mathematics

Georg Hamel

Georg Hamel 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 Georg Hamel rather than just read about it. In short: Georg Karl Wilhelm Hamel (12 September 1877 – 4 October 1954) was a German mathematician with interests in mechanics, the foundations of mathematics and function theory. Biography Hamel was born in Düren, Rhenish Prussia.

Key takeaways

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

Reference excerpt

Georg Karl Wilhelm Hamel (12 September 1877 – 4 October 1954) was a German mathematician with interests in mechanics, the foundations of mathematics and function theory.

Biography Hamel was born in Düren, Rhenish Prussia. He studied at Aachen, Berlin, Göttingen, and Karlsruhe. His doctoral adviser was David Hilbert. He taught at Brünn in 1905, Aachen in 1912, and at Technische Universität Berlin in 1919. In 1927, Hamel studied the size of the key space for the Kryha encryption device. He was an Invited Speaker of the International Congress of Mathematicians in 1932 at Zurich and in 1936 at Oslo. He was the author of several important treatises on mechanics. He became a member of the Prussian Academy of Sciences in 1938 and the Bavarian Academy of Sciences in 1953. He died in Landshut, Bavaria.

Selected publications Über die Geometrieen, in denen die Geraden die Kürzesten sind, Göttigen: Dieterich'schen Universitäts-Buch-Druckerei, 1901 ("On the geometries in which the straight lines are the shortest", Hamel's doctoral dissertation on Hilbert's fourth problem. A version may be found in Mathematische Annalen 57, 1903.) Lagrange-Euler'schen gleichungen der Mechanik, Leipzig: B.G. Teubner, 1903 Hamel, Georg (1905), "Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung f(x+y)=f(x)+f(y)", Mathematische Annalen, 60 (3), Leipzig: 459–462, doi:10.1007/BF01457624, S2CID 120063569 Elementare mechanik, Leipzig und Berlin: B. G. Teubner, 1912 Grundbegriffe der Mechanik, Aus Natur und Geisteswelt,684. BDCHN., Leipzig, 1921{{citation}}: CS1 maint: location missing publisher (link) Integralgleichungen, Berlin: Springer, 1937 Komplexe Form der ebenen Bewegungsgleichungen zäher, inkompressibler Flüssigkeiten, Berlin: Verlag der Akademie der Wissenschaften, in Kommission bei W. de Gruyter, 1941 Aufbau einer Theorie der Häute und der dünnen Schalen nach der Methode von Lagrange, Berlin: Akademie der Wissenschaften, in Kommission bei W. de Gruyter, 1944 Theoretische Mechanik, Berlin: Springer, 1949

See also Hamel basis Hamel dimension Cauchy's functional equation Hilbert's fourth problem

References

Illustrations

Worked examples

Example 1 — a first encounter with Georg Hamel

Start with the simplest possible case. Write down what Georg Hamel 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 Georg Hamel 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 Georg Hamel 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 Georg Hamel

In research: Georg Hamel 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 Georg Hamel 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: Georg Hamel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1877 births, 1954 deaths, 19th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Georg Hamel 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 Georg Hamel in 20 minutes

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

Frequently asked questions

What is Georg Hamel in simple terms?

Georg Karl Wilhelm Hamel (12 September 1877 – 4 October 1954) was a German mathematician with interests in mechanics, the foundations of mathematics and function theory. Biography Hamel was born in Düren, Rhenish Prussia.

Why does Georg Hamel 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 Georg Hamel?

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 Georg Hamel.