mathematics

Nicolaus II Bernoulli

Nicolaus II Bernoulli 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 Nicolaus II Bernoulli rather than just read about it. In short: Nicolaus II Bernoulli (also Niklaus or Nikolaus; 6 February 1695 in Basel – 9 August 1726 in Saint Petersburg) was a Swiss mathematician as were his father Johann Bernoulli and one of his brothers, Daniel Bernoulli. He was one of the many prominent mathematicians in the Bernoulli family.

Key takeaways

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

Reference excerpt

Nicolaus II Bernoulli (also Niklaus or Nikolaus; 6 February 1695 in Basel – 9 August 1726 in Saint Petersburg) was a Swiss mathematician as were his father Johann Bernoulli and one of his brothers, Daniel Bernoulli. He was one of the many prominent mathematicians in the Bernoulli family.

Work Nicolaus worked mostly on curves, differential equations, and probability. He was a friend and contemporary of Leonhard Euler, who studied under Nicolaus' father. He also contributed to fluid dynamics. He was older brother of Daniel Bernoulli, to whom he also taught mathematics. Even in his youth he had learned several languages. From the age of 13, he studied mathematics and law at the University of Basel. In 1711 he received his Master's of Philosophy; in 1715 he received a Doctorate in Law. In 1716–1717 he was a private tutor in Venice. From 1719 he had the Chair in Mathematics at the University of Padua, as the successor of Giovanni Poleni. He served as an assistant to his father, among other areas, in the correspondence over the priority dispute between Isaac Newton and Leibniz, and also in the priority dispute between his father and the English mathematician Brook Taylor. In 1720 he posed the problem of reciprocal orthogonal trajectories, which was intended as a challenge for the English Newtonians. From 1723 he was a law professor at the Berner Oberen Schule. In 1725 he together with his brother Daniel, with whom he was touring Italy and France at this time, was invited by Peter the Great to the newly founded St. Petersburg Academy. Eight months after his appointment he came down with a fever and died. His professorship was succeeded in 1727 by Leonhard Euler, whom the Bernoulli brothers had recommended. His early death cut short a promising career.

See also Bernoulli distribution Bernoulli process Bernoulli trial St. Petersburg paradox

External links O'Connor, John J.; Robertson, Edmund F., "Nicolaus II Bernoulli", MacTutor History of Mathematics Archive, University of St Andrews Weisstein, Eric Wolfgang (ed.). "Bernoulli, Nicholas (1695-1726)". ScienceWorld.

Further reading Fleckenstein, J.O. (1970–1980). "Bernoulli, Nickolaus II". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 57–58. ISBN 978-0-684-10114-9.

Illustrations

Worked examples

Example 1 — a first encounter with Nicolaus II Bernoulli

Start with the simplest possible case. Write down what Nicolaus II Bernoulli 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 Nicolaus II Bernoulli 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 Nicolaus II Bernoulli 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 Nicolaus II Bernoulli

In research: Nicolaus II Bernoulli 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 Nicolaus II Bernoulli 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: Nicolaus II Bernoulli is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1695 births, 1726 deaths, 18th-century Swiss mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Nicolaus II Bernoulli 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 Nicolaus II Bernoulli in 20 minutes

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

Frequently asked questions

What is Nicolaus II Bernoulli in simple terms?

Why does Nicolaus II Bernoulli 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 Nicolaus II Bernoulli?

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 Nicolaus II Bernoulli.