Ada K. Dietz was an American weaver

Weaving

Weaving is a method of fabric production in which two distinct sets of yarns or threads are interlaced at right angles to form a fabric or cloth. The other methods are knitting, lace making and felting. The longitudinal threads are called the warp and the lateral threads are the weft or filling...

 best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines a novel method for generating weaving patterns based on algebraic patterns. Her method employs the expansion of multivariate polynomial

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

s to devise a weaving scheme. Dietz' work is still well-regarded today, by both weavers and mathematicians. Along with the references listed below, Griswold (2001) cites several additional articles on her work.

History

Ada Dietz developed her algebraic method in 1946 while living in Long Beach

Long Beach, California

Long Beach is a city situated in Los Angeles County in Southern California, on the Pacific coast of the United States. The city is the 36th-largest city in the nation and the seventh-largest in California. As of 2010, its population was 462,257...

, California

California

California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...

. 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

Louisville, Kentucky

Louisville is the largest city in the U.S. state of Kentucky, and the county seat of Jefferson County. Since 2003, the city's borders have been coterminous with those of the county because of a city-county merger. The city's population at the 2010 census was 741,096...

, Kentucky

Kentucky

The Commonwealth of Kentucky is a state located in the East Central United States of America. As classified by the United States Census Bureau, Kentucky is a Southern state, more specifically in the East South Central region. Kentucky is one of four U.S. states constituted as a commonwealth...

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.