Willem Abraham Wythoff, born Wijthoff (), (6 October 1865 – 21 May 1939) was a
Dutch
Dutch commonly refers to:
* Something of, from, or related to the Netherlands
* Dutch people ()
* Dutch language ()
Dutch may also refer to:
Places
* Dutch, West Virginia, a community in the United States
* Pennsylvania Dutch Country
People E ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
.
Biography
Wythoff was born in
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the capital and most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 in the urban ar ...
to Anna C. F. Kerkhoven and Abraham Willem Wijthoff, who worked in a sugar refinery.
[.] He studied at the
University of Amsterdam
The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...
, and earned his Ph.D. in 1898 under the supervision of
Diederik Korteweg
Diederik Johannes Korteweg (31 March 1848 – 10 May 1941) was a Dutch mathematician. He is now best remembered for his work on the Korteweg–de Vries equation, together with Gustav de Vries.
Early life and education
Diederik Korteweg's father ...
.
Contributions
Wythoff is known in
combinatorial game theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the player ...
and
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...
for his study of
Wythoff's game, whose solution involves the
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
s.
The
Wythoff array
In mathematics, the Wythoff array is an infinite matrix of integers derived from the Fibonacci sequence and named after Dutch mathematician Willem Abraham Wythoff. Every positive integer occurs exactly once in the array, and every integer sequence ...
, a two-dimensional array of numbers related to this game and to the Fibonacci sequence, is also named after him.
[.]
In geometry, Wythoff is known for the
Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic construction.
Construction process
...
of
uniform tiling
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.
Uniform tilings can exist in both the Euclidean plane and Hyperbolic space, hyperbolic plane. Uniform tilings ar ...
s and
uniform polyhedra
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent.
Uniform polyhedra may be regular (if also ...
and for the
Wythoff symbol used as a notation for these geometric objects.
Selected publications
*.
*.
References
External links
*
1865 births
1939 deaths
19th-century Dutch mathematicians
Combinatorial game theorists
University of Amsterdam alumni
Scientists from Amsterdam
20th-century Dutch mathematicians
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