mathematics

Johann Jakob Rebstein

Johann Jakob Rebstein 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 Johann Jakob Rebstein rather than just read about it. In short: Johann Jakob Rebstein (1840–1907) was a Swiss mathematician and surveyor. Early life Rebstein was born on 4 May 1840 in Töss, Switzerland, to his father, a baker and his mother, a doctor.

Key takeaways

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

Reference excerpt

Johann Jakob Rebstein (1840–1907) was a Swiss mathematician and surveyor.

Early life Rebstein was born on 4 May 1840 in Töss, Switzerland, to his father, a baker and his mother, a doctor.

Education and career Rebstein attended post-secondary school in Winterthur, and after graduating in 1860, went on to study for a year at Collège de France. He was professor of mathematics and physics in Zürich from 1877 to 1898. He was awarded his doctorate in 1895 from the Humboldt University of Berlin for his work Bestimmung aller reellen Minimalflächen, die eine Schaar ebener Curven enthalten, denen auf der Gauss'schen Kugel die Meridiane entsprechen. He is best known for his work in surveying, and for introducing the traverse method in Switzerland. Throughout his career, Rebstein was appointed as surveying expert for a number of cantons, including Thurgau (1863–1881), St. Gallen (1881–1894), Zürich (1886–1892), and Luzern (1894–1907). In 1868 he was elected to the Swiss Concordat of Geometers, and served as its president from 1887 until his death in 1907. In 1905 he was awarded an honorary doctorate from the University of Zürich, for "outstanding contributions to actuarial sciences". Rebstein was a member of the organizing committee for the first meeting of the International Congress of Mathematicians.

Death Rebstein suffered from kidney disease for the last several years of his life, and died in 1907 in Zürich.

Publications Rebstein's publications included:

Lehrbuch über praktische Geometrie mit besonderer Berücksichtigung der Theodolitmessung (1868) Die Kartographie der Schweiz, dargestellt in ihrer historischen Entwicklung (1883) Mitteilungen über die Stadtvermessung von Zürich1 (1892)

See also List of German-language philosophers

Notes

References

Illustrations

Worked examples

Example 1 — a first encounter with Johann Jakob Rebstein

Start with the simplest possible case. Write down what Johann Jakob Rebstein 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 Johann Jakob Rebstein 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 Johann Jakob Rebstein 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 Johann Jakob Rebstein

In research: Johann Jakob Rebstein 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 Johann Jakob Rebstein 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: Johann Jakob Rebstein is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1840 births, 1907 deaths, Swiss mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Johann Jakob Rebstein 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 Johann Jakob Rebstein in 20 minutes

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

Frequently asked questions

What is Johann Jakob Rebstein in simple terms?

Johann Jakob Rebstein (1840–1907) was a Swiss mathematician and surveyor. Early life Rebstein was born on 4 May 1840 in Töss, Switzerland, to his father, a baker and his mother, a doctor.

Why does Johann Jakob Rebstein 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 Johann Jakob Rebstein?

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 Johann Jakob Rebstein.