Olof Hanner (7 December 1922 in

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

– 19 September 2015 in

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) was a Swedish mathematician.

Education and career

Hanner earned his Ph.D. from

Stockholm University Stockholm University (SU) () is a public university, public research university in Stockholm, Sweden, founded as a college in 1878, with university status since 1960. With over 33,000 students at four different faculties: law, humanities, social ...

in 1952. He was a professor at the

University of Gothenburg The University of Gothenburg () is a List of universities in Sweden, university in Sweden's second largest city, Gothenburg. Founded in 1891, the university is the third-oldest of the current List of universities in Sweden#Public universities, S ...

from 1963 to 1989.

Contributions

In a 1956 paper, Hanner introduced the

Hanner polytope In geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after Swedish mathematician Olof Hanner, who introduced them in 1956.. Construction The Hann ...

s and the Hanner spaces having these polytopes as their metric balls. Hanner was interested in a

Helly property In combinatorics, a Helly family of order is a family of sets in which every minimal ''subfamily with an empty intersection'' has or fewer sets in it. Equivalently, every finite subfamily such that every -fold intersection is non-empty has non ...

of these shapes, later used to characterize them by : unlike other

convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the wo ...

s, it is not possible to find three

translated Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...

copies of a Hanner polytope that intersect pairwise but do not have a point of common intersection. Subsequently, the Hanner polytopes formed a class of important examples for the

Mahler conjecture In convex geometry, the Mahler volume of a centrally symmetric convex body is a dimensionless quantity that is associated with the body and is invariant under linear transformations. It is named after German-English mathematician Kurt Mahler. It ...

and for Kalai's 3^''d'' conjecture. 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 Moritz Werner Fenchel (; 3 May 1905 – 24 January 1988) was a German-Danish mathematician known for his contributions to geometry and to optimization theory. Fenchel established the basic results of convex analysis and nonlinear opti ...

's version of Carathéodory's lemma, contributing to ''

The Official Encyclopedia of Bridge ''The Official Encyclopedia of Bridge'' (OEB) presents comprehensive information on the card game contract bridge with limited information on related games and on playing cards. It is "official" in reference to the American Contract Bridge Leag ...

'', and doing early work on

combinatorial game theory Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' ev ...

and the

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

of the board game Go. One of the many proofs of the

Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...

based on the

Pythagorean tiling A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides. Many proofs of the Pythagorean theorem are ...

is sometimes called "Olof Hanner's Jigsaw Puzzle".Olof Hanner's Jigsaw Puzzle

Cut-the-Knot Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet Union, Soviet-born Israeli Americans, Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow ...

, retrieved 2013-05-17.

Selected publications

*. *. *. *. *. *. *

References

External links

Olof Hanner
at

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{{DEFAULTSORT:Hanner, Olof 1922 births 2015 deaths Swedish mathematicians Stockholm University alumni Academic staff of the University of Gothenburg People from Stockholm