mathematics

Johannes Frischauf

Johannes Frischauf 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 Johannes Frischauf rather than just read about it. In short: Johannes Frischauf (17 September 1837 in Vienna – 7 January 1924 in Graz) was an Austrian mathematician, physicist, astronomer, geodesist and alpinist. Life and work Frischauf passed the matura at the Academic Gymnasium in Vienna and in 1857 studied mathematics, physics, astronomy at the University of Vienna, as well as geodesy, chemistry, mechanics at the Technischen Hochschule Vienna.

Key takeaways

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

Reference excerpt

Johannes Frischauf (17 September 1837 in Vienna – 7 January 1924 in Graz) was an Austrian mathematician, physicist, astronomer, geodesist and alpinist.

Life and work

Frischauf passed the matura at the Academic Gymnasium in Vienna and in 1857 studied mathematics, physics, astronomy at the University of Vienna, as well as geodesy, chemistry, mechanics at the Technischen Hochschule Vienna. He obtained the doctorate in 1864, and became Privatdozent for mathematics at the University of Vienna and assistant at the observatory of the university. In 1863 he was habilitated in mathematics. Starting in 1863, he was professor at the University of Graz for pure and applied mathematics. He worked together with Ludwig Boltzmann. Frischauf developed a new method of map design and wrote textbooks on arithmetics and geometry – for instance in 1872 and 1876 he wrote summaries of the then current knowledge about non-Euclidean geometry (which he called "absolute geometry"). In 1885 he was elected as a member of the Leopoldina.

Starting with 1868, Frischauf pioneered the touristic development of the Sannthaler and Steiner Alps by opening ways and huts. The streets over the Paulitschsattel and the connection Sulzbach-Leutsch were built because of his initiatives. Together with Franz von Juraschek and Mathias Spreiz he was the first to climb the Admonter Reichenstein. Frischauf defended the view at a time of violent national conflicts, that alpinism should not be subordinated under nationalism or religion or political views. He participated in the foundation of the Croatian Mountaineering Association. Frischauf's Funerary urn was placed on the Scheichenspitze in the Dachstein Mountains. His estate is located at the University of Graz.

Works (selection) Über die Bahn der Asia. In: Sitz. Berichte Kais. Akad. Wiss. Wien, Mat.-nat. Cl. Band 45, 1862, pp. 435–442. Bahnbestimmung des Planeten 67 Asia. In: Sitz. Berichte Kais. Akad. Wiss. Wien, Mat.-nat. Cl. Band 53, 1866, pp. 96–141. Einleitung in die analytische Geometrie. Leuschner & Lubensky, Graz 1871. Zum Rechnen mit unvollständigen Zahlen. In: Zeitschrift math. naturw. Unterr. Band 26, 1895, pp. 161–172. Beiträge zur Landesaufnahme und Kartographie des Erdsphäroids. B. G. Teubner, Leipzig 1919. Hochthor bei Johnsbach. In: Jahrbuch Steir. Gebirgsverein. 1873, p. 41. Reichenstein bei Admont. In: Jahrbuch Steir. Gebirgsverein. 1873, p. 54. Frischauf, J. (1876). Elemente der absoluten Geometrie. Leipzig.{{cite book}}: CS1 maint: location missing publisher (link) Die Sannthaler Alpen. Brockhausen und Bräuser, Wien 1877. Ein Ausflug auf den Monte Baldo.Wien 1883, Wiener Touristen-Führer.11. "Auf Cherso" [On Cherso]. Mitteilungen des Deutschen und Österreichischen Alpenvereins (in German). 16 (12): 156–159. 1890. Das Uskoken-Gebirge. In: Zeitschrift DÖAV (1890), pp. 474–484. [1] Krakau bei Murau. Steirische Sommerfrischen, Band 1, Leuschner & Lubensky, Graz 1896, Hrg. vom Steirischen Gebirgsvereine.

References

External links

Literature by and about Johannes Frischauf in the German National Library catalogue Martin Fürnkranz: Bibliographie Publications of J. Frischauf in Astrophysics Data System

Illustrations

Worked examples

Example 1 — a first encounter with Johannes Frischauf

Start with the simplest possible case. Write down what Johannes Frischauf 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 Johannes Frischauf 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 Johannes Frischauf 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 Johannes Frischauf

In research: Johannes Frischauf 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 Johannes Frischauf 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: Johannes Frischauf is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1837 births, 1924 deaths, Astronomers from Austria-Hungary, so understanding it makes those chapters shorter.
In everyday life: Look for Johannes Frischauf 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Johannes Frischauf” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Johannes Frischauf in 20 minutes

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

Frequently asked questions

What is Johannes Frischauf in simple terms?

Johannes Frischauf (17 September 1837 in Vienna – 7 January 1924 in Graz) was an Austrian mathematician, physicist, astronomer, geodesist and alpinist. Life and work Frischauf passed the matura at the Academic Gymnasium in Vienna and in 1857 studied mathematics, physics, astronomy at the University…

Why does Johannes Frischauf 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 Johannes Frischauf?

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 Johannes Frischauf.