mathematics

Gabriel Mouton

Gabriel Mouton 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 Gabriel Mouton rather than just read about it. In short: Gabriel Mouton (1618 – 28 September 1694) was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy.

Key takeaways

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

Reference excerpt

Gabriel Mouton (1618 – 28 September 1694) was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy. His 1670 book, the Observationes diametrorum solis et lunae apparentium, proposed a natural standard of length based on the circumference of the Earth, divided decimally. It was influential in the adoption of the metric system in 1799.

The milliare

Based on the measurements of the size of the Earth conducted by Riccioli of Bologna (at 321,815 Bologna feet to the degree), Mouton proposed a decimal system of measurement based on the circumference of the Earth, explaining the advantages of a system based on nature. His suggestion was a unit, the milliare, that was defined as a minute of arc along a meridian arc, and a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima. The virga, 1/1000 of a minute of arc, corresponding to 64.4 Bologna inches, or ~2.04 m, was reasonably close to the then current unit of length, the Parisian toise (~1.95 m) – a feature which was meant to make acceptance of the new unit easier. As a practical implementation, Mouton suggested that the actual standard be based on pendulum movement, so that a pendulum located in Lyon of length one virgula (1/10 virga) would change direction 3959.2 times in half an hour. The resulting pendulum would have a length of ~20.54 cm. His ideas attracted interest at the time, and were supported by Jean Picard as well as Huygens in 1673, and also studied at Royal Society in London. In 1673, Leibniz independently made proposals similar to those of Mouton. It would be over a century later, however, that the French Academy of Sciences weights and measures committee suggested the decimal metric system that defined the Metre as, at least initially, a division of the circumference of the Earth. The first official adoption of this system occurred in France in 1791. By today's measures, his milliare corresponds directly to a nautical mile, and his virga would by definition have been 1.852 m.

See also Introduction to the metric system List of Roman Catholic scientist-clerics

Notes

References G. Bigourdan: Le systeme metrique des poids et mesures, 1901, chapter Les precurseurs de la reforme des poids et mesures Ferdinand Hoefer: Historie de l'astronomie, Paris 1873

External links Metrication - Genesis O'Connor, John J.; Robertson, Edmund F., "Gabriel Mouton", MacTutor History of Mathematics Archive, University of St Andrews Un historique du METRE Archived 28 February 2011 at the Wayback Machine

Worked examples

Example 1 — a first encounter with Gabriel Mouton

Start with the simplest possible case. Write down what Gabriel Mouton 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 Gabriel Mouton 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 Mouton 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 Mouton

In research: Gabriel Mouton 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 Gabriel Mouton 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 Mouton is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1618 births, 1694 deaths, 17th-century French Roman Catholic priests, so understanding it makes those chapters shorter.
In everyday life: Look for Gabriel Mouton 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 Mouton in 20 minutes

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

Frequently asked questions

What is Gabriel Mouton in simple terms?

Gabriel Mouton (1618 – 28 September 1694) was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy.

Why does Gabriel Mouton 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 Gabriel Mouton?

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 Mouton.