My Prime Factorization Sweater
April 29, 2012 6:00 AM   Subscribe

This is the sweater that proves that I am a Certified Math Nut.
posted by Foci for Analysis (54 comments total) 61 users marked this as a favorite

 
Unfortunately, in the system of maritime signal flags, she's given Vanuatu permission to neuter her cats.
posted by Infinity_8 at 6:37 AM on April 29, 2012 [131 favorites]


All I gotta say is that she better be wearing blue pants.
posted by iamkimiam at 6:45 AM on April 29, 2012 [5 favorites]


A single link sweater.
posted by infini at 6:54 AM on April 29, 2012 [1 favorite]


Now, if she can just turn this into a hat, she will be all set!
posted by GenjiandProust at 6:56 AM on April 29, 2012 [4 favorites]


If you want to destroy my sweater, work over the ring of integers of an algebraic number field whose ideal class group is non-trivial, such as Q((-5)^(1/2)).
posted by escabeche at 6:57 AM on April 29, 2012 [58 favorites]


Way to suck the fun right out of ugly sweaters.
posted by item at 7:04 AM on April 29, 2012 [3 favorites]


For bonus nuttery, the sweater is stitched with trefoil knots that lie in E3 space.
posted by Blazecock Pileon at 7:25 AM on April 29, 2012 [4 favorites]


Now, if she can just turn this into a hat, she will be all set!

I was going to suggest this hat instead.
posted by Johnny Assay at 7:30 AM on April 29, 2012 [5 favorites]


At least her sweater isn't a munition.
posted by Obscure Reference at 7:31 AM on April 29, 2012


Golly, I just thought it was kinda pretty.
posted by kinnakeet at 7:37 AM on April 29, 2012 [2 favorites]


I want that sweater in shirt form.
posted by DU at 7:50 AM on April 29, 2012 [1 favorite]


So we had a family joke that if an alien ever came to our door, we’d run and get the sweater to prove that we are intelligent life.

In our own human history, this is not a smart thing to do.
posted by Brian B. at 7:55 AM on April 29, 2012 [3 favorites]


Minus geek points for not using the resistor color code for her number representation.
posted by ZenMasterThis at 7:57 AM on April 29, 2012 [10 favorites]


I was going to suggest this hat instead.

That hat is all one surface, so your head must always be outside it (or the weather inside), so it can't possibly keep you warm!
posted by GenjiandProust at 7:58 AM on April 29, 2012 [10 favorites]


I could never get past the "dividing fractions" sweater.
posted by Slack-a-gogo at 8:01 AM on April 29, 2012


A bunch of knitters and spinners are also bona fide math nerds:
fractal spinning, fibonacci stripes, more fractal knitting, tessellation, and golden ratio blankets.
posted by francesca too at 8:13 AM on April 29, 2012 [11 favorites]


I could never get past the "dividing fractions" sweater.

When dividing fractions, don't ask why
Flip the sucker, and multiply
posted by jcreigh at 8:23 AM on April 29, 2012 [8 favorites]


This does not help dispel the stereotype that maths geeks have absolutely no sense of taste or style.
posted by Decani at 8:29 AM on April 29, 2012 [2 favorites]


Such snark! I think it's a cool sweater, and I like how (as she points out) "... the patterns are wonderful and fascinating. You’ll quickly notice that the yellows and the blues line up, because 5 and 2 are factors of 10. You also might notice that all perfect squares are symmetrical."

Rock on, awesome math sweater lady! That's a great sweater. I hope you got lots of great responses at the kid's lit conference.
posted by barnacles at 8:34 AM on April 29, 2012 [16 favorites]


I want that sweater in shirt form.

There must be a simple transformation that can achieve this....
posted by GenjiandProust at 8:35 AM on April 29, 2012 [2 favorites]


There must be a simple transformation that can achieve this...

Yes, actually ... the Jacquard transform.
posted by ZenMasterThis at 8:39 AM on April 29, 2012 [16 favorites]


That is a great sweater! So much possible learning & observing would be possible for her kid audiences.

Every classroom should have one - would help those of us who see patterns better than numbers.
posted by Heart_on_Sleeve at 8:51 AM on April 29, 2012


Best sweater ever.
posted by ericost at 8:54 AM on April 29, 2012


That's pretty cool! I love graphic representations of stuff like that, so much unexpected pattern falls out.
posted by freebird at 8:58 AM on April 29, 2012


This is the sweater that proves that I am a Certified Math Nut.

Q.E.D.
posted by mazola at 9:27 AM on April 29, 2012


Awesome. I have all I can handle just figuring out how many stitches to put in a row
, never mind what base they are in.
posted by SLC Mom at 9:32 AM on April 29, 2012 [1 favorite]


Not surpisingly, Bill Cosby has three of these.
posted by Blazecock Pileon at 9:40 AM on April 29, 2012 [2 favorites]


I could never get past the "dividing fractions" sweater

Check out this graphical representation of fraction division. (which would also make a cool sweater!)
posted by Wulfhere at 9:58 AM on April 29, 2012


Goes back and looks at every Cosby episode ever created.
posted by Fizz at 10:00 AM on April 29, 2012


They go well with hexidecimal shoes sorry that's all I got
posted by not_on_display at 10:02 AM on April 29, 2012


Not surpisingly, Bill Cosby has three of these.

Well, that show did rule prime time for a reason.
posted by yoink at 10:03 AM on April 29, 2012 [16 favorites]


Oh, it's a sweater version You Can Count on Monsters! (Only without the monsters, which, let's face it, are what makes the book so much fun.)
posted by bakerina at 10:11 AM on April 29, 2012


They go well with hexidecimal shoes sorry that's all I gotsorry that's all I got

You have only eight toes on each foot!?!
posted by GenjiandProust at 10:49 AM on April 29, 2012


You have only eight toes on each foot!?!

Sorry, I retract that. I meant to express wonder, but I can see how it could be read as a callous mocking of your no-doubt painful situation. I guess I was putting the "mal" in the hexidecimal.
posted by GenjiandProust at 11:05 AM on April 29, 2012


You have only eight toes on each foot!?!

The medical term is "polydoctalism".
posted by cortex at 11:23 AM on April 29, 2012 [2 favorites]


I'm pretty sure Bill Cosby's sweaters are all representations of 1/f noise.
posted by GuyZero at 11:58 AM on April 29, 2012


Curiosity required that I write a python script that generates this pattern.

Disclaimer: it uses HTML tables as a crude rendering medium instead of a more sane solution like using a real graphics library, and it's therefore rather ugly and/or convoluted.
posted by Rhomboid at 12:52 PM on April 29, 2012 [20 favorites]


That is excellent! Kind of tempting to produce a room decoration in that theme.
posted by LobsterMitten at 2:13 PM on April 29, 2012


"Minus geek points for not using the resistor color code for her number representation.
posted by ZenMasterThis

Maybe she is a Math Nut not a Physics or Electonics nut: there are 15 entries tagged as maths, but none tagged with physics or electronics, so maybe she doesn't know about resistor colour codes.

Awesome jumper. Keep on geeking.
posted by marienbad at 4:48 PM on April 29, 2012 [3 favorites]


It is not that surprising that craft forms based on tying an elaborate series of knots are appealing to minds that enjoy a bit of mathematizing.
posted by gingerest at 4:56 PM on April 29, 2012


Actually, if she made that up (am not a math nut, could only read first few lines), then she should totally patent that and make it into t-shirts.
posted by bquarters at 5:16 PM on April 29, 2012


Awesome. Is there any reason why some boxes are vertical and some are horizontal?
posted by milestogo at 5:16 PM on April 29, 2012


Can you patent patterns? Can you make a tongue twister from patenting patterns?
posted by bquarters at 5:17 PM on April 29, 2012


Trying to remember where I read about a mathematician laying the blank and white kitchen tiles in a representation of the imaginary plane. That sentence is a kinda random memory splat and just wrong, but I really wanted to see a picture of his kitchen.
posted by sammyo at 5:55 PM on April 29, 2012


Awesome. Is there any reason why some boxes are vertical and some are horizontal?

None stated in the blog post that I saw. I'm guessing it's just to make things a bit more visually interesting. You'll note that the two-factor stripes are always vertical, the three-factors always horizontal; having those two (very prominent) patterns have opposing alignments guarantees you don't get a sort of dull one-directional feel to the way the whitespace within the individual patches aligns.

Actually, if she made that up

Well, she presumably made up the specific choice of visual representation of the factorizations, but what this is is a neat way to represent an extremely well-known (in a math context) bit of fundamental mathematics. This is like coming up with a custom typeface to print the alphabet in; the notable thing is the typeface, but nobody would try take credit for the alphabet itself for having done so.

There's a lot of different neat possibilities for visualizing factorization in different ways; when my wife saw this post this morning she reminded me of the Ulam Spiral, a simple but really interesting way of looking for patterns in the distribution of primes.
posted by cortex at 5:57 PM on April 29, 2012


Right now base six is my favorite way of representing prime factorization. All the primes line up in two columns because every prime number is congruent to 1 or 5 mod 6. Check out this chart of what I call "monohex" representation of numbers.

| 0               |        1 | 2               | 3          | (2 2)         |       5 |
|-----------------+----------+-----------------+------------+---------------+---------|
| (2 3)           |       11 | (2 2 2)         | (3 3)      | (2 5)         |      15 |
| (2 2 3)         |       21 | (2 11)          | (3 5)      | (2 2 2 2)     |      25 |
| (2 3 3)         |       31 | (2 2 5)         | (3 11)     | (2 15)        |      35 |
| (2 2 2 3)       |    (5 5) | (2 21)          | (3 3 3)    | (2 2 11)      |      45 |
| (2 3 5)         |       51 | (2 2 2 2 2)     | (3 15)     | (2 25)        |  (5 11) |
|-----------------+----------+-----------------+------------+---------------+---------|
| (2 2 3 3)       |      101 | (2 31)          | (3 21)     | (2 2 2 5)     |     105 |
| (2 3 11)        |      111 | (2 2 15)        | (3 3 5)    | (2 35)        |     115 |
| (2 2 2 2 3)     |  (11 11) | (2 5 5)         | (3 25)     | (2 2 21)      |     125 |
| (2 3 3 3)       |   (5 15) | (2 2 2 11)      | (3 31)     | (2 45)        |     135 |
| (2 2 3 5)       |      141 | (2 51)          | (3 3 11)   | (2 2 2 2 2 2) |  (5 21) |
| (2 3 15)        |      151 | (2 2 25)        | (3 35)     | (2 5 11)      |     155 |
| (2 2 2 3 3)     |      201 | (2 101)         | (3 5 5)    | (2 2 31)      | (11 15) |
| (2 3 21)        |      211 | (2 2 2 2 5)     | (3 3 3 3)  | (2 105)       |     215 |
| (2 2 3 11)      |   (5 25) | (2 111)         | (3 45)     | (2 2 2 15)    |     225 |
| (2 3 3 5)       |  (11 21) | (2 2 35)        | (3 51)     | (2 115)       |  (5 31) |
| (2 2 2 2 2 3)   |      241 | (2 11 11)       | (3 3 15)   | (2 2 5 5)     |     245 |
| (2 3 25)        |      251 | (2 2 2 21)      | (3 5 11)   | (2 125)       |     255 |
| (2 2 3 3 3)     |      301 | (2 5 15)        | (3 101)    | (2 2 2 2 11)  |     305 |
| (2 3 31)        |   (5 35) | (2 2 45)        | (3 3 21)   | (2 135)       | (11 25) |
| (2 2 2 3 5)     |  (15 15) | (2 141)         | (3 105)    | (2 2 51)      | (5 5 5) |
| (2 3 3 11)      |      331 | (2 2 2 2 2 2 2) | (3 111)    | (2 5 21)      |     335 |
| (2 2 3 15)      |  (11 31) | (2 151)         | (3 3 3 5)  | (2 2 2 25)    |     345 |
| (2 3 35)        |      351 | (2 2 5 11)      | (3 115)    | (2 155)       | (15 21) |
| (2 2 2 2 3 3)   |   (5 45) | (2 201)         | (3 11 11)  | (2 2 101)     |     405 |
| (2 3 5 5)       |      411 | (2 2 2 31)      | (3 3 25)   | (2 11 15)     |  (5 51) |
| (2 2 3 21)      |      421 | (2 211)         | (3 125)    | (2 2 2 2 2 5) | (11 35) |
| (2 3 3 3 3)     |      431 | (2 2 105)       | (3 5 15)   | (2 215)       |     435 |
| (2 2 2 3 11)    |  (21 21) | (2 5 25)        | (3 3 31)   | (2 2 111)     |     445 |
| (2 3 45)        | (5 5 11) | (2 2 2 2 15)    | (3 135)    | (2 225)       |     455 |
| (2 2 3 3 5)     |      501 | (2 11 21)       | (3 141)    | (2 2 2 35)    | (5 101) |
| (2 3 51)        |  (15 25) | (2 2 115)       | (3 3 3 11) | (2 5 31)      |     515 |
| (2 2 2 2 2 2 3) |      521 | (2 241)         | (3 5 21)   | (2 2 11 11)   |     525 |
| (2 3 3 15)      |      531 | (2 2 2 5 5)     | (3 151)    | (2 245)       | (11 45) |
| (2 2 3 25)      |  (5 105) | (2 251)         | (3 3 35)   | (2 2 2 2 21)  | (15 31) |
| (2 3 5 11)      |      551 | (2 2 125)       | (3 155)    | (2 255)       | (5 111) |
...

posted by wobh at 6:13 PM on April 29, 2012 [4 favorites]


All the primes line up in two columns because every prime number is congruent to 1 or 5 mod 6. Check out this chart of what I call "monohex" representation of numbers.

Shouldn't that chart begin like this?

| 0               |        1 | 2               | 3          | (2 2)         |       5 |
|-----------------+----------+-----------------+------------+---------------+---------|
| (2 3)           |        7 | (2 2 2)         | (3 3)      | (2 5)         |      11 |
| (2 2 3)         |       13 | (2 7)           | (3 5)      | (2 2 2 2)     |      17 |
?
posted by kenko at 6:25 PM on April 29, 2012


Base 6! In which 710 is written as 116, 1310 is written as 216, and so on.
posted by cortex at 6:32 PM on April 29, 2012


ahhhh, duh.
posted by kenko at 6:53 PM on April 29, 2012


I want that t-shirt.
posted by benito.strauss at 9:00 PM on April 29, 2012


Great sweater, looks like a lost opportunity to market t-shirts, shirts, sweaters, and boxers on CafePress.com.
posted by Vindaloo at 5:36 AM on April 30, 2012


Looks like the creator is trying to get a t-shirt made.
posted by ashirys at 11:35 AM on April 30, 2012 [1 favorite]


Minus geek points for not using the resistor color code for her number representation.

Her scheme requires a separate color for every prime under 100 (as far as the sweater goes) plus the background (i.e., 1), for a total of 26 colors. The resistor code wouldn't suffice. Unless you wanted to use two-color combinations for numbers greater than 9, but then that makes the sweater base-specific, which her scheme avoids, as she notes. Not to mention ruining all the nice color patterns; not every number that has the digit "2" ("red" in the resistor code) is divisible by 2.
posted by DevilsAdvocate at 12:38 AM on May 1, 2012


As an asian, I feel like I should appreciate that sweater more...but it's just giving me a headache grarg grarg!!
posted by sprezzy at 10:11 AM on May 2, 2012


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