Wednesday, April 9, 2008

Wednesday Math, Vol. 19: Getting all awww-tistic with sprials

Several Wednesdays back, I talked about the golden ratio and the golden rectangle. The idea with the golden rectangle is that you can remove the largest possible square from a golden rectangle, and the little rectangle you leave behind is also a golden rectangle, which is to say the ratio of long side to short side has stayed the same at (1 + sqrt(5))/2, which is about 1.618...

I teach at a digital art school, and in computer art, this infinite regression isn't really possible, since in a computer, any picture is made up of little dots called pixels, and you can't get smaller than the smallest pixel. Given that, the closest approximation of the infinite regression is to use circles whose sizes are the Fibonacci numbers: 1, 2, 3, 5, 8, 13, 21, etc., where the next Fibonacci number can always be found by adding the last two up. In this picture, the circles are nested on inside the other, and they touch (or in math, we would say they are tangent to each other) the next largest and next smallest. The first pair are tangent in the southerly direction, the next pair to the east, then the north, then the west, then back to the south, etc., until you can't fit in a smaller circle that's visible.

What I do then is color in a series of the quarter circles of each circle to make the almost Archimedan spiral. The spiral is in black and the parts of the circle I remove are in grey.

I tried getting arty in a mathematical sort of way, making easy patterns from well defined cyclical sequences, for example, the colors of the rainbow.

I then took the spiral and removed it from the circles, made copies of it either mirrored horizontally or vertically or rotated 180 degrees. I then changed colors around and made trellis like patterns with the spirals.

And since it's a spiral shape, I made four copies rotated 90 degrees each time, and made a multicolored vortex o' doom picture like this.

Sure, I'm no Modigliani, but it was fun to do, and I think they are purdy. How about you?


CDP said...

I think so too! (and thanks for an easy Wednesday math. I'm a little slow on the uptake today)

Tara Mobley said...

I love math spirals.

dguzman said...

Very cool. Only 1 more quiz and the final--and it's hasta la vista to math for this student!

Matty Boy said...

Thanks for the votes of confidence, y'all.

Best of luck on your last quiz, dg.

Distributorcap said...

i was waiting for some geometry from you !

that was my worst math subject -- i could never figure out why the opposite of sine wasnt cosine, like tangent and cotangent

maybe you can do that lesson