astronomy

Olof Hanner

Olof Hanner is a astronomy 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 Olof Hanner rather than just read about it. In short: Olof Hanner (7 December 1922 in Stockholm – 19 September 2015 in Gothenburg) was a Swedish mathematician. Education and career Hanner earned his Ph.D. under the supervision of Fritz Carlson from Stockholm University in 1952.

Key takeaways

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

Reference excerpt

Olof Hanner (7 December 1922 in Stockholm – 19 September 2015 in Gothenburg) was a Swedish mathematician.

Education and career Hanner earned his Ph.D. under the supervision of Fritz Carlson from Stockholm University in 1952. He was a professor at the University of Gothenburg from 1963 to 1989.

Contributions In a 1956 paper, Hanner introduced the Hanner polytopes and the Hanner spaces having these polytopes as their metric balls. Hanner was interested in a Helly property of these shapes, later used to characterize them by Hansen & Lima (1981): unlike other convex polytopes, it is not possible to find three translated copies of a Hanner polytope that intersect pairwise but do not have a point of common intersection. Subsequently, the Hanner polytopes formed a class of important examples for the Mahler conjecture and for Kalai's 3d conjecture. In another paper from the same year, Hanner proved a set of inequalities related to the uniform convexity of Lp spaces, now known as Hanner's inequalities. Other contributions of Hanner include (with Hans Rådström) improving Werner Fenchel's version of Carathéodory's lemma, contributing to The Official Encyclopedia of Bridge, and doing early work on combinatorial game theory and the mathematics of the board game Go. One of the many proofs of the Pythagorean theorem based on the Pythagorean tiling is sometimes called "Olof Hanner's Jigsaw Puzzle".

Selected publications Hanner, Olof (1951), "Some theorems on absolute neighborhood retracts", Arkiv för Matematik, 1 (5): 389–408, Bibcode:1951ArM.....1..389H, doi:10.1007/BF02591376, MR 0043459. Hanner, Olof; Rådström, Hans (1951), "A generalization of a theorem of Fenchel", Proceedings of the American Mathematical Society, 2 (4): 589–593, doi:10.2307/2032012, JSTOR 2032012, MR 0044142. Hanner, Olof (1956a), "Intersections of translates of convex bodies", Mathematica Scandinavica, 4: 65–87, doi:10.7146/math.scand.a-10456, MR 0082696. Hanner, Olof (1956b), "On the uniform convexity of Lp and ℓp", Arkiv för Matematik, 3 (3): 239–244, Bibcode:1956ArM.....3..239H, doi:10.1007/BF02589410, MR 0077087. Hanner, Olof (1959), "Mean play of sums of positional games", Pacific Journal of Mathematics, 9: 81–99, doi:10.2140/pjm.1959.9.81, MR 0104524. Hanner, Olof (1970), "Mathematics, A Solitary Game", The Two-Year College Mathematics Journal, 1 (2): 5–16, doi:10.2307/3027352, JSTOR 3027352. Hallén, Hans-Olof; Hanner, Olof; Jannersten, Per (1994), Rigal, Barry (ed.), Bridge movements: A fair approach, Bridgeakad. (Bridge academy) (Translated by Barry Rigal from the 1990 Swedish Tävlingsledaren (The leader of the tournament) ed.), Alvesta: Jannersten Forlag AB, ISBN 91-85024-86-4

References

External links Olof Hanner at WorldCat

Worked examples

Example 1 — a first encounter with Olof Hanner

Start with the simplest possible case. Write down what Olof Hanner claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Olof Hanner 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 Olof Hanner 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 Olof Hanner

In research: Olof Hanner appears in astronomy 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 Olof Hanner 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: Olof Hanner is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1922 births, 2015 deaths, Academic staff of the University of Gothenburg, so understanding it makes those chapters shorter.
In everyday life: Look for Olof Hanner 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 Olof Hanner in 20 minutes

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

Frequently asked questions

What is Olof Hanner in simple terms?

Olof Hanner (7 December 1922 in Stockholm – 19 September 2015 in Gothenburg) was a Swedish mathematician. Education and career Hanner earned his Ph.D. under the supervision of Fritz Carlson from Stockholm University in 1952.

Why does Olof Hanner matter?

Because it connects several astronomy 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 Olof Hanner?

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 Olof Hanner.