Ada Deitz polynomials

Ada K. Deitz was a lesbian mathematician who lived in Detroit with her "partner" (howdy..) Ruth E. Foster, conveniently also a Mathematically Enclined Lady (ladies they definitely were, at that time, as you can see). In 1946, she learned to weave and figured out how to use solutions to multivariant polynomials to design patterns. They then traveled all over the country in their trailer, teaching this to weaving guilds during the summers of the late 40s. They were last spotted in the 70s, retired in Northern California (aaauw!).

This method was presented as a way to get weaving patterns in Handwoven's January 98 issue. But there's nothing that prevents it from being used for knitting patterns too. And of course you can use either texture or color for the pattern elements, or you could use a combination of them, or patterns going in both directions as in stripes vs plaids etc. Stripes of garter stitch, rows of eyelet, shots of ribbon warp, of fuzzy weft? Ada thought that this method provided "the beautiful space divisions, proportions, and individuality of pattern which the artist strives to achieve".

Here is how to proceed, starting at the very beginning:


(a + b)² =
(a + b)(a + b) =
a(a + b) + b(a + b) =
a² + ab + ab + b² =
aa + ab + ab + bb

And let's get even more complex :-):


(a + b)³ =
(a + b)(a + b)² =
(a + b)(a² + 2ab + b²) =
a(a² + 2ab + b²) + b(a² + 2ab + b²) =
a³ + 2a²b + ab² +a²b + 2ab²  b³ =
a³ + 3a²b + 3ab²  b³ =
aaa+ aabaabaab + abbabbabb + bbb

Here is a closeup of a chenille scarf that we wove, with the solution to (a + b)².

And here is our polynomial riff scarf, with variations of the solution to (a + b)³.

Now, you add more powers, more variables, more whatevers. Have fun.

References:

Handwoven January/February 98 from Interweave Press
Original article by Lana Schneider, who wrote the Handwoven article.
A later take on it from an Arizona geek with further examples, but math concepts should be Fuzzy, not that kind of fuzzy!