifth grade teacher for his appreciation of what I appreciated, but it didn’t improve my grades much; I was still bitter and lacking any motivation, and frankly, my single-minded attitude stunk. I was beginning to fall behind, particularly in pre-algebra.

When I was in sixth grade, my father had an epiphany to appeal to me through the one thing he knew I cared about most: I loved to draw…compulsively, all the time, and on any paper product I could get my hands on. I had always wanted to be an artist, and by then I had told my folks plainly that I simply didn’t see any point in all these other classes that didn’t interest me, so I just wasn’t going to waste any more time or effort in them. This certainly did not sit well with them, yet no manner of wheedling, bribery, threatening, punishment, or gnashing of teeth was swaying my stubborn will.

Through his job, Dad had gotten acquainted with many of the area denizens, including the local art star, and he asked this man’s advice. The artist and muralist offered to talk to me for him. He even arranged to visit me at school, a visit I was very excited about – I felt like I was granted an appointment with a celebrity. It was a topic of curiosity for some of my classmates: “Why is he visiting you?” I just smiled.

When he sat me down to talk I was very nervous, and I wanted to learn all I could. I knew there was still so much more about art I needed to discover, and we were only to talk for about a half-hour…how could I squeeze the most out of this precious time? After introductions, I didn’t know what to say or how to start, so he took his turn first, to ease me in to asking questions later.

He worked around into relating to me how he would daydream in school, and admitted that at first he hadn’t found much interest in math, science, history, or even English (I still liked English class: a bit of a word geek, I actually enjoyed diagramming sentences). I listened intently. Then he said, “But after a while, I learned that I truly needed all those classes to make good art.” I was dumbfounded. How could all this stuff be relevant? All I wanted to do was draw; I didn’t need a slide rule or a dictionary for that. I started to smell a trick from my dad.

The artist continued. He pointed out that all the famous artists used mathematical principles (geometric and algebraic) as the basis for drawing things in linear perspective and in good proportion, so that things look right; he needed to understand fractions and decimals and figure circumferences, and plenty more. He even drew some things to demonstrate. He said science comes into play when mixing pigments and mediums, in chemistry glazes for ceramics, in studying biology and anatomy to draw beautiful birds and animals, and that ultimate Holy Grail for artists, the human form. Artists study, illustrate, and draw inspiration from literature. And artists throughout time recorded history either from their own pasts or actually as it unfolded; they worked jobs where they charted maps, relating to geography; they illuminated planets in astronomy books, and illustrated characters in yet more literature – they touched on every other subject in school.

It all was relevant! My mind shifted so suddenly that I nearly fell over.

He told me my drawings showed advance and promise; that he could tell by the complexity and focus of my few questions that I was a bright girl; he hated to think of me wasting my talent, potential, and obvious passion for my art. He was convinced I would be a brilliant artist if I applied myself. So he struck me a deal: if I brought my grades up in my other subjects, then he would give me a lesson on how to draw any category of thing I wanted to learn to draw…and then he asked me what that would be. I thought for only a few seconds before proclaiming, “Trees!”  I so very much wanted my trees to be not the stiff, tortured things I created, but more realistic and believable, like the botanical illustrations in my mother’s bird books; I loved nature. So he agreed to teach me to draw trees if my grades improved.

It worked. I strived hard all through sixth grade to get back on track in all my classes. I had some hiccups but I brought all my grades up at least one letter grade, and several two and one three. I started communicating more with my folks, and soon proudly showed my report card to my Dad, and asked him about my pending art lesson. He followed up with that artist, who, sadly, had become too busy to keep his promise to me, for which I was bitterly disappointed…but…that didn’t stop me from learning how to draw trees! Now armed with biology lessons from my science book and studies from encyclopedias and botany books from the library, I became a photorealistic tree-drawing powerhouse on my determined own. I don’t think it was to spite him, as he likely wouldn’t have noticed me either way, being in our separate bubbles of society. I think it was just I was that passionate about trees. (Apparently I still am!) And I learned about the inconstancy of human nature and that we all make mistakes and disappoint people – but I also learned that we could still choose to move on anyway, and take accountability for our own respective paths in life.

Years passed, and I evolved far beyond just trees, and eventually beyond mere realism. Even without the initial tree lesson, that artist gave me something priceless: the gift of learning with intention. I finally noticed that my mother also modeled a love of learning, and my father was a self-taught professional as well. As I matured, I came to appreciate being better rounded, both as a thinker and as a creative. I learned to adapt to my new environment, and made more friends…and I learned that a lot of the barrier to that gain had been my own attitude. I learned that many distinct, seemingly separate things actually could be integrally related and interdependent. I realized that the payoff to effort might not be immediately apparent or accessible, but that compiled knowledge accumulates and bands together to make powerful structures on which you can build bigger and better ideas. I learned that taking a studious approach could render me more self-sufficient. I learned that I can develop many different facets to myself, and that in doing so, I would never be bored again. Indeed – I never am.

In junior and senior high, I made honor roll more often than not, and only really struggled once getting to advanced Algebra and Chemistry…my mind wasn’t yet to the point of very abstract thought (and that still showed in my ultrarealistic artwork, which I started showing in a gallery at 16, since I had already begun selling portraits at 14). My folks pushed me on these classes in the college bound track in high school, but they finally recognized I was truly besieged by material a bit too advanced for me just yet. Our state was plagued with math teachers who may have known math really well but did not have the communication skills to teach it to students who struggled with it like me. My high school geometry teacher did pretty well, though, and it helped that it was a more concrete category of math because that was how my mind operated then.

I had to take algebra three times in college to pass it, and the third time, I got my first really good math teacher ever, and realized it wasn’t so much my fault as the system was failing me up to that point: my university at that time had the highest math failure rate in the state; however, with this specific professor’s patience and her devoted tutoring, I made 96% on the comprehensive final – including trigonometry and logarithms. At the university I still had some difficulty focusing on some studies due to my newfound freedom, but I grew exponentially in my depth and breadth of artistic skills. I took a myriad of classes including sculpture, printmaking, ceramics, various painting classes, and lots of art history; I learned new media and techniques; and I even made a tentative breakthrough to abstraction for the first time: something I struggled with for years.

My years at the art institute were even more intense, allowing me to apply my artistic abilities, problem solving prowess and creative imagination in new ways in the industrial design program. I learned to manipulate new media and utilize new materials and processes. Woodworking, welding, plastic production, sand casting and the design process and projects in all of those and more made me a much more well rounded artist, and everything involved math, science, history, literature, and/or more, as well as building on foundations I already had. It was exciting and my mind grew both hungrier and far more productive. I was designing things spontaneously in my sleep, and began keeping a sketch journal next to my bed to record lucid ideas to someday bring to fruition.

Nowadays I am a glutton for knowledge; I want to know what makes everything tick. I earned two college degrees. While getting my K-12 art teaching degree, I discovered that in children, artistic giftedness routinely walks hand in hand with academic giftedness, so if you’re a parent reading this and my story rings familiar in your own progeny, look into testing your own kid(s) and arrange for them to get the mental stimulation they need, even from a tutor or mentor if necessary.

I want to point out that a child needn’t have a high IQ to be a good student: passion is nearly everything. Zig Ziglar, an American author, salesman and motivational speaker of many inspirational quotes, rightly said, “Your attitude, not your aptitude, will determine your altitude.” I’m a living case study. So-called “natural” talent is worthless and fruitless without concentrated effort. The unmotivated will be outpaced by the motivated. Passion can overcome any lack of ability, and it drives gaining any nuts-and-bolts skills one requires in one’s quest.

Einstein said, “The true sign of intelligence is not knowledge but imagination.” I say they both work in concert; he himself proved that. I continued studying on my own, outside of school, ever since my last graduation, and if I ever won the lottery I’d go to “school” the rest of my life – at least intermittently; I am at my creative and intellectual best while in the stimulation of some sort of an academic environment, even if self-created. I’ve taught myself foreign languages, web design, auto repair, musical instruments, tons of artistic techniques and mediums, and most importantly, I taught myself to always be learning and that there’s nothing I can’t study; if I don’t know something, I know how to find out. I can enrich my understanding of the world through diverse sources, and I can always find ways to improve myself: not just as an artist but also as a human being in society, and my passion can spread far, far beyond its own selfish little island.

That is a priceless lesson, and one that has a huge return on investment.

It’s important for artists to constantly be gaining knowledge in many areas, devouring books, news of new things in science, understanding, human psychology, staying up to date in politics, knowing milestone literary works, being informed on historical foundations, learning new techniques and media, and being in touch with pop culture. Professional artists may be some of the smartest people you will meet; they are natural tinkerers who want to know how everything works and what makes people tick. Good art has a message and competent artists strive to know what they’re talking about, to extend the conversation to society at large.

No matter who said it or exactly word-for-word how, (and there are some debates and misunderstandings), but there is truth to the quote that says, “Beware of artists; they mix with all levels of society and are therefore most dangerous.” People in power are often intimidated by anyone who is well informed; they hold those in power accountable and expose corruption, as well as those who help to whistle blow or educate others to do the same. It’s important work.

This post is the introduction and inspiration for my new blog series, “the well rounded artist”. Look for more entries in the future that tie art to other subjects in school, and in life.

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