mathematics

Imre Bárány

Imre Bárány 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 Imre Bárány rather than just read about it. In short: Imre Bárány (Mátyásföld, Budapest, 7 December 1947) is a Hungarian mathematician, working in combinatorics and discrete geometry. He works at the Rényi Mathematical Institute of the Hungarian Academy of Sciences, and has a part-time appointment at University College London.

Key takeaways

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

Reference excerpt

Imre Bárány (Mátyásföld, Budapest, 7 December 1947) is a Hungarian mathematician, working in combinatorics and discrete geometry. He works at the Rényi Mathematical Institute of the Hungarian Academy of Sciences, and has a part-time appointment at University College London.

Notable results He gave a surprisingly simple alternative proof of László Lovász's theorem on Kneser graphs. He gave a new proof of the Borsuk–Ulam theorem. Bárány gave a colored version of Carathéodory's theorem. He solved an old problem of James Joseph Sylvester on the probability of random point sets in convex position. With Van H. Vu proved a central limit theorem on random points in convex bodies. With Zoltán Füredi he gave an algorithm for mental poker. With Füredi he proved that no deterministic polynomial time algorithm determines the volume of convex bodies in dimension d within a multiplicative error dd. With Füredi and János Pach he proved the following six circle conjecture of László Fejes Tóth: if in a planar circle packing each circle is tangent to at least 6 other circles, then either it is the hexagonal system of circles with identical radii, or there are circles with arbitrarily small radius.

Career Bárány received the Mathematical Prize (now Paul Erdős Prize) of the Hungarian Academy of Sciences in 1985. He was an invited speaker at the Combinatorics session of the International Congress of Mathematicians, in Beijing, 2002. He was an Erdős Lecturer at Hebrew University of Jerusalem in 2004. He was elected a corresponding (2010), full (2016) member of the Hungarian Academy of Sciences. In 2012 he became a fellow of the American Mathematical Society. Since 2021, he is a member of the Academia Europaea. He is an editor-in-chief for the journal Combinatorica, and an Editorial Board member for Mathematika and the Online Journal of Analytic Combinatorics. He is area editor of the journal Mathematics of Operations Research.

References

External links Imre Bárány at the Mathematics Genealogy Project "Personal webpage". Mathematical Institute of the Hungarian Academy of Sciences. "Personal webpage". Department of Mathematics, University College London. Archived from the original on 2010-03-14.

Illustrations

Worked examples

Example 1 — a first encounter with Imre Bárány

Start with the simplest possible case. Write down what Imre Bárány 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 Imre Bárány 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 Imre Bárány 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 Imre Bárány

In research: Imre Bárány 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 Imre Bárány 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: Imre Bárány is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, Academics of University College London, Combinatorialists, so understanding it makes those chapters shorter.
In everyday life: Look for Imre Bárány 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 Imre Bárány in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Imre Bárány means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Imre Bárány out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Imre Bárány in simple terms?

Why does Imre Bárány 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 Imre Bárány?

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 Imre Bárány.