211:
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
31:
231:
in 1950. Hadwiger popularized it by including it in a problem collection in 1961; 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
219:
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
227:
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
92:. He continued at Bern for his graduate studies, and received his Ph.D. in 1936 under the supervision of Willy Scherrer. He was for more than forty years a professor of mathematics at Bern.
369:"Über eine Klassifikation der Streckenkomplexe", Vierteljahresschrift der Naturforschenden Gesellschaft Zürich, vol. 88, 1943, pp. 133–143 (Hadwiger's conjecture in graph theory)
682:
208:
940:
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372:
749:
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460:
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352:
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289:, enhanced the system by using ten rotors instead of five. The system was used by the Swiss army and air force between 1947 and 1992.
177:
609:
545:
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to
Hadwiger, on the occasion of his 60th birthday, in honor of Hadwiger's work editing a column on unsolved problems in the journal
881:
838:
357:
142:
935:
739:
158:
122:-dimensional Euclidean space. According to this theorem, any such valuation can be expressed as a linear combination of the
945:
479:
312:
166:
304:
216:
200:
that can be formed as a minor in the graph; the
Hadwiger conjecture states that this is always at least as large as the
224:
455:, Encyclopedia of Mathematics and its Applications, vol. 58, Cambridge University Press, 2006, pp. 389–390,
955:
661:
266:
165:. In the same 1937 paper in which Hadwiger and Finsler published this inequality, they also published the
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246:
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162:
100:
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135:
108:
184:“one of the deepest unsolved problems in graph theory,” describes a conjectured connection between
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960:
717:
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85:
77:
42:
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Lineare additive
Polyederfunktionale und Zerlegungsgleichheit, Math. Z., vol. 58, 1953, pp. 4-14
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104:
89:
81:
46:
741:
The
Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators
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857:
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172:
Hadwiger's name is also associated with several important unsolved problems in mathematics:
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709:
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285:. The Swiss, fearing that the Germans and Allies could read messages transmitted on their
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154:
250:
185:
785:
Hadwiger, Hugo (1945), "Ăśberdeckung des euklidischen Raumes durch kongruente Mengen",
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61:
53:
905:
862:
721:
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123:
65:
50:
212:
Hadwiger's conjecture implies that only eight light sources are always sufficient.
317:
189:
112:
115:
680:(2002), "Pushing disks apart – the Kneser-Poulsen conjecture in the plane",
475:
131:
30:
705:
297:
150:
57:
580:
Hadwiger, Hugo (1943), "Ăśber eine
Klassifikation der Streckenkomplexe",
17:
824:
558:
696:
253:. He found a higher-dimensional generalization of the space-filling
29:
656:
Boltjansky, V.; Gohberg, I. (1985), "11. Hadwiger's
Conjecture",
126:; for instance, in two dimensions, the intrinsic volumes are the
607:(1980), "Hadwiger's conjecture is true for almost every graph",
169:
on a square derived from two other squares that share a vertex.
127:
347:, Springer, Grundlehren der mathematischen Wissenschaften, 1957
88:, where he majored in mathematics but also studied physics and
398:
Zum
Problem der Zerlegungsgleichheit k-dimensionaler Polyeder
149:, is an inequality relating the side lengths and area of any
310:
The first article in the "Research
Problems" section of the
543:; Hadwiger, Hugo (1937), "Einige Relationen im Dreieck",
277:
Hadwiger was one of the principal developers of a Swiss
375:
Zerlegungsgleichheit ebener Polygone, Elemente der Math
884:
Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
345:
Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
259:
Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
765:
Hadwiger, Hugo (1961), "Ungelöste Probleme No. 40",
196:
of a graph is the number of vertices in the largest
400:, Mathematische Annalen vol. 127, 1954, pp. 170–174
181:
636:Hadwiger, H. (1957), "Ungelöste Probleme Nr. 20",
418:BrĂĽggenthies, Wilhelm; Dick, Wolfgang R. (2005),
281:for encrypting military communications, known as
245:, systems of points in Euclidean space formed by
805:Hadwiger, H. (1951), "Hillsche Hypertetraeder",
683:Journal fĂĽr die reine und angewandte Mathematik
385:, Math. Zeitschrift, vol. 55, 1952, pp. 292-298
658:Results and Problems in Combinatorial Geometry
383:Ergänzungsgleichheit k-dimensionaler Polyeder
356:, Holt, Rinehart and Winston, New York 1964;
209:Hadwiger conjecture in combinatorial geometry
8:
422:, Acta historica astronomiae, vol. 26,
490:
488:
180:, posed by Hadwiger in 1943 and called by
96:Mathematical concepts named after Hadwiger
84:. He did his undergraduate studies at the
904:
861:
695:
447:
445:
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241:Hadwiger proved a theorem characterizing
410:
582:Vierteljschr. Naturforsch. Ges. ZĂĽrich
526:Introduction to Geometric Probability
7:
841:Altes und Neues über konvexe Körper
827:, Jerry Proc, retrieved 2010-04-18.
420:Biographischer Index der Astronomie
353:Combinatorial Geometry in the Plane
339:Altes und Neues über konvexe Körper
261:was foundational for the theory of
182:Bollobás, Catlin & Erdős (1980)
178:Hadwiger conjecture in graph theory
217:Hadwiger–Kneser–Poulsen conjecture
107:classifies the isometry-invariant
25:
941:20th-century Swiss mathematicians
610:European Journal of Combinatorics
546:Commentarii Mathematici Helvetici
497:Dictionary of minor planet names
237:Other mathematical contributions
966:German emigrants to Switzerland
906:10.1090/s0002-9904-1959-10263-9
863:10.1090/s0002-9904-1956-10023-2
499:, Springer, 2003, p. 174,
161:and was generalized in turn by
27:Swiss mathematician (1908–1981)
1:
623:10.1016/s0195-6698(80)80001-1
480:Mathematics Genealogy Project
313:American Mathematical Monthly
837:Boothby, William M. (1956).
528:, Cambridge University Press
350:with H. Debrunner, V. Klee
307:, is named after Hadwiger.
143:Hadwiger–Finsler inequality
45:– 29 October 1981 in
982:
825:NEMA (Swiss Neue Maschine)
807:Gazeta Matemática (Lisboa)
662:Cambridge University Press
377:, vol. 6, 1951, pp. 97-106
145:, proven by Hadwiger with
951:University of Bern alumni
303:, discovered in 1977 by
167:Finsler–Hadwiger theorem
159:Weitzenböck's inequality
56:, known for his work in
787:Portugaliae Mathematica
638:Elemente der Mathematik
322:Elemente der Mathematik
267:mathematical morphology
225:Hadwiger–Nelson problem
744:, New York: Springer,
287:Enigma cipher machines
249:of higher-dimensional
80:, Hadwiger grew up in
35:
936:Modern cryptographers
893:Bull. Amer. Math. Soc
850:Bull. Amer. Math. Soc
706:10.1515/crll.2002.101
263:Minkowski functionals
247:orthogonal projection
41:(23 December 1908 in
34:Hugo Hadwiger in 1973
33:
946:Scientists from Bern
453:Geometric Tomography
424:Verlag Harri Deutsch
257:. And his 1957 book
136:Euler characteristic
603:; Catlin, Paul A.;
495:Schmadel, Lutz D.,
559:10.1007/BF01214300
358:Dover reprint 2015
273:Cryptographic work
163:Pedoe's inequality
101:Hadwiger's theorem
86:University of Bern
78:Karlsruhe, Germany
43:Karlsruhe, Germany
36:
956:Combinatorialists
751:978-0-387-74640-1
736:Soifer, Alexander
506:978-3-540-00238-3
462:978-0-521-86680-4
433:978-3-8171-1769-7
341:, Birkhäuser 1955
316:was dedicated by
293:Awards and honors
157:. It generalizes
124:intrinsic volumes
105:integral geometry
90:actuarial science
82:Bern, Switzerland
76:Although born in
47:Bern, Switzerland
16:(Redirected from
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678:Connelly, Robert
676:Bezdek, Károly;
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373:with Paul Glur
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255:Hill tetrahedra
251:cross polytopes
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194:Hadwiger number
155:Euclidean plane
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617:(3): 195–199,
601:Bollobás, Béla
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186:graph coloring
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541:Finsler, Paul
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476:Hugo Hadwiger
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279:rotor machine
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62:combinatorics
59:
55:
54:mathematician
52:
48:
44:
40:
39:Hugo Hadwiger
32:
19:
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697:math/0108098
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190:graph minors
171:
147:Paul Finsler
140:
119:
99:
75:
66:cryptography
38:
37:
931:1981 deaths
926:1908 births
813:(50): 47–48
767:Elem. Math.
605:Erdős, Paul
318:Victor Klee
220:dimensions.
116:convex sets
920:Categories
406:References
265:, used in
134:, and the
109:valuations
961:Geometers
899:(1): 20.
882:"Review:
839:"Review:
793:: 238–242
773:: 103–104
588:: 133–143
567:122841127
305:Paul Wild
132:perimeter
72:Biography
880:(1959).
878:RadĂł, T.
738:(2008),
722:15297926
524:(1997),
364:Articles
298:Asteroid
151:triangle
58:geometry
49:) was a
18:Hadwiger
714:1944813
478:at the
153:in the
113:compact
748:
720:
712:
565:
503:
459:
430:
198:clique
192:. The
130:, the
64:, and
889:(PDF)
846:(PDF)
718:S2CID
692:arXiv
644:: 121
563:S2CID
333:Books
232:sets.
51:Swiss
746:ISBN
688:2002
501:ISBN
457:ISBN
428:ISBN
283:NEMA
223:The
215:The
207:The
188:and
176:The
141:The
128:area
901:doi
858:doi
702:doi
619:doi
555:doi
118:in
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103:in
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