Willem Abraham Wythoff (; born Wijthoff; 6 October 1865 – 21 May 1939) was a

Dutch Dutch or Nederlands commonly refers to: * Something of, from, or related to the Netherlands ** Dutch people as an ethnic group () ** Dutch nationality law, history and regulations of Dutch citizenship () ** Dutch language () * In specific terms, i ...

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, mathematical structure, structure, space, Mathematica ...

Biography

Wythoff was born in

Amsterdam Amsterdam ( , ; ; ) is the capital of the Netherlands, capital and Municipalities of the Netherlands, largest city of the Kingdom of the Netherlands. It has a population of 933,680 in June 2024 within the city proper, 1,457,018 in the City Re ...

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, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ...

, 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. Research in this field has primarily focused on two-player games in which a ''position'' ev ...

and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

for his study of

Wythoff's game Wythoff's game is a two-player mathematical subtraction game, played with two piles of counters. Players take turns removing counters from one or both piles; when removing counters from both piles, the numbers of counters removed from each pile m ...

, whose solution involves the

Fibonacci number In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

s. The

Wythoff array In mathematics, the Wythoff array is an infinite Matrix (mathematics), matrix of positive integers derived from the Fibonacci sequence and named after Dutch mathematician Willem Abraham Wythoff. Every positive integer occurs exactly once in the arr ...

, 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 ...

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 plane. Uniform tilings are related to t ...

s and

uniform polyhedra In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fac ...

and for the Wythoff symbol used as a notation for these geometric objects.

Personal life

Willem Abraham Wythoff was the youngest of four children born into the wealthy family of Abraham Willem Wijthoff and Anna Catharina Frederika Kerkhoven. His father was a Lutheran and son of the Amsterdam sugar refinery family Wijthoff & Son. His older sisters were: mathematician Geertruida "Truida" Wijthoff, writer Henriëtte Wijthoff and illustrator Anna Catharina Frederika Wijthoff.

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 {{mathematician-stub