# Olof Hanner

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{{short description|Swedish mathematician}}
'''Olof Hanner''' (7 December 1922 in [Stockholm](/source/Stockholm) – 19 September 2015 in [Gothenburg](/source/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](/source/Google_Books)</ref>
was a [Swedish](/source/Swedish_people) 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](/source/Fritz_Carlson) from [Stockholm University](/source/Stockholm_University) in 1952.<ref>{{mathgenealogy|id=20636}}</ref> He was a professor at the [University of Gothenburg](/source/University_of_Gothenburg) from 1963 to 1989.<ref>[http://www.ne.se/olof-hanner Olof Hanner], [Nationalencyklopedin](/source/Nationalencyklopedin), retrieved 2013-05-17.</ref>

==Contributions==
In a 1956 paper,{{sfnp|Hanner|1956a}} Hanner introduced the [Hanner polytope](/source/Hanner_polytope)s and the [Hanner space](/source/Hanner_space)s having these polytopes as their metric balls. Hanner was interested in a [Helly property](/source/Helly_property) of these shapes, later used to characterize them by {{harvtxt|Hansen|Lima|1981}}: unlike other [convex polytope](/source/convex_polytope)s, it is not possible to find three [translated](/source/translation_(geometry)) 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](/source/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](/source/Kalai's_3%5Ed_conjecture).<ref>{{citation
 | last = Kalai | first = Gil | authorlink = Gil Kalai
 | doi = 10.1007/BF01788696
 | issue = 1
 | journal = [Graphs and Combinatorics](/source/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](/source/Uniformly_convex_space) of ''L''<sup>''p''</sup> spaces, now known as [Hanner's inequalities](/source/Hanner's_inequalities).

Other contributions of Hanner include (with [Hans Rådström](/source/Hans_R%C3%A5dstr%C3%B6m)) improving [Werner Fenchel](/source/Werner_Fenchel)'s version of [Carathéodory's lemma](/source/Carath%C3%A9odory's_theorem_(convex_hull)),{{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](/source/The_Official_Encyclopedia_of_Bridge)'', and doing early work on [combinatorial game theory](/source/combinatorial_game_theory) and the [mathematics](/source/Go_and_mathematics) of the board game [Go](/source/Go_(game)).{{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](/source/Pythagorean_theorem) based on the [Pythagorean tiling](/source/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](/source/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](/source/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](/source/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

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Adapted from the Wikipedia article [Olof Hanner](https://en.wikipedia.org/wiki/Olof_Hanner) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Olof_Hanner?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.