Hugo Hadwiger
Hugo Hadwiger (23 December 1908 in
Biography
Although born in
Mathematical concepts named after Hadwiger
The Hadwiger–Finsler inequality, proven by Hadwiger with Paul Finsler, is an inequality relating the side lengths and area of any triangle in the Euclidean plane.[6] It generalizes Weitzenböck's inequality and was generalized in turn by Pedoe's inequality. In the same 1937 paper in which Hadwiger and Finsler published this inequality, they also published the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex.
Hadwiger's name is also associated with several important unsolved problems in mathematics:
- The chromatic number.
- The Hadwiger conjecture in combinatorial geometry concerns the minimum number of smaller copies of a convex body needed to cover the body, or equivalently the minimum number of light sources needed to illuminate the surface of the body; for instance, in three dimensions, it is known that any convex body can be illuminated by 16 light sources, but Hadwiger's conjecture implies that only eight light sources are always sufficient.[9][10]
- The Hadwiger–Kneser–Poulsen conjecture states that, if the centers of a system of balls in Euclidean space are moved closer together, then the volume of the union of the balls cannot increase. It has been proven in the plane, but remains open in higher dimensions.[11]
- The Hadwiger–Nelson problem concerns the minimum number of colors needed to color the points of the Euclidean plane so that no two points at unit distance from each other are given the same color. It was first proposed by Edward Nelson in 1950. Hadwiger popularized it by including it in a problem collection in 1961;[12][13] already in 1945 he had published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets.[14]
Other mathematical contributions
Hadwiger proved a theorem characterizing
Cryptographic work
Hadwiger was one of the principal developers of a Swiss
Awards and honors
Asteroid 2151 Hadwiger, discovered in 1977 by Paul Wild, is named after Hadwiger.[4]
The first article in the "Research Problems" section of the
Selected works
Books
- Altes und Neues über konvexe Körper, Birkhäuser 1955[17]
- Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer, Grundlehren der mathematischen Wissenschaften, 1957[18]
- with H. Debrunner, V. Klee Combinatorial Geometry in the Plane, Holt, Rinehart and Winston, New York 1964; Dover reprint 2015
Articles
- "Über eine Klassifikation der Streckenkomplexe", Vierteljahresschrift der Naturforschenden Gesellschaft Zürich, vol. 88, 1943, pp. 133–143 (Hadwiger's conjecture in graph theory)
- with Paul Glur Zerlegungsgleichheit ebener Polygone, Elemente der Math, vol. 6, 1951, pp. 97-106
- Ergänzungsgleichheit k-dimensionaler Polyeder, Math. Zeitschrift, vol. 55, 1952, pp. 292-298[permanent dead link]
- Lineare additive Polyederfunktionale und Zerlegungsgleichheit, Math. Z., vol. 58, 1953, pp. 4-14[permanent dead link]
- Zum Problem der Zerlegungsgleichheit k-dimensionaler Polyeder, Mathematische Annalen vol. 127, 1954, pp. 170–174[permanent dead link]
References
- ISBN 978-3-8171-1769-7.
- ^ ISBN 978-0-521-86680-4.
- ^ Hugo Hadwiger at the Mathematics Genealogy Project.
- ^ ISBN 978-3-540-00238-3.
- ^ Klain, Daniel; Rota, Gian-Carlo (1997), Introduction to Geometric Probability, Cambridge University Press.
- S2CID 122841127.
- ^ Hadwiger, Hugo (1943), "Über eine Klassifikation der Streckenkomplexe", Vierteljschr. Naturforsch. Ges. Zürich, 88: 133–143.
- .
- ^ Hadwiger, H. (1957), "Ungelöste Probleme Nr. 20", Elemente der Mathematik, 12: 121.
- ^ Boltjansky, V.; Gohberg, I. (1985), "11. Hadwiger's Conjecture", Results and Problems in Combinatorial Geometry, Cambridge University Press, pp. 44–46.
- S2CID 15297926.
- ISBN 978-0-387-74640-1.
- ^ Hadwiger, Hugo (1961), "Ungelöste Probleme No. 40", Elem. Math., 16: 103–104.
- ^ Hadwiger, Hugo (1945), "Überdeckung des euklidischen Raumes durch kongruente Mengen", Portugaliae Mathematica, 4: 238–242.
- ^ Hadwiger, H. (1951), "Hillsche Hypertetraeder", Gazeta Matemática (Lisboa), 12 (50): 47–48.
- ^ NEMA (Swiss Neue Maschine), Jerry Proc, retrieved 2010-04-18.
- .
- .