3 ms·
why a circle and why NOT a straight line which is equally plausible visualization
by dedalus 11y ago
why a circle and why NOT a straight line which is equally plausible visualization
- chki 11y agoBecause of the prime numbers! I always thought of them as ugly but they are actually the _complete_ numbers, which have to be represented in those beautiful circles :)
- rspeer 11y agoYou sound a little demanding when you capitalize "NOT" like that. I didn't make the visualization but I find the circles to be a good choice. Not only is it pretty, it makes use of two-dimensional space in a consistent way. A factor of 5 has the same shape whenever it appears. If you factorized things into a straight line, do you just line everything up horizontally, in which case you just see hundreds of dots with gaps in them and there would be nothing interesting about the visualization? Or do you make rectangles, with some of the factors going vertically? In that case, sometimes your 5s will go horizontally and sometimes they'll go vertically, making a distinction out of nothing.
- d4n3 11y agoI think this actually wasn't an arbitrary choice, but a result of the algorithm.. e.g. factors are displayed as clusters ordered in a circle (factors of 2 is a circle with groups of 2, factors of 3 is a circle of groups of 3). So for primes, you have a circle of groups of 1.
- tamana 11y agoThey aren't circles, they are p-gons. A factorization is drawn as a tree where each level has p radially symmetric branches, corresponding to a prime factor p. (Only the leafs are drawn, but you can fill in the branches and node). A prime number has only one level