Quotients that signify nothing
September 11th, 2009
Ever wondered how many quotients 4372 has? You’d be surprised! For an even number, it has only 6 quotients: 4372, 2186, 1093, 4, 2, and 1. Not quite a prime, but certainly a good effort!
I’ve misused Processing once again to visually depict something completely useless. How many quotients does a number have? I’ve made a grid of 500 wide by 400 long and used Processing to colour each point in that grid according to how many quotients that number has. Of course, numbers with only 1 quotients are primes (as you can see in the diagram, they’re red). But it is very interesting to see lines and patterns in the diagram below. The grid shows a red point for a prime, and a gradient grey colour that gets brighter the more quotients a number has. The brightest spots make up lines and patterns that, to my knowledge, signify absolutely nothing. 
The vertical lines are easy. As this grid is 500 pixels wide, the bright vertical lines are the 100’s. The vertical lines that are slightly less pronounced are the 20’s. There’s a diagonal line from the top left that might have something to do with 3’s (and one with 5’s), but I have no idea what causes the other diagonal that starts at the top right.
Still, pretty picture 
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My name is Marco Hokke. My blog is about the things that interest me and things I might forget if I would not blog them.
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