BERTRAND HAUCHECORNE
179 articles published in Tangente
Math for everyoneN°216Feb 20, 2024Equivalent functions: a tool for calculating limits
Why go to the trouble of finding equivalents for seemingly well-behaved functions? To gain detailed insight into local or asymptotic behavior—and for applications, too! Without these techniques, even spreadsheets would be unable to perform seemingly innocuous calculations.
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Math for everyoneN°216Feb 20, 2024Some troubling counterexamples
Think you know everything about asymptotic expansions? Here are a few perplexing counterexamples...
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History and CultureN°89Feb 20, 2024The language of fractions
The word fraction seems to have appeared in its modern sense in 1549, in an arithmetic book published that year by the mathematician and Pléiade poet Jacques Peletier du Mans (1517–1582).
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Math for everyoneN°89Feb 19, 2024Endless sums
Adding several fractions always produces another fraction. But when the sum continues indefinitely, things are very different. If chosen carefully, such sums can approximate numbers like π and yield a wealth of fascinating, unexpected results.
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History and CultureN°88Nov 21, 2023Laplace is in the house
The scientist's legacy lives on today in the various places and institutions… that bear his name!
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Math for everyoneN°88Nov 21, 2023The ebb and flow of the sea: a dynamic theory
Laplace took an interest in "the ebb and flow of the sea," as he put it. After examining the approaches taken by his predecessors, he grasped the impact of the Earth's rotation and studied the tides, paving the way for their times to be calculated accurately.
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Math for everyoneN°88Nov 21, 2023The philosopher of chance
The chief architect of determinism, Laplace marked a crucial milestone in the transformation of probability theory into a fully fledged branch of mathematics. Is that a paradox, or a coherent intellectual approach? Let's return to his writings to find out!
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History and CultureN°88Nov 20, 2023Census-taking and the normal distribution
To calculate France's population, Laplace proposes a sampling method based on births and introduces the normal distribution to estimate the error. It would take until the 21st century for Insee to draw inspiration from his method.
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History and CultureN°88Nov 20, 2023The beginnings of linear algebra
Linear algebra took off in the mid-19th century, notably through the work of Arthur Cayley (1821–1895) and Hermann Günther Grassmann (1809–1877), and was formalized fifty years later with the emergence of algebraic structures.
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Reading noteN°88Nov 16, 2023Editorial
"Laplace's name has resounded in every part of the world where science is held in honor." With these words, Joseph Fourier began his funeral oration for the great scientist in 1827. Nearly two centuries later, this remains true. His Wikipedia page is available in more than a hundred languages!
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History and CultureN°214Oct 17, 2023From rhomb to rhombus
For many people, the rhombus—originally called a "rhomb" (see In Brief, "The origin of the rhombus"; the associated adjective is still "rhombic")—is characterized by its acute angles pointing upward and downward. Yet, as Euclid already observed, this quadrilateral is defined by the equal lengths of its sides. Its ability to form tilings accounts for its use in architecture and decoration.
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Math for everyoneN°214Oct 13, 2023Square matrices and transformations of the plane
The notion of a square root can be extended to very general sets. One may then obtain more than two square roots—even infinitely many! Matrices provide one example. Orientation-preserving similarities, viewed through the lens of complex numbers, lead us back to less startling results.
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