What does math have to do with drawing? A lot, actually. In today's post, I thought I'd highlight two different approaches to drawing. These are time-honored methods that I've encountered in many books and art classes. They overlap, and I don't think one is necessarily superior to the other.

The first approach is taught by the instructor in my Saturday life session. He urges artists to start their drawing with straight lines, not curves. Part of his approach partakes of geometry. He emphasizes plumb lines to line things up, and he urges us to check angles and proportions constantly. And part of his approach reminds me of derivatives in calculus. To describe a curve, he suggests drawing the tangent to it in several spots, then gradually refining each tangent until the series of angled lines becomes a smooth curve. He discourages any shading until the basic contours are right. In this approach, you draw from the outside in.

Here's an example of one drawing I did with him on Saturday. You can still see some of the construction lines I used at the start. This was a short pose; I don't remember whether it was 5 or 10 minutes, but it was no more than that.

The instructor at my Friday life session emphasizes a different approach. She urges us to mass shapes in without drawing contour lines at the outset. She wants light and shadow from the start. She encourages us to draw gesture lines with curves, not straight lines. She wants us to draw and paint from the inside out, not the outside in. Charles Sovek, in his fantastic book "Oil Painting - Develop Your Natural Ability," urges the same approach. This reminds me a bit of integration in calculus, in which you find the mass or volume under a curve. Or of the pretty curvy graphs you make in trig. OK, the connection to math may be more tenuous here, but I hope you get the picture (so to speak).

Here's an example of this more curvy, intuitive approach. This was a VERY quick gesture sketch -- 1 or 2 minutes, tops. So it's not really a fair comparison to the "linear" sketch above, which was a 5- or even 10-minute drawing. But I hope you get the idea.