Daina Taimiņa (born August 19, 1954) is a
Latvian 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 ...
, retired adjunct associate professor of mathematics at
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...
, known for discovering a groundbreaking way of modelling hyperbolic planes by
crochet
Crochet (; ) is a process of creating textiles by using a crochet hook to interlock loops of yarn, thread (yarn), thread, or strands of other materials. The name is derived from the French term ''crochet'', meaning 'hook'. Hooks can be made from ...
ing objects to illustrate
hyperbolic space
In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to -1. It is homogeneous, and satisfies the stronger property of being a symmetric space. Th ...
and innovative use of them teaching geometry.
Education and career
Taimiņa received all of her formal education in
Riga
Riga (; lv, Rīga , liv, Rīgõ) is the capital and largest city of Latvia and is home to 605,802 inhabitants which is a third of Latvia's population. The city lies on the Gulf of Riga at the mouth of the Daugava river where it meets the Ba ...
,
Latvia
Latvia ( or ; lv, Latvija ; ltg, Latveja; liv, Leţmō), officially the Republic of Latvia ( lv, Latvijas Republika, links=no, ltg, Latvejas Republika, links=no, liv, Leţmō Vabāmō, links=no), is a country in the Baltic region of ...
, where in 1977 she graduated
summa cum laude
Latin honors are a system of Latin phrases used in some colleges and universities to indicate the level of distinction with which an academic degree has been earned. The system is primarily used in the United States. It is also used in some Sou ...
from the
University of Latvia
University of Latvia ( lv, Latvijas Universitāte, shortened ''LU'') is a state-run university located in Riga, Latvia established in 1919.
The ''QS World University Rankings'' places the university between 801st and 1000th globally, seventh ...
and completed her graduate work in Theoretical Computer Science (with thesis advisor Prof.
Rūsiņš Mārtiņš Freivalds) in 1990. As one of the restrictions of the Soviet system at that time, a doctoral thesis was not allowed to be defended in Latvia, so she defended hers in
Minsk
Minsk ( be, Мінск ; russian: Минск) is the capital and the largest city of Belarus, located on the Svislach and the now subterranean Niamiha rivers. As the capital, Minsk has a special administrative status in Belarus and is the admi ...
, receiving the title of
Candidate of Sciences
Candidate of Sciences (russian: кандидат наук, translit=kandidat nauk) is the first of two doctoral level scientific degrees in Russia and the Commonwealth of Independent States. It is formally classified as UNESCO's ISCED level 8, "do ...
. This explains the fact that Taimiņa's doctorate was formally issued by the Institute of Mathematics of the
National Academy of Sciences of Belarus
The National Academy of Sciences of Belarus (NASB) ( be, Нацыянальная акадэмія навук Беларусі, russian: Национальная академия наук Беларуси, НАН Беларуси, НАНБ) is ...
. After Latvia regained independence in 1991, Taimiņa received her higher doctoral degree (
doktor nauk
Doctor of Sciences ( rus, доктор наук, p=ˈdoktər nɐˈuk, abbreviated д-р наук or д. н.; uk, доктор наук; bg, доктор на науките; be, доктар навук) is a higher doctoral degree in the Russi ...
) in mathematics from the
University of Latvia
University of Latvia ( lv, Latvijas Universitāte, shortened ''LU'') is a state-run university located in Riga, Latvia established in 1919.
The ''QS World University Rankings'' places the university between 801st and 1000th globally, seventh ...
, where she taught for 20 years.
Daina Taimiņa joined the Cornell Math Department in December 1996.
Combining her interests in mathematics and crocheting, she is one of 24 mathematicians and artists who make up the
Mathemalchemy
Mathemalchemy is a traveling art installation dedicated to a celebration of the intersection of art and mathematics. It is a collaborative work led by Duke mathematician Ingrid Daubechies and fiber artist Dominique Ehrmann. Team.
Hyperbolic crochet
While attending a geometry workshop at Cornell University about teaching geometry for university professors in 1997, Taimiņa was presented with a fragile paper model of a hyperbolic plane, made by the professor in charge of the workshop, David Henderson (designed by
geometer
A geometer is a mathematician whose area of study is geometry.
Some notable geometers and their main fields of work, chronologically listed, are:
1000 BCE to 1 BCE
* Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra
* ...
William Thurston
William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
Thurston ...
.
) It was made «out of thin, circular strips of paper taped together». She decided to make more durable models, and did so by crocheting them.
The first night after first seeing the paper model at the workshop she began experimenting with algorithms for a crocheting pattern, after visualising hyperbolic planes as exponential growth.
The following fall, Taimiņa was scheduled to teach a geometry class at Cornell. She was determined to find what she thought was the best possible way to teach her class. So while she, together with her family, spent the preceding summer at a tree farm in Pennsylvania, she also spent her days by the pool watching her two daughters learning how to swim whilst simultaneously making a classroom set of models of the hyperbolic plane. This was the first ever made from yarn and crocheting.
The models made a significant difference to her students, according to themselves. They said they "liked the tactile way of exploring hyperbolic geometry" and that it helped them acquire experiences that helped them move on in said geometry. This was what Taimina herself had been missing when first learning about hyperbolic planes and is also what has made her models so effective, as these models have later become the preferred way of explaining hyperbolic space within geometry.
In a TedxRiga by Taimiņa she tells the story of how the need for a visual, intuitive way of understanding hyperbolic planes spurred her toward inventing crocheted geometry models. In the talk she also gives a basic introduction to hyperbolic geometry using her models as well as rendering some of the negative responses she initially received from some who viewed crocheting as unfitting in mathematics.
In the foreword to Taimiņa's book Crocheting Adventures with Hyperbolic Planes mathematician William Thurston, the designer of the paper model of hyperbolic planes, called Taimiņa's models «deceptively interesting». He attributed much of his view on them to how they make possible a tactile, non-symbolic, cognitively holistic way of understanding the highly abstract and complex part of mathematics non-euclidean geometry, is.
Taimiņa has led several workshops at Cornell University for college geometry instructors together with professor David Henderson (of the aforementioned 1997 workshop and who later became her husband).
[.]
Crocheted mathematical models later appeared in three geometry textbooks they wrote together, of which the most popular is ''Experiencing Geometry: Euclidean and non-Euclidean with History''. In 2020 Taimiņa published 4th edition of this book as open sourc
An article about Taimiņa's innovation in ''
New Scientist
''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publishe ...
'' was spotted by the
Institute For Figuring The Institute For Figuring (IFF) is an organization based in Los Angeles, California that promotes the public understanding of the poetic and aesthetic dimensions of science, mathematics and the technical arts. Founded by Margaret Wertheim and Chris ...
, a small non-profit organisation based in
Los Angeles
Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the largest city in the state of California and the second most populous city in the United States after New York City, as well as one of the world' ...
, and she was invited to speak about hyperbolic space and its connections with nature to a general audience which included artists and movie producers.
Taimiņa's initial lecture and following other public presentations sparked great interest in this new tactile way of exploring concepts of hyperbolic geometry, making this advanced topic accessible to wide audiences. Originally creating purely mathematical models, Taimiņa soon became popular as a fiber artist and public presenter for general audiences of ages five and up. In June 2005, her work was first shown as art in an exhibition "Not The Knitting You Know" at
Eleven Eleven Sculpture Space
Eleven or 11 may refer to:
*11 (number), the natural number following 10 and preceding 12
* one of the years 11 BC, AD 11, 1911, 2011, or any year ending in 11
Literature
* ''Eleven'' (novel), a 2006 novel by British author David Llewellyn
*''E ...
, an art gallery in
Washington, D.C.
)
, image_skyline =
, image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...
Since then she has participated regularly in various shows in galleries in US, UK, Latvia, Italy, Belgium, Ireland, Germany. Her artwork is in the collections of several private collectors, colleges and universities, and has been included in the American Mathematical Model Collection of the
Smithsonian Museum
The Smithsonian Institution ( ), or simply the Smithsonian, is a group of museums and education and research centers, the largest such complex in the world, created by the U.S. government "for the increase and diffusion of knowledge". Founded ...
,
Cooper–Hewitt, National Design Museum
Cooper Hewitt, Smithsonian Design Museum is a design museum housed within the Andrew Carnegie Mansion in Manhattan, New York City, along the Upper East Side's Museum Mile. It is one of 19 museums that fall under the wing of the Smithsonian Inst ...
, and
Institut Henri Poincaré
The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrond ...
.
Her work has received wide interest in media. It has been written about in 'Knit Theory' in
Discover magazine
''Discover'' is an American general audience science magazine launched in October 1980 by Time Inc. It has been owned by Kalmbach Publishing since 2010.
History
Founding
''Discover'' was created primarily through the efforts of ''Time'' mag ...
and in ''The Times'',
explaining how a hyperbolic plane can be ''crocheted'' by increasing the number of stitches:
Margaret Wertheim
Margaret Wertheim (born 20 August 1958) is an Australian-born science writer, curator, and artist based in the United States. She is the author of books on the cultural history of physics, and has written about science, including for the ''New Yo ...
interviewed Daina Taimiņa and David Henderson for Cabinet Magazine
Later, based on Taimiņa's work, the Institute For Figuring published a brochure "A Field Guide to Hyperbolic Space". In 2005 the IFF decided to incorporate Taimiņa's ideas and approach of explaining hyperbolic space in their mission of popularizing mathematics, and curated an exhibition at Machine Project gallery, which was the subject of a piece in the
Los Angeles Times
The ''Los Angeles Times'' (abbreviated as ''LA Times'') is a daily newspaper that started publishing in Los Angeles in 1881. Based in the LA-adjacent suburb of El Segundo since 2018, it is the sixth-largest newspaper by circulation in the Un ...
.
Taimiņa's way of exploring hyperbolic space via crochet and connections with nature, combatting
math phobia, was adapted by
Margaret Wertheim
Margaret Wertheim (born 20 August 1958) is an Australian-born science writer, curator, and artist based in the United States. She is the author of books on the cultural history of physics, and has written about science, including for the ''New Yo ...
in her talks and became highly successful in the IFF-curated
Hyperbolic Crochet Coral Reef project.
Books
Taimiņa's book "
Crocheting Adventures with Hyperbolic Planes
''Crocheting Adventures with Hyperbolic Planes'' is a book on crochet and hyperbolic geometry by Daina Taimiņa. It was published in 2009 by A K Peters, with a 2018 second edition by CRC Press.
Topics
The book is on the use of crochet to make p ...
" (
A K Peters, Ltd., 2009, ) won the 2009
Bookseller/Diagram Prize for Oddest Title of the Year
The ''Bookseller''/Diagram Prize for Oddest Title of the Year, originally known as the Diagram Group Prize for the Oddest Title and commonly known as the Diagram Prize, is a humorous literary award that is given annually to a book with an unusua ...
.
It also won the 2012
Euler Book Prize
The Euler Book Prize is an award named after Swiss mathematician and physicist Leonhard Euler (1707-1783) and given annually at the Joint Mathematics Meetings by the Mathematical Association of America to an outstanding book in mathematics that is ...
of the
Mathematical Association of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...
.
Taimiņa also contributed to
David W. Henderson's book ''Differential Geometry: A Geometric Introduction'' (Prentice Hall, 1998) and, with Henderson, wrote ''Experiencing Geometry: Euclidean and Non-Euclidean with History'' (Prentice Hall, 2005).
See also
*
Mathematics and fiber arts
Ideas from mathematics have been used as inspiration for fiber arts including quilt making, knitting, cross-stitch, crochet, embroidery and weaving. A wide range of mathematical concepts have been used as inspiration including topology, graph the ...
Notes
References
* David W. Henderson, Daina Taimina Experiencing Geometry: Euclidean and non-Euclidean with History, Pearson Prentice Hall, 2005 https://projecteuclid.org/euclid.bia/1598805354
Further reading
*.
External links
Personal web pageat
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...
*.
*.
*.
*.
*TEDxRiga talk https://www.youtube.com/watch?v=w1TBZhd-sN0T
{{DEFAULTSORT:Taimina, Daina
1954 births
Topologists
Latvian emigrants to the United States
Women mathematicians
Cornell University faculty
20th-century Latvian mathematicians
Living people
Latvian women writers
Mathematical artists
Mathematics popularizers
Riga State Gymnasium No.1 alumni
University of Latvia alumni
Latvian women scientists
21st-century Latvian mathematicians