mathematics

Stanisław Gołąb

Stanisław Gołąb 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 Stanisław Gołąb rather than just read about it. In short: Stanisław Gołąb (July 26, 1902 – April 30, 1980) was a Polish mathematician from Kraków, working in particular on the field of affine geometry. In 1932, he proved that the perimeter of the unit disc respect to a given metric can take any value in between 6 and 8, and that these extremal values are obtained if and only if the unit disc is an affine regular hexagon resp. a parallelogram.

Key takeaways

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

Reference excerpt

Stanisław Gołąb (July 26, 1902 – April 30, 1980) was a Polish mathematician from Kraków, working in particular on the field of affine geometry. In 1932, he proved that the perimeter of the unit disc respect to a given metric can take any value in between 6 and 8, and that these extremal values are obtained if and only if the unit disc is an affine regular hexagon resp. a parallelogram. He worked at the State Institute of Mathematics, which was incorporated into the Polish Academy of Sciences in 1952.

Selected works S. Gołąb: Quelques problèmes métriques de la géometrie de Minkowski, Trav. de l'Acad. Mines Cracovie 6 (1932), 1–79 Golab, S., Über einen algebraischen Satz, welcher in der Theorie der geometrischen Objekte auftritt, Beiträge zur Algebra und Geometrie 2 (1974) 7–10. Golab, S.; Swiatak, H.: Note on Inner Products in Vector Spaces. Aequationes Mathematicae (1972) 74. Golab, S.: Über das Carnotsche Skalarprodukt in schwach normierten Vektorräumen. Aequationes Mathematicae 13 (1975) 9–13. Golab, S., Sur un problème de la métrique angulaire dans la géometrie de Minkowski, Aequationes Mathematicae (1971) 121. Golab, S., Über die Grundlagen der affinen Geometrie., Jahresbericht DMV 71 (1969) 138–155.

Notes

External links List of Golab's articles at U. of Göttingen, Germany Stanisław Gołąb at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Stanisław Gołąb

Start with the simplest possible case. Write down what Stanisław Gołąb 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 Stanisław Gołąb 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 Stanisław Gołąb 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 Stanisław Gołąb

In research: Stanisław Gołąb 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 Stanisław Gołąb 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: Stanisław Gołąb is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1902 births, 1980 deaths, 20th-century Polish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Stanisław Gołąb 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 Stanisław Gołąb in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Stanisław Gołąb 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 Stanisław Gołąb out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Stanisław Gołąb in simple terms?

Why does Stanisław Gołąb 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 Stanisław Gołąb?

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 Stanisław Gołąb.