Haken, Wolfgang
Overview
Works:  17 works in 31 publications in 3 languages and 416 library holdings 

Roles:  Author 
Classifications:  QA611, 513.83 
Publication Timeline
.
Most widely held works by
Wolfgang Haken
Every planar map is four colorable by
Kenneth I Appel(
Book
)
14 editions published between 1989 and 1992 in English and held by 354 WorldCat member libraries worldwide
14 editions published between 1989 and 1992 in English and held by 354 WorldCat member libraries worldwide
Les Progrès des mathématiques by
Kenneth I Appel(
Book
)
1 edition published in 1981 in French and held by 9 WorldCat member libraries worldwide
Un ouvrage de haute vulgarisation, constitué d'une quinzaine d'articles de qualité, parus dans ##Scientific American## et dans ##Pour la science##. Trois grandes parties: Le kaléidoscope géométrique  Les mathématiques du hasard  Mathématiques et informatique. Les annexes comprennent: un index des matières, de brèves biographies des auteurs et des bibliographies sélectives correspondant à chacun des articles
1 edition published in 1981 in French and held by 9 WorldCat member libraries worldwide
Un ouvrage de haute vulgarisation, constitué d'une quinzaine d'articles de qualité, parus dans ##Scientific American## et dans ##Pour la science##. Trois grandes parties: Le kaléidoscope géométrique  Les mathématiques du hasard  Mathématiques et informatique. Les annexes comprennent: un index des matières, de brèves biographies des auteurs et des bibliographies sélectives correspondant à chacun des articles
Handbuch der FlakEntfernungsmesser : Verf. im Auftr. d. Kommandierenden Generals d. Luftstreitkräfte. Nur f. d. Dienstgebrauch by
Wolfgang Haken(
Book
)
2 editions published in 1917 in German and held by 3 WorldCat member libraries worldwide
2 editions published in 1917 in German and held by 3 WorldCat member libraries worldwide
The solution of the fourcolormap problem by
Kenneth I Appel(
Book
)
1 edition published in 1977 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1977 in English and held by 2 WorldCat member libraries worldwide
The existence of unavoidable sets of geographically good configurations by
Kenneth I Appel(
Book
)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
A set of configurations is unavoidable if every planar map contains at least one element of the set. A configuration L is called geographically good if whenever a member country M of L has any three neighbors N₁, N₂, N₃ which are not members of L then N₁, N₂, N₃ are consecutive (in some order) about M. The main result is a constructive proof that there exist finite unavoidable sets of geographically good configurations. This result is the first step in an investigation of an approach towards the Four Color Conjecture
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
A set of configurations is unavoidable if every planar map contains at least one element of the set. A configuration L is called geographically good if whenever a member country M of L has any three neighbors N₁, N₂, N₃ which are not members of L then N₁, N₂, N₃ are consecutive (in some order) about M. The main result is a constructive proof that there exist finite unavoidable sets of geographically good configurations. This result is the first step in an investigation of an approach towards the Four Color Conjecture
Theorie der Normalflächen : ein Isotopiekriterium für den Kreisnoten by
Wolfgang Haken(
Book
)
in German and held by 1 WorldCat member library worldwide
in German and held by 1 WorldCat member library worldwide
Spectral geometry of hyperbolic 3manifolds by Patrick James Callahan(
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
This thesis uses techniques from spectral geometry and builds from the work of Schoen, Culler and Shalen, Meyerhoff, and others to obtain various estimates and inequalities involving geometric data of hyperbolic 3manifolds. These give numerical relationships between quantities like volume, length of geodesics, area of embedded surfaces, isoperimetric constants, eigenvalues of the Laplacian, and Margulis numbers for hyperbolic 3manifolds
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
This thesis uses techniques from spectral geometry and builds from the work of Schoen, Culler and Shalen, Meyerhoff, and others to obtain various estimates and inequalities involving geometric data of hyperbolic 3manifolds. These give numerical relationships between quantities like volume, length of geodesics, area of embedded surfaces, isoperimetric constants, eigenvalues of the Laplacian, and Margulis numbers for hyperbolic 3manifolds
Enumeration and classification of ribbon knots by Scott Allen Brown(
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
A ribbon knot is one which bounds a certain type of singular disk in the 3sphere. In this work we investigate an enumeration procedure for such disks and study a natural topological grouping of related ribbons which differ by twists along imbedded bands. When the knots under consideration possess a hyperbolic structure, we use a limiting process to show that a given knot can only be obtained in finitely many ways by adding twists to a suitably chosen ribbon. The resulting families of ribbons yield, even for relatively simple cases, ribbon surfaces for many knots in the knot tables
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
A ribbon knot is one which bounds a certain type of singular disk in the 3sphere. In this work we investigate an enumeration procedure for such disks and study a natural topological grouping of related ribbons which differ by twists along imbedded bands. When the knots under consideration possess a hyperbolic structure, we use a limiting process to show that a given knot can only be obtained in finitely many ways by adding twists to a suitably chosen ribbon. The resulting families of ribbons yield, even for relatively simple cases, ribbon surfaces for many knots in the knot tables
Studies in modern topology by
Peter Hilton(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
Nachtrag zu: Theorie der Normalflaechen : ein Isotopiekriterium für den Kreisknoten by
Wolfgang Haken(
Book
)
1 edition published in 1959 in German and held by 1 WorldCat member library worldwide
1 edition published in 1959 in German and held by 1 WorldCat member library worldwide
Only Four Colours by
John Fauvel(
Visual
)
1 edition published in 2002 and held by 1 WorldCat member library worldwide
1 edition published in 2002 and held by 1 WorldCat member library worldwide
Über das Homöomorphieproblem der 3Mannigfaltigkeiten by
Wolfgang Haken(
Book
)
1 edition published in 1962 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1962 in Undetermined and held by 1 WorldCat member library worldwide
Theorie der Normalflächen : ein Isotopiekriterium für den Kreisknoten by
Wolfgang Haken(
Book
)
1 edition published in 1961 in German and held by 1 WorldCat member library worldwide
1 edition published in 1961 in German and held by 1 WorldCat member library worldwide
Every planar map is four colorable : part I : discharging by
Kenneth Appel(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Theorie der Normalflaechen : ein Isotopiekriterium für den Kreisknoten by
Wolfgang Haken(
Book
)
1 edition published in 1958 in German and held by 1 WorldCat member library worldwide
1 edition published in 1958 in German and held by 1 WorldCat member library worldwide
The Four color theorem by
Wolfgang Haken(
Visual
)
1 edition published in 1976 in English and held by 0 WorldCat member libraries worldwide
A lecture on the history, development and survey of the proof of the fourcolor theorem
1 edition published in 1976 in English and held by 0 WorldCat member libraries worldwide
A lecture on the history, development and survey of the proof of the fourcolor theorem
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Alternative Names
Haken, W.
Haken, W. (Wolfgang)
Wolfgang Haken Duits wiskundige
Wolfgang Haken German topologist
Wolfgang Haken matematico tedesco
Wolfgang Haken mathématicien américain
Wolfgang Haken tysk matematikar
Wolfgang Haken tysk matematiker
ヴォルフガング・ハーケン
沃夫冈·哈肯
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