mathematics

Pierre Varignon

Pierre Varignon 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 Pierre Varignon rather than just read about it. In short: Pierre Varignon (French pronunciation: [pjɛʁ vaʁiɲɔ̃]; 1654 – 23 December 1722) was a French mathematician. He was educated at the Jesuit College and the University of Caen, where he received his M.A. in 1682.

Key takeaways

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

Reference excerpt

Pierre Varignon (French pronunciation: [pjɛʁ vaʁiɲɔ̃]; 1654 – 23 December 1722) was a French mathematician. He was educated at the Jesuit College and the University of Caen, where he received his M.A. in 1682. He took Holy Orders the following year. Varignon gained his first exposure to mathematics by reading Euclid and then René Descartes' La Géométrie. He became professor of mathematics at the Collège Mazarin in Paris in 1688 and was elected to the Académie Royale des Sciences in the same year. In 1704, he held the departmental chair at Collège Mazarin and also became professor of mathematics at the Collège Royal. He was elected to the Berlin Academy in 1713 and to the Royal Society in 1718. Many of his works were published in Paris in 1725, three years after his death. His lectures at Mazarin were published in Elements de mathematique in 1731. Varignon was a friend of Isaac Newton, Gottfried Wilhelm Leibniz, and the Bernoulli family. Varignon's principal contributions were to graphic statics and mechanics. Except for Guillaume de l'Hôpital, Varignon was the earliest and strongest French advocate of infinitesimal calculus, and exposed the errors in Michel Rolle's critique thereof. He recognized the importance of a test for the convergence of series, but analytical difficulties prevented his success. Nevertheless, he simplified the proofs of many propositions in mechanics, adapted Leibniz's calculus to the inertial mechanics of Newton's Principia, and treated mechanics in terms of the composition of forces in Projet d'une nouvelle mécanique in 1687. Among Varignon's other works was a 1699 publication concerning the application of differential calculus to fluid flow and to water clocks. In 1690, he created a mechanical explanation of gravitation. In 1702, he applied calculus to spring-driven clocks. In 1704, he invented the U-tube manometer, a device capable of measuring rarefaction in gases.

Works

Projet d'une nouvelle mechanique (in French). Paris: Edme Martin, veuve. 1687. Traité du mouvement et de la mesure des eaux coulantes et jaillissantes (in French). Bologna: Lelio Dalla Volpe. 1736.

See also Varignon's theorem Varignon's theorem (mechanics) List of Roman Catholic scientist-clerics

References

An original entry was based on the book A Short Account of the History of Mathematics (4th edition, 1908) by W. W. Rouse Ball. Pierre Varignon at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Pierre Varignon

Start with the simplest possible case. Write down what Pierre Varignon 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 Pierre Varignon 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 Pierre Varignon 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 Pierre Varignon

In research: Pierre Varignon 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 Pierre Varignon 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: Pierre Varignon is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1654 births, 1722 deaths, 17th-century French Roman Catholic priests, so understanding it makes those chapters shorter.
In everyday life: Look for Pierre Varignon 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 Pierre Varignon in 20 minutes

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

Frequently asked questions

What is Pierre Varignon in simple terms?

Why does Pierre Varignon 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 Pierre Varignon?

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 Pierre Varignon.