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- ConnieLv 79 years agoFavorite Answer
Ada Dietz developed her algebraic method in 1946 while living in Long Beach, California. An avid weaver, Dietz drew upon her experience as a former math teacher to devise a threading pattern based on a cubic binomial expansion. She describes her idea as follows:

"Taking the cube of a binomial [ (x + y)3], I approached [the pattern] in the way applied algebraic problems are approached - by letting x equal one unknown and y equal the other unknown.

"In this case, x equaled the first and second harnesses, and y equaled the third and fourth harnesses. Then it was simply a matter of expanding the cube of the binomial and substituting the values of x and y to write the threading draft." (Dietz, 1949)

A piece based on the formula (a + b + c + d + e + f)2, submitted to the Little Loomhouse Country Fair in Louisville, Kentucky received such a positive response, which prompted a collaboration between Dietz and Little Loomhouse's founder, Lou Tate. The fruits of the collaboration included the booklet Algebraic Expressions in Handwoven Textiles and a traveling exhibit which continued throughout the 1950s.

http://en.wikipedia.org/wiki/Ada_Dietz

The little niche of history that captures Ada Dietz’ work is significant as well. It is an opportunity to drop back a few decades and connect with weavers whose enthusiasm and creativity mirrors our own. As a weaving student in 1946, Ada was encouraged to create original work rather than simply follow established patterns. She logically fell back onto her career in mathematics. She and Ruth Foster began to see where the idea would lead them, which ultimately was to Louisville, KY.

Ada submitted a hanging woven in summer and winter with the formula (a+b+c+d+e+f)2 to the Country Fair held at the Little Loomhouse. The response to this piece was so remarkable that Lou Tate, founder of The Little Loomhouse, invited the two weavers to conduct a summer-long study for her experimental weaving group.

The booklet, Algebraic Expressions in Handwoven Textiles arose out of that collaboration. A travelling exhibit was also developed which, during the fifties, the two women took to weavers throughout the United States, sharing the concept of designing by formula. Two articles that chronicle the development of the use of algebraic expressions were published in Handweaver and Craftsman Magazine indicating the enthusiasm with which it was received at the time. They were published in Spring, 1953 and Summer, 1959.

Basically the idea Ada Dietz developed is to create an algebraic equation, giving a value to each element you wish to utilize in a specific textile. Two colors would be a simple formula (a + b). You then decide on a degree of complexity with which you want these chosen elements to interact -- 2 or 3 being the more common choices. Expanding the formula to its simplest level, you establish the order in which an element is used. For example, (a + b)2

multiply the phrase by itself (a + b)(a + b)

multiply the individual elements in the first parentheses by all the elements in the second parentheses a(a + b) and b(a + b)

which becomes a2 + ab + ab + b2

which breaks down to aa abab bb

http://fiberarts.org/design/articles/algebra.html

Actual examples of weaving done to different formulas on this link: