{{short description|Swedish mathematician}} '''Olof Hanner''' (7 December 1922 in Stockholm – 19 September 2015 in Gothenburg)<ref>{{citation | last = Pratesi | first = Franco | author-link = Franco Pratesi | date = 2004 | issue = 2 | journal = Nordisk GoBlad | pages = 9–10 | title = A Swedish pioneer of go and of its mathematical investigation | url = http://goforbundet.se/web/sites/default/files/Nordisk_GoBlad_2004_2.pdf#page=9 | access-date = 2014-10-07 | archive-date = 2014-10-11 | archive-url = https://web.archive.org/web/20141011180310/http://goforbundet.se/web/sites/default/files/Nordisk_GoBlad_2004_2.pdf#page=9 | url-status = dead }}</ref><ref>[https://books.google.com/books?id=wrzkAAAAMAAJ&q=hanner ''Who's who in Scandinavia'', 1980] at Google Books</ref> was a Swedish mathematician.<ref>{{cite web|title=Olaf Hanner|url=http://www.pressreader.com/sweden/svenska-dagbladet/20151102/281857232407275/TextView|accessdate=12 January 2016|language=Swedish}}</ref><ref>{{cite journal | last = Sjögren | first = Peter | date = February 2016 | journal = Svenska Matematikersamfundet Bulletinen | pages = 22–24 | title = Olof Hanner in memoriam | url = http://www.swe-math-soc.se/pdf/SMSbull1602.pdf#page=24}}</ref>
==Education and career== Hanner earned his Ph.D. under the supervision of Fritz Carlson from Stockholm University in 1952.<ref>{{mathgenealogy|id=20636}}</ref> He was a professor at the University of Gothenburg from 1963 to 1989.<ref>[http://www.ne.se/olof-hanner Olof Hanner], Nationalencyklopedin, retrieved 2013-05-17.</ref>
==Contributions== In a 1956 paper,{{sfnp|Hanner|1956a}} Hanner introduced the Hanner polytopes and the Hanner spaces having these polytopes as their metric balls. Hanner was interested in a Helly property of these shapes, later used to characterize them by {{harvtxt|Hansen|Lima|1981}}: unlike other convex polytopes, it is not possible to find three translated copies of a Hanner polytope that intersect pairwise but do not have a point of common intersection.<ref>{{citation | last1 = Hansen | first1 = Allan B. | last2 = Lima | first2 = Ȧsvald | doi = 10.1007/BF02392457 | issue = 1–2 | journal = Acta Mathematica | mr = 594626 | pages = 1–23 | title = The structure of finite-dimensional Banach spaces with the 3.2. intersection property | volume = 146 | year = 1981| doi-access = free }}.</ref> Subsequently, the Hanner polytopes formed a class of important examples for the Mahler conjecture<ref>{{citation | last = Kim | first = Jaegil | arxiv = 1212.2544 | title = Minimal volume product near Hanner polytopes | year = 2012| bibcode = 2012arXiv1212.2544K}}.</ref> and for Kalai's 3<sup>''d''</sup> conjecture.<ref>{{citation | last = Kalai | first = Gil | authorlink = Gil Kalai | doi = 10.1007/BF01788696 | issue = 1 | journal = Graphs and Combinatorics | mr = 1554357 | pages = 389–391 | title = The number of faces of centrally-symmetric polytopes | volume = 5 | year = 1989| s2cid = 8917264 }}.</ref> In another paper from the same year,{{sfnp|Hanner|1956b}} Hanner proved a set of inequalities related to the uniform convexity of ''L''<sup>''p''</sup> spaces, now known as Hanner's inequalities.
Other contributions of Hanner include (with Hans Rådström) improving Werner Fenchel's version of Carathéodory's lemma,{{sfnp|Hanner|Rådström|1951}}<ref>{{citation | last = Reay | first = John R. | mr = 0188891 | series = Memoirs of the AMS | title = Generalizations of a theorem of Carathéodory | volume = 54 | year = 1965}}.</ref> contributing to ''The Official Encyclopedia of Bridge'', and doing early work on combinatorial game theory and the mathematics of the board game Go.{{sfnp|Hanner|1959}}<ref>{{citation | last1 = Raussen | first1 = Martin | last2 = Skau | first2 = Christian | date = March 2012 | issue = 3 | journal = Notices of the AMS | pages = 400–408 | title = Interview with John Milnor | url = https://www.ams.org/notices/201203/rtx120300400p.pdf | volume = 59 | doi=10.1090/noti803| doi-access = free }}.</ref><ref>{{citation|contribution=The History of Combinatorial Game Theory|first=Richard J.|last=Nowakowski|title=Proceedings of the Board Game Studies Colloquium XI (Lisbon, 2008)|year=2009|url=http://www.eos.tuwien.ac.at/OR/Mehlmann/Andis/publ/Spielmod10/HistoryCGT.pdf|access-date=2013-05-17|archive-url=https://web.archive.org/web/20140531105607/http://www.eos.tuwien.ac.at/OR/Mehlmann/Andis/publ/Spielmod10/HistoryCGT.pdf|archive-date=2014-05-31|url-status=dead}}</ref> One of the many proofs of the Pythagorean theorem based on the Pythagorean tiling is sometimes called "Olof Hanner's Jigsaw Puzzle".<ref>[http://www.cut-the-knot.org/pythagoras/Hanner.shtml Olof Hanner's Jigsaw Puzzle], Cut-the-Knot, retrieved 2013-05-17.</ref>
==Selected publications== *{{citation | last = Hanner | first = Olof | doi = 10.1007/BF02591376 | journal = Arkiv för Matematik | mr = 0043459 | pages = 389–408 | title = Some theorems on absolute neighborhood retracts | volume = 1 | issue = 5 | year = 1951| bibcode = 1951ArM.....1..389H | doi-access = free }}. *{{citation | last1 = Hanner | first1 = Olof | last2 = Rådström | first2 = Hans | doi = 10.2307/2032012 | journal = Proceedings of the American Mathematical Society | mr = 0044142 | pages = 589–593 | title = A generalization of a theorem of Fenchel | volume = 2 | issue = 4 | year = 1951| jstor = 2032012 | doi-access = free }}. *{{citation | last = Hanner | first = Olof | journal = Mathematica Scandinavica | mr = 0082696 | pages = 65–87 | title = Intersections of translates of convex bodies | volume = 4 | year = 1956a | doi = 10.7146/math.scand.a-10456 | doi-access = free }}. *{{citation | last = Hanner | first = Olof | doi = 10.1007/BF02589410 | issue = 3 | journal = Arkiv för Matematik | mr = 0077087 | pages = 239–244 | title = On the uniform convexity of ''L''<sup>''p''</sup> and ''ℓ''<sup>''p''</sup> | volume = 3 | year = 1956b| bibcode = 1956ArM.....3..239H | doi-access = free }}. *{{citation | last = Hanner | first = Olof | journal = Pacific Journal of Mathematics | mr = 0104524 | pages = 81–99 | title = Mean play of sums of positional games | volume = 9 | year = 1959 | url = http://projecteuclid.org/euclid.pjm/1103039454 | doi=10.2140/pjm.1959.9.81| doi-access = free }}. *{{citation | last = Hanner | first = Olof | journal = The Two-Year College Mathematics Journal | pages = 5–16 | title = Mathematics, A Solitary Game | volume = 1 | issue = 2 | year = 1970 | jstor = 3027352 | doi=10.2307/3027352}}. *{{citation|title=Bridge movements: A fair approach|first1=Hans-Olof|last1=Hallén|first2=Olof|last2=Hanner|first3=Per|last3=Jannersten|editor-first=Barry|editor-last=Rigal|edition=Translated by Barry Rigal from the 1990 Swedish ''Tävlingsledaren'' (''The leader of the tournament'')|location=Alvesta|series=Bridgeakad. (Bridge academy)|isbn=91-85024-86-4|publisher=Jannersten Forlag AB|year=1994}}
==References== {{reflist|colwidth=30em}}
==External links== * [http://www.worldcat.org/search?q=hanner%2C+olof&dblist=638&fq=ap%3A%22hanner%2C+olof%22&qt=facet_ap%3A Olof Hanner] at WorldCat <!-- search report in lieu of LCCN id -->
{{Authority control}} <!-- in LC "old catalog"; http://lccn.loc.gov/77506662 ; not yet in name authorities file ? -->
{{DEFAULTSORT:Hanner, Olof}} Category:1922 births Category:2015 deaths Category:Swedish mathematicians Category:Stockholm University alumni Category:Academic staff of the University of Gothenburg Category:People from Stockholm