astronomy

Otto Hesse

Otto Hesse 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 Otto Hesse rather than just read about it. In short: Ludwig Otto Hesse (22 April 1811 – 4 August 1874) was a German mathematician. Hesse was born in Königsberg, Prussia, and died in Munich, Bavaria.

Key takeaways

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

Reference excerpt

Ludwig Otto Hesse (22 April 1811 – 4 August 1874) was a German mathematician. Hesse was born in Königsberg, Prussia, and died in Munich, Bavaria. He worked mainly on algebraic invariants, and geometry. The Hessian matrix, the Hesse normal form, the Hesse configuration, the Hessian group, Hessian pairs, Hesse's theorem, Hesse pencil, and the Hesse transfer principle are named after him. Many of Hesse's research findings were presented for the first time in Crelle's Journal or Hesse's textbooks.

Life Hesse was born in Königsberg (today Kaliningrad) as the son of Johann Gottlieb Hesse, a businessman and brewery owner and his wife Anna Karoline Reiter (1788–1865). He studied in his hometown at the Albertina under Carl Gustav Jacob Jacobi. Among his teachers were count Friedrich Wilhelm Bessel and Friedrich Julius Richelot. He earned his doctorate in 1840 at the University of Königsberg with the dissertation De octo punctis intersectionis trium superficium secundi ordinis. In 1841, Hesse completed his habilitation thesis. In the same year he married Sophie Marie Emilie Dulk, the daughter of pharmacists and chemistry professor Friedrich Philipp Dulk (1788–1852). The couple had a son and five daughters. Hesse taught for some time physics and chemistry at the Vocational School in Königsberg and lectured at the Albertina. In 1845 he was appointed associate professor in Königsberg. In 1855 he moved to Halle and in 1856 to Heidelberg until 1868, when he finally moved to Munich to the newly established Polytechnic School. In 1869 he joined the Bavarian Academy of Sciences. His doctoral students include Olaus Henrici, Gustav Kirchhoff, Jacob Lüroth, Adolph Mayer, Carl Neumann, Max Noether, Ernst Schröder, and Heinrich Martin Weber.

Works Vorlesungen über analytische Geometrie des Raumes. (Lectures on analytic geometry of space) Leipzig (3. A. 1876) (Internet Archive) Vorlesungen aus der analytischen Geometrie der geraden Linie, des Punktes und des Kreises. (Lectures from the analytical geometry of the straight line, the point and the circle) Leipzig (1881). Hrsg. A. Gundelfinger (Internet Archive) Die Determinanten elementar behandelt. (Determinants elementary treated) Leipzig (2. A. 1872) (Göttinger Digitalisierungszentrum) Die vier Species. (The four Species) Leipzig (1872) (Internet Archive) His collected works were published in 1897 by Bavarian Academy of Sciences and Humanities.

Hesse, Ludwig Otto (1972) [1897], Dyck, W.; Gundelfinger, S.; Lüroth, J.; et al. (eds.), Ludwig Otto Hesse's gesammelte Werke, New York: Chelsea Publishing Co., ISBN 978-0-8284-0261-3, MR 0392474 (Internet Archive)

References

External links O'Connor, John J.; Robertson, Edmund F., "Otto Hesse", MacTutor History of Mathematics Archive, University of St Andrews Otto Hesse at the Mathematics Genealogy Project Vorlesungen über analytische Geometrie des Raumes, insbesondere über Oberflächen zweiter Ordnung Complete Dictionary of Scientific Biography: "Hesse, Ludwig Otto"

Illustrations

Worked examples

Example 1 — a first encounter with Otto Hesse

Start with the simplest possible case. Write down what Otto Hesse 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 Otto Hesse 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 Otto Hesse 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 Otto Hesse

In research: Otto Hesse 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 Otto Hesse 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: Otto Hesse is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1811 births, 1874 deaths, 19th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Otto Hesse 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 Otto Hesse in 20 minutes

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

Frequently asked questions

What is Otto Hesse in simple terms?

Ludwig Otto Hesse (22 April 1811 – 4 August 1874) was a German mathematician. Hesse was born in Königsberg, Prussia, and died in Munich, Bavaria.

Why does Otto Hesse 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 Otto Hesse?

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 Otto Hesse.