mathematics

Willem Abraham Wythoff

Willem Abraham Wythoff is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Willem Abraham Wythoff rather than just read about it. In short: Willem Abraham Wythoff (Dutch pronunciation: [ˈʋɪləm ˈaːbraːɦɑɱ ˈʋɛithɔf]; born Wijthoff; 6 October 1865 – 21 May 1939) was a Dutch mathematician. Biography Wythoff was born in Amsterdam to Anna C.

Key takeaways

Willem Abraham Wythoff belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Willem Abraham Wythoff to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Willem Abraham Wythoff from memory before moving on to harder problems.

Reference excerpt

Willem Abraham Wythoff (Dutch pronunciation: [ˈʋɪləm ˈaːbraːɦɑɱ ˈʋɛithɔf]; born Wijthoff; 6 October 1865 – 21 May 1939) was a Dutch mathematician.

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

Contributions Wythoff is known in combinatorial game theory and number theory for his study of Wythoff's game, whose solution involves the Fibonacci numbers. The Wythoff array, 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 of uniform tilings and uniform polyhedra 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 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, 20, Koninklijke Akademie van Wetenschappen te Amsterdam: 966–970, Bibcode:1918KNAB...20..966W.

References

External links Media related to Willem Wijthoff at Wikimedia Commons

Kimberling, Clark, Willem Abraham Wythoff (1865–1939) number-theorist

Illustrations

Worked examples

Example 1 — a first encounter with Willem Abraham Wythoff

Start with the simplest possible case. Write down what Willem Abraham Wythoff claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Willem Abraham Wythoff before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Willem Abraham Wythoff ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Willem Abraham Wythoff

In research: Willem Abraham Wythoff appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Willem Abraham Wythoff in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Willem Abraham Wythoff is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1865 births, 1939 deaths, 19th-century Dutch mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Willem Abraham Wythoff outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Willem Abraham Wythoff in 20 minutes

Read the reference excerpt below once, without taking notes.
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Frequently asked questions

What is Willem Abraham Wythoff in simple terms?

Willem Abraham Wythoff (Dutch pronunciation: [ˈʋɪləm ˈaːbraːɦɑɱ ˈʋɛithɔf]; born Wijthoff; 6 October 1865 – 21 May 1939) was a Dutch mathematician. Biography Wythoff was born in Amsterdam to Anna C.

Why does Willem Abraham Wythoff matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Willem Abraham Wythoff?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Willem Abraham Wythoff.