astronomy

Paul Finsler

Paul Finsler 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 Paul Finsler rather than just read about it. In short: Paul Finsler (11 April 1894 – 29 April 1970) was a German and Swiss mathematician. Born in Heilbronn, Germany, Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory.

Key takeaways

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

Reference excerpt

Paul Finsler (11 April 1894 – 29 April 1970) was a German and Swiss mathematician. Born in Heilbronn, Germany, Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory. He studied for his habilitation at the University of Cologne, receiving it in 1922. He joined the faculty of the University of Zurich in 1927, and was promoted to ordinary professor there in 1944. He died on 29 April 1970. Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger, as is the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex. Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox.

Publications Finsler, Paul (1918), Über Kurven und Flächen in allgemeinen Räumen, Dissertation, Göttingen, JFM 46.1131.02 (Reprinted by Birkhäuser (1951)) Finsler, Paul (1926). "Gibt es Widersprüche in der Mathematik?". Jahresbericht der Deutschen Mathematiker-Vereinigung. 34: 143–154. Finsler, Paul (1926). "Formale Beweise und die Entscheidbarkeit". Mathematische Zeitschrift. 25: 676–682. doi:10.1007/bf01283861. S2CID 121054124. Finsler, Paul (1926). "Über die Grundlegung der Mengenlehre. Erster Teil". Mathematische Zeitschrift. 25: 683–713. doi:10.1007/bf01283862. Finsler, Paul (1963). "Über die Grundlegung der Mengenlehre. Zweiter Teil". Commentarii Mathematici Helvetici. 38 (1): 172–218. doi:10.1007/bf02566915. S2CID 124928448. Finsler, P. (1933). "Die Existenz der Zahlenreihe und des Kontinuums". Commentarii Mathematici Helvetici. 5: 88–94. doi:10.1007/BF01297507. S2CID 120768947. Finsler: Aufsätze zur Mengenlehre. (ed. G. Unger) 1975. Booth, David; Ziegler, Renatus, eds. (1996). Finsler Set Theory: Platonism and Circularity. "Translation of Paul Finsler's papers on set theory with introductory comments". Birkhäuser Basel. doi:10.1007/978-3-0348-9031-1. ISBN 978-3-0348-9876-8.

References

Further reading Burckhardt, J. J. (1980), Die Mathematik an der Universität Zurich 1916-1950 unter den Professoren R. Fueter, A. Speiser und P. Finsler, Basel{{citation}}: CS1 maint: location missing publisher (link).

Worked examples

Example 1 — a first encounter with Paul Finsler

Start with the simplest possible case. Write down what Paul Finsler 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 Paul Finsler 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 Paul Finsler 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 Paul Finsler

In research: Paul Finsler 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 Paul Finsler 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: Paul Finsler is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1894 births, 1970 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Finsler 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 Paul Finsler in 20 minutes

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

Frequently asked questions

What is Paul Finsler in simple terms?

Why does Paul Finsler 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 Paul Finsler?

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 Paul Finsler.