My weblog ELECTRON BLUE, which concentrated on science and mathematics, ran from 2004-2008. It is no longer being updated. My current blog, which is more art-related, is here.
Wed, 05 May, 2004
A stylized reality: art deco equations
I'm doing trigonometric equations. LOTS of trigonometric equations. You can find a list of them at the SOS Math trigonometric equations page. I can solve at least the first six, but after that it gets into things that I haven't learned yet, and wonder whether I need to learn at all. I am also working through a list of about fifty of them in Schaum's Red-spine book. Not only can't I solve all of them, they ask for answers in many different forms. They are not satisfied with simple degree measurements, they also want their answers listed in radian measurements. And the SOS Math page lists its answers in general formulas for where you can find the answers in radian measurement, using negative-sine notation. This isn't in my books anywhere, at least I haven't found it yet. Just as in my previous experience with trigonometry, this is like biting off something that is too big for me to chew. If I want to do all of these equations correctly and learn every angle, corner, and radian, I'll be doing this for the rest of the year. Maybe for the rest of the life of the universe, from how it looks to me.
But what is interesting, and also convenient for me and whoever else toils with these books and sites, is that the answers to these trigonometric equations are often recognizable angles and sets of angles, such as the series of angles which fit sin x = 0.5 or cos x = 1. I often visualize the unit circle's indicator spinning round and round, stopping at the familiar spots of 30, 60, 90 degrees, and 120, 150, 270 degrees. It doesn't usually stop at 47.43957349 degrees, or something like that. True, if you translate these familiar angles into radian measures, you get something suitably irrational, but in sensible old degrees, they are the stuff of the Pythagorean ideal, that divine 30-60-90 form that makes up the drafting triangle on my art table.
I am very fond of the Art Deco style and these trigonometric manipulations and equations, with their stylized, repeating patterns of solutions, remind me of the geometric gestures of Deco. While other art styles use plenty of geometry, hidden in their compositions, Deco is openly geometric. It uses circles, triangles, rectangles and squares, and repeating patterns to build its constructions. I haven't seen a sine wave in any Deco design, but I'm sure that they are there somewhere. This is art which speaks of mathematical confidence and power. The answers to the trigonometric equations, whether degree, radian, or pattern, have that same kind of artificial clarity.
These equations describe something in the "real world" relevant to physics; I'm told that they have to do with oscillations, vibrations, and anything periodic in nature. Sooner or later, if I persevere, I'll be solving these equations regarding experimental data and getting solutions which are no longer in the artificial realm of Art Deco style. I am looking forward to it. One of the reasons I want to study physics is so that I can talk about "energy," "frequency," and "vibrations," and not sound like an idiot.
Posted at 1:47 am | link