# Doris Jean Wood Schattschneider

### Quick Info

Born
19 October 1939
Staten Island, New York City, New York, USA

### Biography

Doris Schattschneider was given the name Doris Wood and was only known as Doris Schattschneider after her marriage. In this biography we will call her Doris up to the time of her marriage and Schattschneider from that time onwards. Her parents were Robert W Wood, Jr (30 December 1907 - 14 August 1992), and Charlotte Lucile Ingalls (22 August 1908 - 6 November 2000). Robert Wood's parents were Robert Walter Wood (1881-1939) and Maude Marguerite Tuthill (1883-1952). He was born in Richmond, New York, had graduated from the City College of New York and was employed as a mechanical engineer for the City of New York's Bureau of Bridges. Doris's mother, Charlotte Ingalls' parents were Frank G Ingalls and Leona E Smith. She was born in Staten Island, New York, and had become a classical scholar having a Master's Degree in Classics from Cornell University. She taught Latin at several High Schools on Staten Island and had authored a popular Latin textbook. Doris was the second of her parents four children having one older sister Leona A Wood and one younger sister Charlotte L Wood and a younger brother Robert A Wood.

At the time of the April 1940 census, the family were living at 72 Otis Street, Staten Island, New York. However, the United States entered World War II on 8 December 1941, the day after Japan attacked the U.S. fleet at Pearl Harbour. The result of this was that Doris's father served as an engineer in the 36th Engineers of the U.S. Army and was posted overseas, mainly in North Africa and Sicily. While he was away the rest of the family moved to Lake Placid, New York. It was there that Doris began her schooling which she enjoyed. In fact she had learnt to read and print write at the age of four so found primary school easy. By the time the war was over and the family returned to Staten Island, she was well ahead of the children of her age. She enjoyed all her subjects and for a time considered a career as a nurse.

Doris attended Public School 41 and New Dorp High School in New Dorp, Staten Island. There she was concerned with the success of her fellow students more than her own success and she tutored her friends for the Regents Examinations. These are state-wide examinations in New York State leading to a Regents Diploma which was required to graduate. The examinations covered core subjects, one of which was mathematics, and it was mathematics that Doris helped her friends to score well in. It was at this high school that she exhibited her natural love and skill for teaching. At this school she was encouraged by the mathematics teacher who gave her the challenge that she was seeking. Her experiences with physics were less encouraging for, although she enjoyed the subject, her lecturer at College dissuaded her from continuing her studies in that subject. Another of her loves was art but her main university subject was mathematics. She graduated from the University of Rochester, New York, with an A.B. in 1961.

She married David Allen Schattschneider on 2 June 1962 at Staten Island, New York. David, the only child of Allen Wilbur Schattschneider and Naomi Wartman, was born on 30 March 1939 in Philadelphia, Pennsylvania. He had received a Bachelor of Arts degree from the Moravian College in 1960, a Master of Divinity from Yale University in 1964, and a Ph.D. from the University of Chicago in 1975. He was ordained a Deacon in the Moravian Church on 11 May 1969 and consecrated a Presbyter 2 October 1977. Doris and David had one daughter, Laura Ellen Schattschneider.

After graduating from the University of Rochester, Doris Schattschneider studied at Yale University. She was awarded an M.A. and then in 1966 a Ph,D. for her 45-page thesis Restricted roots of a semi-simple algebraic group. Her thesis advisors were Tsuneo Tamagawa and Ichiro Satake. A paper giving the main results of her thesis appeared in 1969 with the title On restricted roots of semi-simple algebraic groups. Schattschneider spent a year teaching at Northwestern University, in Evanston, Illinois and then taught for three years at University of Illinois's Chicago Circle campus, before being appointed to Moravian College, Bethlehem, Pennsylvania, in the autumn of 1968. We note that her husband David Schattschneider was awarded the degree of Master of Arts from the University Chicago Divinity School in 1966 and was appointed as an Instructor in church history at Moravian Theological Seminary, Bethlehem, in 1968. Doris Schattschneider taught at Moravian College for the rest of her career. Her husband taught at Moravian Theological Seminary, Bethlehem, for the rest of his career, also serving as Dean of the Seminary from 1988 until his retirement in 2001.

We must now take a brief look at the contributions that Schattschneider has made to mathematics [15]:-
Doris Schattschneider worked on many aspects of mathematics. Symmetry and geometric models have long held a special fascination with her. Doris was interested in both geometry and art and this led naturally to the study of tiling problems and the work of the Dutch artist M C Escher. She has written many scholarly articles that have dealt with many subjects within mathematics.
Her papers published prior to 1990 include A multiplicative metric (1976), The plane symmetry groups: their recognition and notation (1978), Tiling the plane with congruent pentagons (1978), Will it tile? Try the Conway criterion! (1980), The taxicab group (1984), The Mystery of the MAA Logo (1985), In black and white: how to create perfectly colored symmetric patterns (1986), Escher's classification system for his colored periodic drawings (1986), The Pólya-Escher connection (1987), Extending the Conway criterion (1988), Escher: a mathematician in spite of himself (1988). Let us look at her interest in tilings by quoting from her paper The Fascination of Tiling (1992):-
Dutch artist M C Escher (1898-1972) often described regular divisions of the plane as "the richest source of inspiration I have ever struck." Interlocking shapes displayed in majolica tile, inlaid wood, brickwork, carved stucco, stone pavement, sewn patchwork or printed fabric hold a special fascination for many people that goes far beyond the aesthetic pleasure that these patterns provide. Tiling can serve as a paradigm: it is wholly visual (and perhaps seems to be purely in the provenance of design) yet incredibly rich as a source of mathematical questions. Many of these questions have implications for those who (like Escher) design intricate and unusual tilings. Other questions probe the limits of possibilities for tilings, investigate the structure of tilings, aim to produce methods of classification or link tilings to physical structures in nature or to invented mathematical structures. Mathematicians seek to know how tiles can pave surfaces - not just the Euclidean (flat) plane, but also the hyperbolic plane and the surfaces of three-dimensional objects such as spheres, tori (doughnuts) or Möbius bands. They also investigate tilings on surfaces impossible to fully represent in our three-dimensional world, such as a Klein bottle or surfaces in higher dimensions. And tiling problems are not only restricted to surfaces - there are marvellous problems that ask questions about how three-dimensional 'tiles' (such as polyhedra) can pack space, or how higher-dimensional spaces can be packed with tiles. Most of these problems are difficult, and most are unsolved.
As two further examples, let us look at extracts from two reviews of her papers. First a review by Donald Coxeter of Schattschneider's paper The Pólya-Escher connection (1987) summarises the contents of the paper:-
One of M C Escher's favourite activities, inspired by his two visits to the Alhambra, was to draw a pattern of congruent replicas of a particular shape so as to fill and cover the plane, leaving no gaps. In this project, he was encouraged by his geologist brother, B G Escher, who showed him, in 1936, a paper by G Pólya (1924). In that paper, Pólya had rediscovered Fedorov's enumeration of the seventeen two-dimensional space groups, cleverly illustrating each group by a plane-filling in Escher's style: the author's Figure 1. Escher copied the whole paper, enlarged the illustrations, and added his own two special contributions. The first contribution, anticipating the subsequent work of Russian crystallographers, was his introduction of perfect colouring, more systematic than the often haphazard use of colours by the Moors in the Alhambra and Mezquita. The second contribution was his deformation of Pólya's simple motifs (bounded by line segments or arcs of circles) into recognizable birds, lizards, fishes, etc. The author's Figure 2 is a photograph of a particularly striking entry in one of Escher's unpublished notebooks, where he used 3 colours to enhance Pólya's $D°_{3}$.
Our second quote is a review by Marjorie Senechal of Schattschneider's paper In black and white: how to create perfectly colored symmetric patterns:-
This article is intended primarily for students, teachers and designers who are interested in exploring the field of colour symmetry but are bewildered by the inconsistency and lack of clarity in the mathematical literature on the subject. The author carefully discusses the isometries of the plane and how they can be used to generate patterns and tilings, explains how designs are classified by symmetry, and thoroughly analyzes the problem of colouring a design with two colours in a way that is compatible with its symmetry. Her sensitivity to the concerns of the artist is manifest throughout; especially interesting is the discussion of the interpretation of figure and ground in coloured patterns.
We gain further insight into Schattschneider's work by looking at reviews of her books. We give some extracts from reviews of three of her books at THIS LINK.

Another project in which Schattschneider played a major role was the Visual Geometry Project [3]:-
As senior associate of the Visual Geometry Project, a project funded by the National Science Foundation, she collaborated with colleagues (including Eugene Klotz from Swarthmore College) to develop and produce three activity books with hands-on geometric models and computer animated videotapes. These materials, designed to teach about two- and three-dimensional forms, include three videotapes and the computer program "The Geometer's Sketchpad" to be used in teaching geometry.
Schattschneider attended many conferences on topics related to her interests and, not surprisingly, she attended the Escher Centennial Congress in June 1998. Marjorie Senechal, a conference participant, wrote [1]:-
After three days of lectures, expositions, and discussions in Rome - home to M C Escher and his family from 1925 to 1935 - the Congress moved south to Ravello, a small mountain town that Escher had loved.
Another participant at that conference was Michele Emmer who explained that Schattschneider's research had involved Ravello many years before [1]:-
Years ago when Doris Schattschneider was preparing her book "Visions of Symmetry" she sent me a letter asking me if I could help to locate some Arabic mosaics she thought might be in Ravello; she had found loose sketches of them in Escher's materials. I contacted a friend of mine, Francesco Fortunato, an architect who lives in Ravello and is a great fan of Escher, who immediately recognized the sketches by Escher. You can find the original mosaics adorning the pulpit of the Duomo in Ravello. Doris thought that it was rare to find Arabic mosaics or motifs in Ravello. In fact it is not; the Moors occupied the Amalfi coast for centuries. They are part of the history of Ravello, a place so loved by Escher; he was in Ravello many times. In particular, at the Hotel Toro it is possible to see an Escherian motif on the wall, made to commemorate his staying there.
Let us mention one other conference that Schattschneider attended, namely "Renaissance Banff: Mathematics, Music, Art, Culture" held 30 July to 3 August, 2005, in Banff, Canada. Schattschneider wrote an article 'Math and Art in the Mountains' for the Mathematical Intelligencer 28 (3) (2006) describing the conference, summarising the talks given at it, as well as describing the conference outings. This piece clearly shows Schattschneider's love of travel and her love of walking in mountains.

We next give some indication of the high quality of her teaching. The following was written after she was awarded the 1991 Meritorious Service Award from the Eastern Pennsylvania and Delaware section of the Mathematical Association of America [21]:-
Her students say Schattschneider's enthusiasm for mathematics is contagious, and her penchant for visual teaching tools helps them to better "see" complex mathematical concepts. "Doris is well-respected and highly effective in the classroom," states the award nomination, "In a recent evaluation of all professors at Moravian, conducted by students and published in the campus newspaper, Doris scored an overall score of 3.66 out of 4.0, one of the highest on campus. She was praised by students as a great mathematician and teacher. Students felt that she understood her material extremely well and presented it to the class in the same way. One math major wrote, 'Her enthusiasm for the subject made me want to do better'." "Certainly, seeing students go on and mature, that's a great satisfaction," she said. "Many do keep in touch. It's also satisfying to see some students I've guided teaching today. I've been supervising student teachers for the last seven years. I really enjoy that."
In 1991 the Mathematical Association of America instituted Awards for Distinguished College or University Teaching of Mathematics in order to honour college or university teachers who had been widely recognized as extraordinarily successful and whose teaching effectiveness had been shown to have had influence beyond their own institutions. In 1993 the Board of Governors of the Mathematical Association of America renamed the award to honour Deborah and Franklin Tepper Haimo and in that year made the award to Doris W Schattschneider, Moravian College. In reply to receiving the award she said [18]:-
I am deeply honoured by this recognition by my colleagues in the MAA. I especially want to thank the teachers, including my mother, who inspired me - those who awakened my sense of curiosity, showed me that there was 'wow!' in mathematics and appealed to the ham in me.
In 1995 she was made the Mathematical Association of America's Earle Raymond Hedrick Lecturer.

It was not only for teaching that Schattschneider received awards; she also received awards for her papers. In 1979 the Mathematical Association of America gave her their Carl B Allendoerfer Award, given to authors of exceptional expository articles published in Mathematics Magazine. It was Schattschneider's article Tiling the plane with congruent pentagons (1978) for which she received the award.

Schattschneider was active in the Mathematical Association of America, being editor of Mathematics Magazine 1981-1985, and First Vice President in 1994-95 [3]:-
In addition to her extensive professional affiliation with the MAA, Schattschneider is involved with the American Mathematical Society; the Association for Women in Mathematics; the National Council of Teachers of Mathematics. She is a member of Phi Beta Kappa and Pi Mu Epsilon, having served as national councillor for several years.
She was also the first woman to deliver Pi Mu Epsilon's J Sutherland Frame Lecture (1988). In 2012 she was honoured by being elected a Fellow of the American Mathematical Society.

Schattschneider's husband David died at their home in Bethlehem Pennsylvania on Thursday, 29 September 2016.

### References (show)

1. M Emmer and D Schattschneider (eds), M C Escher's Legacy: A centennial Celebration (Springer, 2007).
2. Basic Library Committee, Review: M C Escher: Visions of Symmetry, by Doris Schattschneider, Mathematical Association of America (11 May 2009). https://www.maa.org/press/maa-reviews/m-c-escher-visions-of-symmetry
3. R B Brunner, Doris Schattschneider (1939-), in C Morrow and T Perl (eds.), Notable Women in Mathematics (Greenwood Press, Westport, Connecticut, 1998), 214-219.
4. B Cain, Review: M C Escher Kaleidocycles, by Doris Schattschneider and Wallace Walker, Mathematics Teaching in the Middle School 2 (6) (1997), 443.
5. J K Colligan, Review: Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M C Escher, by Doris Schattschneider, The Mathematics Teacher 86 (8) (1993), 695.
6. L Dembart, Review: M C Escher Kaleidocycles, by Doris Schattschneider and Wallace Walker, Los Angeles Times (27 May 1988).
7. D J Dunham, Review: Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M C Escher, by Doris Schattschneider, Amer. Math. Monthly 99 (1) (1992), 78-81.
8. Editors, Review: M C Escher: Visions of Symmetry, by Doris Schattschneider, The Journal of Technology Studies 32 (1/2) (2006), 121.
9. Editors, Review: M C Escher: Visions of Symmetry, by Doris Schattschneider, New Scientist Magazine 1848 (21 November 1992).
10. M Emmer, Review: Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M C Escher, by Doris Schattschneider, Leonardo 25 (3/4), Visual Mathematics: Special Double Issue (1992), 389.
11. J Galloway, Review: M C Escher: Visions of Symmetry, by Doris Schattschneider, New Scientist (2 March 1991).
12. D Garcia, Review: Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M C Escher, by Doris Schattschneider, The Mathematical Gazette 75 (473) (1991), 366-367.
13. G Goldstein, Review: M C Escher: Visions of Symmetry, by Doris Schattschneider, Print Quarterly 22 (2) (2005), 225-227.
14. S J Greenwald, Doris Wood Schattschneider, Computer Science Department, Appalacian State University. http://www.cs.appstate.edu/~sjg/womenandminoritiesinmath/final/schattschnedierfinal/Main.htm
15. S J Greenwald, Doris Wood Schattschneider, Computer Science Department, Appalacian State University. http://www.cs.appstate.edu/~sjg/womenandminoritiesinmath/student/schattschneider/Schattp.pdf
16. J M Jensen, Review: M C Escher Kaleidocycles, by Doris Schattschneider and Wallace Walker, The Mathematics Teacher 90 (5) (1997), 413.
17. J P Martin, Calculus Made Easier Professors Publish Book To Aid Students, The Morning Call (18 December 1993).
18. Moravian Professor Gets Math Teaching Award, The Morning Call (8 April 1993).
19. R Penrose, Review: M C Escher: Visions of Symmetry, by Doris Schattschneider, Times Higher Education (14 January 2005).
20. D Quadling, Review: M C Escher Kaleidocycles, by Doris Schattschneider and Wallace Walker, The Mathematical Gazette 62 (421) (1978), 217-219.
21. T Schroeder, Math Professor's Watchword: Visual, The Morning Call (11 June 1992).
22. M Senechal, Review: Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M C Escher, by Doris Schattschneider, Mathematical reviews MR1189799 (93i:52001).