5 ms·

This is brilliant! Now i want (to build) a drag and drop toy where i can multiply or summarize numbers that are represented in this way. To see how factors mov

This is brilliant! Now i want (to build) a drag and drop toy where i can multiply or summarize numbers that are represented in this way. To see how factors move (like boids). Is this visualization algorithm called something? The explanation link from a previous HN post seems to be broken: http://mathlesstraveled.com/2012/10/05/factorization-diagrams/ http://mathlesstraveled.com/2012/10/05/factorization-diagram...

CGMthrowaway 1y ago
Kind of makes me wish that there were recognizable shapes for primes bigger 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) that didn't just look like circles. Because my favorite part about this is how you can see at a glance what the factors are. Except for primes 7 or greater I find myself cheating and looking at the top left for which prime it is. Is there some non-regular polygon that would be more distinctly recognizable to use for 7, 11, etc?
- GaggiX 1y ago
  Aren't 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) also "circles" with less resolution? The visualization is just consistent.
  - CGMthrowaway 1y ago
    Yes I dont disagree and it is elegant as is, but the way our eyes/ brain works it's much harder to ID septagon, nonagon, triacontahenagon etc at a glance. A non-regular shape would be better fit for purpose
- worldsayshi 1y ago
  Couldn't you draw it in a recognizable way using summation? 7 = 2*3+1 11 = (2*2+1)*2+1 etc...
  - CGMthrowaway 1y ago
    Interesting idea
- Liftyee 1y ago
  Agree. I watched for a while to see some larger primes and was a little disappointed. Filled polygons would offer some more shapes. Filled hexagon = 7, etc etc...
- drdeca 1y ago
  4 isn’t prime. You could probably use the binary expansion to group the dots? So, 1 is • 2 is •• 3 is _• •_• 5 is _• •_• •_• 7 is ____• _•_____• •_•___•_• 11 is ____• _•_____• •_•___•_• •_•___•_• And so on. (So, 2n is represented as n next to n, unless n is 2 in which case it is n above n, and 2n+1 is 1 above 2n ) Alternatively, using stars instead of n-gons could also be clearer?
- tocs3 1y ago
  I asked somewhere here about the algorithm for the position of the dots and got an answer (can I link directly to a post?) below. Putting things on a circle sounds like a good way to do it but it sort of precludes special arrangement for specific numbers. Not that it could not be done but what would the algorithm look like? Edit: I looked more at the animation some more and maybe I am wrong. Anyway I may try to make one.
  - hhhAndrew 1y ago
    In what is surely not a coincidence, 2012 is also the year in which a Stack Exchange question about how to generate these beautiful diagrams in Mathematica came up: https://mathematica.stackexchange.com/questions/11657/factorisation-diagrams https://mathematica.stackexchange.com/questions/11657/factor... I wrote an answer there that produced these diagrams from fairly few lines of code. The question there referred to same now-broken link mentioned above so the origin still unknown.
ashwinsundar 1y ago
I believe it's called prime factorization. Each number is placed in a group of numbers (or group of groups, etc...) E.g. 24 -> 2 * 3 * 4 = Two groups of (three groups of (four items)) Also try this for the archived version of that explanation -> https://web.archive.org/web/20130206023100/http://mathlesstraveled.com/2012/10/05/factorization-diagrams/ https://web.archive.org/web/20130206023100/http://mathlesstr...
- deleted 1y ago
  [deleted]
- nroets 1y ago
  Note that 4 isn't prime

CGMthrowaway 1y ago

Kind of makes me wish that there were recognizable shapes for primes bigger 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) that didn't just look like circles. Because my favorite part about this is how you can see at a glance what the factors are. Except for primes 7 or greater I find myself cheating and looking at the top left for which prime it is. Is there some non-regular polygon that would be more distinctly recognizable to use for 7, 11, etc?

GaggiX 1y ago
Aren't 2 (pair), 3 (triangle), 4 (square) and 5 (pentagon) also "circles" with less resolution? The visualization is just consistent.
- CGMthrowaway 1y ago
  Yes I dont disagree and it is elegant as is, but the way our eyes/ brain works it's much harder to ID septagon, nonagon, triacontahenagon etc at a glance. A non-regular shape would be better fit for purpose
worldsayshi 1y ago
Couldn't you draw it in a recognizable way using summation? 7 = 2*3+1 11 = (2*2+1)*2+1 etc...
- CGMthrowaway 1y ago
  Interesting idea
Liftyee 1y ago
Agree. I watched for a while to see some larger primes and was a little disappointed. Filled polygons would offer some more shapes. Filled hexagon = 7, etc etc...
drdeca 1y ago
4 isn’t prime. You could probably use the binary expansion to group the dots? So, 1 is • 2 is •• 3 is _• •_• 5 is _• •_• •_• 7 is ____• _•_____• •_•___•_• 11 is ____• _•_____• •_•___•_• •_•___•_• And so on. (So, 2n is represented as n next to n, unless n is 2 in which case it is n above n, and 2n+1 is 1 above 2n ) Alternatively, using stars instead of n-gons could also be clearer?
tocs3 1y ago
I asked somewhere here about the algorithm for the position of the dots and got an answer (can I link directly to a post?) below. Putting things on a circle sounds like a good way to do it but it sort of precludes special arrangement for specific numbers. Not that it could not be done but what would the algorithm look like? Edit: I looked more at the animation some more and maybe I am wrong. Anyway I may try to make one.
- hhhAndrew 1y ago
  In what is surely not a coincidence, 2012 is also the year in which a Stack Exchange question about how to generate these beautiful diagrams in Mathematica came up: https://mathematica.stackexchange.com/questions/11657/factorisation-diagrams https://mathematica.stackexchange.com/questions/11657/factor... I wrote an answer there that produced these diagrams from fairly few lines of code. The question there referred to same now-broken link mentioned above so the origin still unknown.

ashwinsundar 1y ago

I believe it's called prime factorization. Each number is placed in a group of numbers (or group of groups, etc...) E.g. 24 -> 2 * 3 * 4 = Two groups of (three groups of (four items)) Also try this for the archived version of that explanation -> https://web.archive.org/web/20130206023100/http://mathlesstraveled.com/2012/10/05/factorization-diagrams/ https://web.archive.org/web/20130206023100/http://mathlesstr...

deleted 1y ago
[deleted]
nroets 1y ago
Note that 4 isn't prime