Dietz & Foster on Lou Tate Little Looms at LLH

Ada K. Dietz (October 7, 1888 – January 12, 1981) was an American weaver best known for her 1949 monograph ''Algebraic Expressions in Handwoven Textiles'', which defines a novel method for generating weaving patterns based on

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

ic patterns. Her method employs the expansion of multivariate

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example ...

s to devise a weaving scheme. Dietz' work is still well-regarded today, by both weavers and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

s. Along with the references listed below, Griswold (2001) cites several additional articles on her work.

Algebraic weaving

Ada Dietz developed her algebraic method in 1946 while living in

Long Beach Long Beach is a city in Los Angeles County, California. It is the 42nd-most populous city in the United States, with a population of 466,742 as of 2020. A charter city, Long Beach is the seventh-most populous city in California. Incorporate ...

California California is a state in the Western United States, located along the Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the most populous U.S. state and the 3rd largest by area. It is also the m ...

. An avid weaver, Dietz drew upon her experience as a former math teacher to devise a threading pattern based on a cubic

binomial expansion In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where the ...

. She describes her idea as follows: :"Taking the cube of a binomial /nowiki> (''x'' + ''y'')³/nowiki>, I approached he pattern/nowiki> 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 ( , , ) is the largest city in the Commonwealth of Kentucky and the 28th most-populous city in the United States. Louisville is the historical seat and, since 2003, the nominal seat of Jefferson County, on the Indiana border. ...

Kentucky Kentucky ( , ), officially the Commonwealth of Kentucky, is a state in the Southeastern region of the United States and one of the states of the Upper South. It borders Illinois, Indiana, and Ohio to the north; West Virginia and Virginia ...

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. Square of a trinomial (1)

History and development

Dietz was a high school biology and math teacher when she met Ruth E. Foster, a professional weaver with the Hewson Studios in Los Angeles. Foster's work inspired Dietz to begin studying weaving at Wayne University in Detroit under Nellie Sargent Johnson. Her experiments in writing weaving drafts began in Johnson's classes. It was later when Dietz and Foster were driving north to study at the Banff School of Fine Arts in Canada that she began using mathematical equations. She wanted "a reason for writing a draft in a definite way", and went to the mathematical equations she had worked with for so long.

References

Sources

* * *Redfield, Gail (1959). "Variations on an Algebraic Equation". ''Handweaver & Craftsman'' (Summer): 46-49 * * {{DEFAULTSORT:Dietz, Ada 1880s births 1950 deaths American weavers American textile designers Mathematical artists Women textile artists

Algebraic weaving

History and development

See also

References

Sources