I think that's my bottom line reason why I didn't include it. This is all about factorization. 1 is the background color, because anything times 1 is itself. But I don't think 0 would quite fit with the pattern.
I am trying to get the graphics I made for the children's book I wrote with this concept (not yet published, but now it's time to try) uploaded in a decent form onto cafepress. I'll post if it comes out okay and I can sell t-shirts.
I have spent so much time looking at graphs, I wanted smaller to be on the bottom and to the left, as in Cartesian coordinates. Though I know it's a bit weak. The color differentiation is even worse in the photo than it is with just the yarn. And it's tricky to find a yarn with enough distinct shades.
That's interesting, because in CompSci screen coordinates (and vector coordinates when programming graphics) are usually rooted at the top-left, so we have a more "consistent" natural perception of it - those of us using mainly left-to-right language scripts.
Anyway, I really don't see graphs as sequences. I have my perception of cartesian graphs and sequenced lists completely separated.
No, but when people say, "Nice Sweater," and I ask, with a sparkle in my eye, "Do you want to hear about it?" they often say, "I thought they were flags."
Your age isn't on your website, but my calculation (got Master's degree in 1986 at likely approximate age of 24) couldn't have been TOO far off, right?
Well, it was farther off two years ago when I posted the picture. And I got my MA in 1986 on my 22nd birthday. (Later got an MLIS on another birthday.) I put a math problem in my follow-up post. You should be able to calculate my age and my son's ages from these clues: http://sonderbooks.com/blog/?p=10000
My age estimate was from your LinkedIn profile. If I was guessing by pictures, I would have said 39. (Is that the right answer? (I mean in the sense of Right Answer to say to someone of how old they are, not mathematically correct. :-) ))
The Right Answer is to have not brought up the age issue because it is rather immaterial to the discussion. Can you really say that the authors age, when considered independently from the article subject, has significant bearing on the voting?
The idea of making a chart from prime numbers is definitely not copywrite-able. So go for it! I got the idea from a knitting magazine where someone described a blanket with a chart of prime numbers that fascinated a student who walked by who was in a remedial math class. They had a small picture of part of the blanket, and I couldn't figure out how their method worked, but I put those ideas into a sweater.
I have attempted to write a children's book about using this idea to make cyphers or just fun art. But I haven't tried to sell it yet. And I did a library program that went over very well with kids. Anyway, if anyone makes a t-shirt let me know -- I'd order one.
Though maybe I should do it -- I've got several colored charts already made from when I was working on my book. Give me some time, and I'll make a cafe press account....
I can see how it's easy to get hooked (sorry) on knitting and maths. You might start off doing visualisations of various sequences. Next, you wonder what happens if Fink and Mao's necktie analysis [1] is extended to an exhaustive analysis of knitting stitches, and end up with all sorts of multidimensional stuff. Finally that becomes too easy and you attempt to use a length of yarn to model the world line of a single electron [2] and accidentally win a Nobel Prize! :-)
I thought about putting in zero, but I'm thinking of this in the mathematical group Z sub n, the natural numbers. That ring does not include zero, and it's as if it doesn't exist. One, on the other hand, is the multiplicative identity, so it is the background color, a factor of all the other numbers.
Certainly the ring `Z/nZ` has 0, meaning an additive identity (the image under the natural homomorphism `Z \to Z/nZ` of the 'true' `0 \in Z`). Do you mean that the group `(Z/nZ)^\times` of units of `Z/nZ` doesn't contain 0?
(I think that it's also confusing to call `Z/nZ`, or `Z_n` or whatever you like, the group of natural numbers; rather, it is a quotient of the semigroup (or semiring) of natural numbers by a normal subsemigroup (or semiideal).)
Okay, you passed me. I knew I should have pulled out my very old Modern Algebra book. I was thinking in terms of modulo groups. You can show lots of number theory with the sweater, granted that the number on the end is the equivalent of zero. I want a group under multiplication. Is that making any sense?
If you want a group under multiplication, the easy options are: (1) Integers modulo a prime number, not counting 0 mod p. (2) Integers modulo anything (call it n), not counting ones that have a common factor with n. (3) Rational numbers.
In this case you've got 1..100, and 101 is prime. So the numbers on (the front of) the sweater, mod 101, form a group under multiplication. But of course in that group you lose all the prime-number structure shown on the sweater -- you can't really talk about, say, "multiples of 3 (mod 101)" because 101 isn't a multiple of 3.
What do you think of my plans for a prime factorization scarf? http://sonderbooks.com/blog/?p=10000