Bored of the Rings

I’ve been experimenting with circles again. I found a way to get Flash to make me some perfect divisions; much more accurate than my real life attempts. My circles are all 360 pixels wide and high. The grid I work with is 20×20 pixels so that the total grid squares across the circle are 18; 9 on each side (20×18=360).

The 60-based system we use for calculating time came from the Babylonians, who had a 60-based number system (as opposed to our 10-based number system.) They did it like that because a whole lot of crap factors into 60 quite beautifully without having a remainder or a fraction. (Although, it could be argued that they developed a 60-based system based on astronomical observations.)

Ahh, Babylon. Remember how we were taught in school that human life probably developed between the Tigris and Euphrates river valleys? (Ed. Note – very doubtful!) Well, in homage to that beautiful seed of life and reservoir of ancient history we are now bombing them back to creation. The place we called Babylon we now call Iraq. Sorry about the museum of antiquities buddies, as Donald Rumsfeld said, “looting happens.” I wouldn’t be surprised if we were in on it.

So a circle made of 0 equal parts was the void. A circle divided into 1 equal parts was an empty circle. A circle divided into 2 equal parts was split into hemispheres. By having one radius at the top, copying it over and over, and changing the angle by a number of degrees (360 divided by the number of slices) I could divide circles perfectly any way I wanted. And it doesn’t matter if you increase or decrease the size of the circle because the angles will always remain the same.

So, here’s my little chart. I removed any of them that had a trailing fraction as they would not be represented properly. I made a minor allowance for fractional remainders like .2, .5 or .4 because I felt I could still get them pretty accurate, although drawing these on paper would be much more difficult.

Number of Equal Circle Slices -> Degree Arc
(360 divided by #)

01 – 360
02- 180
03- 120
04- 90
05- 72
06- 60
08- 45
09- 40
10- 36
12 – 30
15- 24
16- 22.5
18- 20
20- 18
24- 15
25- 14.4
30- 12
32- 11.25
36- 10
40- 9
45- 8
48- 7.5
50- 7.2
60- 6

Conflict:

The first 10 numbers (except 7 – the Babylonians agree: fuck 7. It sucks.)
Notice how they don’t line up, although I do like this pattern. It reminds me of bird’s wings for some reason.

Unity:

If I were to create a kind of make-your-own-board-game online, there would have to be rules about the number of divisions you could use in succession. You can only use numbers that can factor into each other. I could do 1,3,9,18… or 1,3,6,12, but I couldn’t do 1,3,9,12 or 1,3,5.

As this is all a question of “how many cells does the cell above have control over”:

It is easier if you just take the number of divisions in the ring you are working with, and then for the next level down multiplying it by 1,2,3,4,5.. etc. (i.e. 1 man could control 4 men) although anything higher and it is going to get ridiculously complicated very fast. I have made 60 as the maximum number of divisions (6 degrees each) as a hat tip to the Babylonians and that seems like a pretty good number for board game spaces if you want to represent a whole planet. I’d need a ring of 12 in there for my constellations and that factors in nicely as well.

Not sure I’ll ever finish this thing because I’m so racked with indecision. I wish I could just release myself to make a mistake and then learn from that process, rather than trying to achieve perfection on first brush stroke. I wish that about a lot of things.