Willem Abraham Wythoff


Willem Abraham Wythoff, born Wijthoff (Dutch pronunciation: [ʋɛithɔf]), (6 October 1865 – 21 May 1939) was a Dutch mathematician.

Willem Abraham Wythoff
Willem Abraham Wijthoff

(1865-10-06)6 October 1865
Died21 May 1939(1939-05-21) (aged 73)
Alma materUniversity of Amsterdam
Known forWythoff's game, Wythoff construction, Wythoff symbol
Scientific career
Doctoral advisorDiederik Korteweg


Wythoff was born in Amsterdam to Anna C. F. Kerkhoven and Abraham Willem Wijthoff,[1] who worked in a sugar refinery.[2] He studied at the University of Amsterdam, and earned his Ph.D. in 1898 under the supervision of Diederik Korteweg.[3]


Wythoff is known in combinatorial game theory and number theory for his study of Wythoff's game, whose solution involves the Fibonacci numbers.[2] The Wythoff array, a two-dimensional array of numbers related to this game and to the Fibonacci sequence, is also named after him.[4][5]

In geometry, Wythoff is known for the Wythoff construction of uniform tilings and uniform polyhedra and for the Wythoff symbol used as a notation for these geometric objects.

Selected publicationsEdit

  • Wythoff, W. A. (1905–1907), "A modification of the game of nim", Nieuw Archief voor Wiskunde, 2: 199–202.
  • Wythoff, W. A. (1918), "A relation between the polytopes of the C600-family", Proceedings of the Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam, 20: 966–970, Bibcode:1918KNAB...20..966W.


  1. ^ W.A. Wijthoff genealogy
  2. ^ a b Stakhov, Alexey; Stakhov, Alekseĭ Petrovich; Olsen, Scott Anthony (2009), The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science, K & E Series on Knots and Everything, vol. 22, World Scientific, pp. 129–130, ISBN 9789812775825.
  3. ^ Willem Abraham Wythoff at the Mathematics Genealogy Project
  4. ^ Kimberling, Clark (1995), "The Zeckendorf array equals the Wythoff array" (PDF), Fibonacci Quarterly, 33 (1): 3–8.
  5. ^ Morrison, D. R. (1980), "A Stolarsky array of Wythoff pairs", A Collection of Manuscripts Related to the Fibonacci Sequence (PDF), Santa Clara, Calif: The Fibonacci Association, pp. 134–136.

External linksEdit