Olof Hanner

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,^[7] 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 3^d conjecture.^[10] In another paper from the same year,^[11] 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,^[12][13] contributing to The Official Encyclopedia of Bridge, and doing early work on combinatorial game theory and the mathematics of the board game Go.^[14][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: 389–408, 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: 589–593, doi:10.2307/2032012, MR 0044142.
• Hanner, Olof (1956a), "Intersections of translates of convex bodies", Mathematica Scandinavica 4: 65–87, MR 0082696.
• Hanner, Olof (1956b), "On the uniform convexity of L^p and ℓ^p", Arkiv för Matematik 3 (3): 239–244, 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.
• 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

1. Pratesi, Franco (2004), "A Swedish pioneer of go and of its mathematical investigation" (PDF), Nordisk GoBlad (2): 9–10
2. Who's who in Scandinavia, 1980 at Google Books
3. "Olaf Hanner" (in Swedish). Retrieved 12 January 2016.
4. Sjögren, Peter (2016), "Olof Hanner in memoriam" (PDF), Svenska matematikersamfundet Bulletinen (Feburari 2016): 22–24
5. Olof Hanner at the Mathematics Genealogy Project
6. Olof Hanner, Nationalencyklopedin, retrieved 2013-05-17.
7. Hanner (1956a).
8. 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 594626.
9. Kim, Jaegil (2012), Minimal volume product near Hanner polytopes, arXiv:1212.2544.
10. Kalai, Gil (1989), "The number of faces of centrally-symmetric polytopes", Graphs and Combinatorics 5 (1): 389–391, doi:10.1007/BF01788696, MR 1554357.
11. Hanner (1956b).
12. Hanner & Rådström (1951).
13. Reay, John R. (1965), Generalizations of a theorem of Carathéodory, Memoirs of the AMS 54, MR 0188891.
14. Hanner (1959).
15. Raussen, Martin; Skau, Christian (March 2012), "Interview with John Milnor" (PDF), Notices of the AMS 59 (3): 400–408, doi:10.1090/noti803.
16. Nowakowski, Richard J. (2009), "The History of Combinatorial Game Theory", Proceedings of the Board Game Studies Colloquium XI (Lisbon, 2008) (PDF)
17. Olof Hanner's Jigsaw Puzzle, Cut-the-Knot, retrieved 2013-05-17.

External links

• Olof Hanner at WorldCat