biology

Gabriel Cramer

Gabriel Cramer is a biology 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 Gabriel Cramer rather than just read about it. In short: Gabriel Cramer (French: [kʁamɛʁ]; 31 July 1704 – 4 January 1752) was a Genevan mathematician. Biography Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet.

Key takeaways

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

Reference excerpt

Gabriel Cramer (French: [kʁamɛʁ]; 31 July 1704 – 4 January 1752) was a Genevan mathematician.

Biography Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet. The progenitor of the Cramer family in Geneva was Jean-Ulrich Cramer, Gabriel's great-grandfather, who immigrated from Strasbourg in 1634. Cramer's mother, a member of the Mallet family, was of Huguenot origin. Cramer showed promise in mathematics from an early age. In 1722, aged 18, he received his doctorate from the Academy of Geneva, and at 20 he was made co-chair (along with Jean-Louis Calandrini) of mathematics at the Academy. He became the sole professor of mathematics in 1734 and was appointed professor of philosophy at the Academy in 1750. Cramer was also involved in the politics of the Republic of Geneva, entering first the Council of Two Hundred in 1734 then the Council of Sixty in 1750. He was a member of the science academies of Bologna, Lyon, and Montpellier, as well as a foreign member of the Royal Society of London and the Royal Academy of Sciences of Berlin. Cramer died on 4 January 1752 at Bagnols-sur-Cèze while traveling in southern France to restore his health.

Contributions to mathematics In 1728, Cramer proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. He did extensive travel throughout Europe in the late 1730s, which greatly influenced his works in mathematics. Cramer published his best-known work in his forties. This included his treatise on algebraic curves (1750). It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position (see Cramer's theorem (algebraic curves)). This led to the misconception that is Cramer's paradox, concerning the number of intersections of two curves compared to the number of points that determine a curve. Cramer edited the works of the two elder Bernoullis, and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746). In 1750 he published Cramer's rule, giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of determinants implied by the system. This rule is still standard.

Selected works

Quelle est la cause de la figure elliptique des planètes et de la mobilité de leur aphélies?, Geneva, 1730 Introduction à l'analyse des lignes courbes algébriques at Google Books. Geneva: Frères Cramer & Cl. Philibert, 1750

See also Cramer–Castillon problem Devil's curve

Notes

References

"Gabriel Cramer", in Rousseau et les savants genevois, p. 29 (in French) W. W. Rouse Ball, A Short Account of the History of Mathematics, (4th Edition, 1908) Isaac Benguigui, Gabriel Cramer : illustre mathématicien, 1704–1752, Genève, Cramer & Cie, 1998 (in French) O'Connor, John J.; Robertson, Edmund F., "Gabriel Cramer", MacTutor History of Mathematics Archive, University of St Andrews (in German) Johann Christoph Strodtmann, « Geschichte des Herrn Gabriel Cramer », in Das neue gelehrte Europa […], 4th part, Meissner, 1754 Also digitized by e-rara.ch

External links Media related to Gabriel Cramer at Wikimedia Commons O'Connor, John J.; Robertson, Edmund F., "Gabriel Cramer", MacTutor History of Mathematics Archive, University of St Andrews

Illustrations

Worked examples

Example 1 — a first encounter with Gabriel Cramer

Start with the simplest possible case. Write down what Gabriel Cramer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In biology, 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 Gabriel Cramer 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 Gabriel Cramer 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 Gabriel Cramer

In research: Gabriel Cramer appears in biology 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 Gabriel Cramer 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: Gabriel Cramer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1704 births, 1752 deaths, 18th-century mathematicians from the Republic of Geneva, so understanding it makes those chapters shorter.
In everyday life: Look for Gabriel Cramer 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 Gabriel Cramer in 20 minutes

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

Frequently asked questions

What is Gabriel Cramer in simple terms?

Gabriel Cramer (French: [kʁamɛʁ]; 31 July 1704 – 4 January 1752) was a Genevan mathematician. Biography Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet.

Why does Gabriel Cramer matter?

Because it connects several biology 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 Gabriel Cramer?

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 Gabriel Cramer.