# Branko Grünbaum

Branko Grünbaum | |
---|---|

Born | 2 October 1929 |

Died | 14 September 2018 Seattle, Washington, U.S. | (aged 88)

Nationality | Croatian American |

Alma mater | Hebrew University of Jerusalem |

Awards | Lester R. Ford Award (1976) Carl B. Allendoerfer Award (1978) Leroy P. Steele Prize (2005) |

Scientific career | |

Fields | Mathematics |

Institutions | University of Washington |

Thesis | On Some Properties of Minkowski Spaces (1957) |

Doctoral advisor | Aryeh Dvoretzky |

Doctoral students |

**Branko Grünbaum** (Hebrew: ברנקו גרונבאום; 2 October 1929 – 14 September 2018)^{[1]} was a Croatian-born mathematician of Jewish descent^{[2]} and a professor emeritus at the University of Washington in Seattle. He received his Ph.D. in 1957 from Hebrew University of Jerusalem in Israel.^{[3]}

## Life

[edit]Grünbaum was born in Osijek, then part of the Kingdom of Yugoslavia, on 2 October 1929. His father was Jewish and his mother was Catholic, so during World War II the family survived the Holocaust by living at his Catholic grandmother's home. After the war, as a high school student, he met Zdenka Bienenstock, a Jew who had lived through the war hidden in a convent while the rest of her family were killed. Grünbaum became a student at the University of Zagreb, but grew disenchanted with the communist ideology of the Socialist Federal Republic of Yugoslavia, applied for emigration to Israel, and traveled with his family and Zdenka to Haifa in 1949.^{[4]}

In Israel, Grünbaum found a job in Tel Aviv, but in 1950 returned to the study of mathematics,^{[4]} at the Hebrew University of Jerusalem.^{[1]} He earned a master's degree in 1954 and in the same year married Zdenka, who continued as a master's student in chemistry. He served a tour of duty as an operations researcher in the Israeli Air Force beginning in 1955, and he and Zdenka had the first of their two sons in 1956.^{[4]} He completed his Ph.D. in 1957;^{[4]}^{[3]} his dissertation concerned convex geometry and was supervised by Aryeh Dvoretzky.^{[3]}

After finishing his military service in 1958, Grünbaum and his family came to the US so that Grünbaum could become a postdoctoral researcher at the Institute for Advanced Study. He then became a visiting researcher at the University of Washington in 1960. He agreed to return to Israel as a lecturer at the Hebrew University, but his plans were disrupted by the Israeli authorities determining that he was not a Jew (because his mother was not Jewish) and annulling his marriage; he and Zdenka remarried in Seattle before their return.^{[4]}

Grünbaum remained affiliated with the Hebrew University until 1966, taking long research visits to the University of Washington and in 1965–1966 to Michigan State University. However, during the Michigan visit, learning of another case similar to their marriage annulment, he and Zdenka decided to stay in the US instead of returning to Israel, where Zdenka was still a doctoral student in chemistry. Grünbaum was given a full professorship at the University of Washington in 1966, and he remained there until retiring in 2001.^{[4]}

## Works

[edit]Grünbaum authored over 200 papers, mostly in discrete geometry, an area in which he is known for various classification theorems. He wrote on the theory of abstract polyhedra.

His paper on line arrangements may have inspired a paper by N. G. de Bruijn on quasiperiodic tilings (the most famous example of which is the Penrose tiling of the plane). This paper is also cited by the authors of a monograph on hyperplane arrangements as having inspired their research.

Grünbaum also devised a multi-set generalisation of Venn diagrams. He was an editor and a frequent contributor to *Geombinatorics*.

Grünbaum's classic monograph *Convex Polytopes*, first published in 1967, became the main textbook on the subject. His monograph *Tilings and patterns*, coauthored with G. C. Shephard, helped to rejuvenate interest in this classic field, and has proved popular with nonmathematical audiences, as well as with mathematicians.

In 1976 Grünbaum won a Lester R. Ford Award for his expository article *Venn diagrams and independent families of sets*.^{[5]} In 2004, Gil Kalai and Victor Klee edited a special issue of *Discrete and Computational Geometry* in his honor, the "Grünbaum Festschrift". In 2005, Grünbaum was awarded the Leroy P. Steele Prize for Mathematical Exposition from the American Mathematical Society. He was a Guggenheim Fellow, a Fellow of the AAAS and in 2012 he became a fellow of the American Mathematical Society.^{[6]}^{[7]}
Grünbaum supervised 19 Ph.D.s and currently has at least 200 mathematical descendants.^{[3]}

## Books

[edit]- Grünbaum, Branko (2003) [1967], Kaibel, Volker; Klee, Victor; Ziegler, Günter M. (eds.),
*Convex Polytopes*, Graduate Texts in Mathematics, vol. 221 (2nd ed.), Springer-Verlag, ISBN 0-387-00424-6.^{[8]} - Grünbaum, B. (1972),
*Arrangements and Spreads*, Regional Conference Series in Mathematics, vol. 10, Providence, R.I.: American Mathematical Society, ISBN 0-8218-1659-4.^{[9]} - Grünbaum, Branko; Shephard, G. C. (1987),
*Tilings and Patterns*, New York: W. H. Freeman, ISBN 0-7167-1193-1.^{[10]} - Grünbaum, Branko (2009),
*Configurations of Points and Lines*, Graduate Studies in Mathematics, vol. 103, American Mathematical Society, ISBN 978-0-8218-4308-6, MR 2510707.^{[11]}

### as editor

[edit]- Davis, Chandler; Grünbaum, B.; Sherk, F. A., eds. (2012) [1981],
*The Geometric Vein: The Coxeter Festschrift*, Springer Science & Business Media, ISBN 978-1-4612-5648-9

## See also

[edit]- Configuration (geometry)
- Convex uniform honeycomb
- Elongated square gyrobicupola
- Goldner–Harary graph
- Pentagram map
- Simplicial sphere
- Star coloring
- Star polygon
- Grünbaum's theorem
- Grünbaum–Rigby configuration

## References

[edit]- ^
^{a}^{b}Choi, Rose (September 18, 2018),*Branko Grünbaum (1929—2018)*, University of Washington Mathematics Department **^**Branko Grünbaum, Hrvatska enciklopedija LZMK.- ^
^{a}^{b}^{c}^{d}Branko Grünbaum at the Mathematics Genealogy Project - ^
^{a}^{b}^{c}^{d}^{e}^{f}Williams, Gordon (2018), "Branko Grünbaum, Geometer",*Ars Mathematica Contemporanea*,**15**(1) **^**Grünbaum, Branko (1975), "Venn diagrams and independent families of sets",*Mathematics Magazine*,**48**(1): 12–23, Bibcode:1975MathM..48...12G, doi:10.2307/2689288, JSTOR 2689288**^**List of Fellows of the American Mathematical Society, retrieved 2013-01-19.**^**Pircea, M., ed. (2011),*The Best Writing on Mathematics 2010*, Princeton University Press, ISBN 9780691148410**^**Reviews of*Convex Polytopes*:- Sallee, G. T., "Review of 1st ed.",
*MathSciNet*, MR 0226496 - Jucovič, E., "Review of 1st ed.",
*zbMATH*(in German), Zbl 0163.16603 - Fenchel, Werner (Winter 1968), "Review of 1st ed.",
*American Scientist*,**56**(4): 476A–477A, JSTOR 27828384 - Baxandall, P. R. (October 1969), "Review of 1st ed.",
*The Mathematical Gazette*,**53**(385): 342–343, doi:10.2307/3615008, JSTOR 3615008 - Ehrig, G., "Review of 2nd ed.",
*zbMATH*(in German), Zbl 1024.52001 - Zvonkin, Alexander (2004), "Review of 2nd ed.",
*MathSciNet*, MR 1976856 - Lord, Nick (March 2005), "Review of 2nd ed.",
*The Mathematical Gazette*,**89**(514): 164–166, doi:10.1017/S0025557200177307, JSTOR 3620690, S2CID 126343422 - McMullen, Peter (July 2005), "Review of 2nd ed.",
*Combinatorics, Probability and Computing*,**14**(4): 623–626, doi:10.1017/s0963548305226998

- Sallee, G. T., "Review of 1st ed.",
**^**Reviews of*Arrangements and Spreads*:- Jucovič, E.,
*zbMATH*, Zbl 0249.50011`{{citation}}`

: CS1 maint: untitled periodical (link) - Coxeter, H. S. M.,
*MathSciNet*, MR 0307027`{{citation}}`

: CS1 maint: untitled periodical (link)

- Jucovič, E.,
**^**Reviews of*Tilings and patterns*:- Schulte, E.,
*zbMATH*, Zbl 0601.05001`{{citation}}`

: CS1 maint: untitled periodical (link) - Malkevitch, Joseph (May 22, 1987), "Shapes in the plane",
*Science*, New Series,**236**(4804): 996–997, doi:10.1126/science.236.4804.996, JSTOR 1699674, PMID 17812775 - Wenzel, John A. (September 1987),
*The Mathematics Teacher*,**80**(6): 497–498, JSTOR 27965474`{{citation}}`

: CS1 maint: untitled periodical (link) - Senechal, Marjorie (September–October 1987),
*American Scientist*,**75**(5): 521–522, JSTOR 27854795`{{citation}}`

: CS1 maint: untitled periodical (link) - Fejes Tóth, L. (October 1987),
*Bulletin of the American Mathematical Society*,**17**(2): 369–373, doi:10.1090/s0273-0979-1987-15600-x`{{citation}}`

: CS1 maint: untitled periodical (link) - Williams, H. C. (December 1987),
*The Mathematical Gazette*,**71**(458): 347–348, doi:10.2307/3617109, JSTOR 3617109, S2CID 132315491`{{citation}}`

: CS1 maint: untitled periodical (link) - Coxeter, H. S. M. (1988),
*Mathematical Reviews*, MR 0857454`{{citation}}`

: CS1 maint: untitled periodical (link) - Roman, Tiberiu (1988),
*Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie*, Nouvelle Série,**32**(4): 379–380, JSTOR 43681480`{{citation}}`

: CS1 maint: untitled periodical (link) - Golomb, Solomon W. (January 1988),
*American Mathematical Monthly*,**95**(1): 63–64, doi:10.2307/2323457, JSTOR 2323457`{{citation}}`

: CS1 maint: untitled periodical (link) - Donegan, Joe (February 1990),
*The Mathematics Teacher*,**83**(2): 167, JSTOR 27966586`{{citation}}`

: CS1 maint: untitled periodical (link) - Schwarzenberger, R. L. E. (March 1988),
*Bulletin of the London Mathematical Society*,**20**(2): 167–170, doi:10.1112/blms/20.2.167`{{citation}}`

: CS1 maint: untitled periodical (link) - Garcia, Paul (June 1990),
*The Mathematical Gazette*,**74**(468): 207–209, doi:10.2307/3619416, JSTOR 3619416, S2CID 117084478`{{citation}}`

: CS1 maint: untitled periodical (link) - Paufler, P. (1991),
*Crystal Research and Technology*,**26**(8), Wiley: 1038, doi:10.1002/crat.2170260812`{{citation}}`

: CS1 maint: untitled periodical (link) - Satzer, William J. (November 2016), "Review",
*MAA Reviews*, Mathematical Association of America

- Schulte, E.,
**^**Reviews of*Configurations of Points and Lines*:- Riesinger, Rolf,
*zbMATH*, Zbl 1205.51003`{{citation}}`

: CS1 maint: untitled periodical (link) - Glass, Darren (November 2009), "Review",
*MAA Reviews*, Mathematical Association of America

- Riesinger, Rolf,

## Further reading

[edit]- Kahle, Matthew (2019), "Branko Grünbaum in many dimensions",
*Geombinatorics*,**28**(3): 140–146, arXiv:1901.08622, MR 3821744 - Kalai, Gil; Mohar, Bojan; Novik, Isabella (June 2020), "Guest Editors' Foreword", Branko Grünbaum Memorial Issue,
*Discrete & Computational Geometry*,**64**(2): 229–232, doi:10.1007/s00454-020-00214-y

## External links

[edit]- 1929 births
- 2018 deaths
- People from Osijek
- Yugoslav emigrants to Israel
- American people of Croatian-Jewish descent
- 20th-century American mathematicians
- Croatian mathematicians
- Combinatorialists
- University of Washington faculty
- Einstein Institute of Mathematics alumni
- Geometers
- Fellows of the American Mathematical Society
- Fellows of the American Association for the Advancement of Science
- American textbook writers