From Wikipedia, the free encyclopedia
Swedish mathematician
Olof Hanner (7 December 1922 in
Stockholm – 19 September 2015 in
Gothenburg )
[1]
[2]
was a
Swedish mathematician.
[3]
[4]
Education and career
Hanner earned his Ph.D. from
Stockholm University in 1952.
[5] He was a professor at the
University of Gothenburg from 1963 to 1989.
[6]
Contributions
In a 1956 paper, 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
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.
[8] Subsequently, the Hanner polytopes formed a class of important examples for the
Mahler conjecture
[9] and for
Kalai's 3d conjecture .
[10] In another paper from the same year, Hanner proved a set of inequalities related to the
uniform convexity of L p spaces, now known as
Hanner's inequalities .
Other contributions of Hanner include (with
Hans Rådström ) improving
Werner Fenchel 's version of
Carathéodory's lemma ,
[13] contributing to
The Official Encyclopedia of Bridge , and doing early work on
combinatorial game theory and the
mathematics of the board game
Go .
[15]
[16] One of the many proofs of the
Pythagorean theorem based on the
Pythagorean tiling
is sometimes called "Olof Hanner's Jigsaw Puzzle".
[17]
Selected publications
Hanner, Olof (1951), "Some theorems on absolute neighborhood retracts", Arkiv för Matematik , 1 (5): 389–408,
Bibcode :
1951ArM.....1..389H ,
doi :
10.1007/BF02591376 ,
MR
0043459 .
Hanner, Olof; Rådström, Hans (1951), "A generalization of a theorem of Fenchel", Proceedings of the American Mathematical Society , 2 (4): 589–593,
doi :
10.2307/2032012 ,
JSTOR
2032012 ,
MR
0044142 .
Hanner, Olof (1956a), "Intersections of translates of convex bodies", Mathematica Scandinavica , 4 : 65–87,
doi :
10.7146/math.scand.a-10456 ,
MR
0082696 .
Hanner, Olof (1956b), "On the uniform convexity of L p and ℓ p ", Arkiv för Matematik , 3 (3): 239–244,
Bibcode :
1956ArM.....3..239H ,
doi :
10.1007/BF02589410 ,
MR
0077087 .
Hanner, Olof (1959),
"Mean play of sums of positional games" , Pacific Journal of Mathematics , 9 : 81–99,
doi :
10.2140/pjm.1959.9.81 ,
MR
0104524 .
Hanner, Olof (1970), "Mathematics, A Solitary Game", The Two-Year College Mathematics Journal , 1 (2): 5–16,
doi :
10.2307/3027352 ,
JSTOR
3027352 .
Hallén, Hans-Olof; Hanner, Olof; Jannersten, Per (1994), Rigal, Barry (ed.), Bridge movements: A fair approach , Bridgeakad. (Bridge academy) (Translated by
Barry Rigal from the 1990 Swedish Tävlingsledaren (The leader of the tournament ) ed.), Alvesta: Jannersten Forlag AB,
ISBN
91-85024-86-4
References
^
Pratesi, Franco (2004),
"A Swedish pioneer of go and of its mathematical investigation" (PDF) , Nordisk GoBlad (2): 9–10
^
Who's who in Scandinavia , 1980 at
Google Books
^
"Olaf Hanner" (in Swedish). Retrieved 12 January 2016 .
^ Sjögren, Peter (February 2016).
"Olof Hanner in memoriam" (PDF) . Svenska Matematikersamfundet Bulletinen : 22–24.
^
Olof Hanner at the
Mathematics Genealogy Project
^
Olof Hanner ,
Nationalencyklopedin , retrieved 2013-05-17.
^ Hansen, Allan B.; Lima, Ȧsvald (1981), "The structure of finite-dimensional Banach spaces with the 3.2. intersection property", Acta Mathematica , 146 (1–2): 1–23,
doi :
10.1007/BF02392457 ,
MR
0594626 .
^ Kim, Jaegil (2012), Minimal volume product near Hanner polytopes ,
arXiv :
1212.2544 ,
Bibcode :
2012arXiv1212.2544K .
^
Kalai, Gil (1989), "The number of faces of centrally-symmetric polytopes",
Graphs and Combinatorics , 5 (1): 389–391,
doi :
10.1007/BF01788696 ,
MR
1554357 ,
S2CID
8917264 .
^ Reay, John R. (1965), Generalizations of a theorem of Carathéodory , Memoirs of the AMS, vol. 54,
MR
0188891 .
^ Raussen, Martin; Skau, Christian (March 2012),
"Interview with John Milnor" (PDF) , Notices of the AMS , 59 (3): 400–408,
doi :
10.1090/noti803 .
^ Nowakowski, Richard J. (2009), "The History of Combinatorial Game Theory",
Proceedings of the Board Game Studies Colloquium XI (Lisbon, 2008) (PDF) , archived from
the original (PDF) on 2014-05-31, retrieved 2013-05-17
^
Olof Hanner's Jigsaw Puzzle ,
Cut-the-Knot , retrieved 2013-05-17.
External links
International Academics Other