FRANCOIS LAVALLOU
64 articles published in Tangente
History and CultureN°84Nov 15, 2022The tangent at X
The right to wear a sword, formerly reserved for sergeants, was not granted to students at the École polytechnique until after the three revolutionary days of July 1830.
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Math for everyoneN°208Oct 21, 2022Inverting the power
The notion of power defined with respect to a circle naturally leads to the notions of inversion and polars. These pedagogical tools, which have vanished from school curricula, are central to the birth of the concept of duality and of representations of non-Euclidean geometry.
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Math for everyoneN°208Oct 20, 2022A concept with a long history
The power of a point with respect to a circle appears implicitly as early as Book III of Euclid's Elements. This notion, elementary as it may be, would be redefined in the 19th century and become the basis for numerous applications in geometry.
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Math for everyoneN°83Aug 18, 2022The Mathematics of Tchoukaillon
Mancala is the generic name for traditional sowing games in Africa and Asia. One of the solitaire variants of these games gave rise to a mathematical recreation with unexpected properties and consequences.
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Math for everyoneN°206Jun 22, 2022Polar vectors and axial vectors
In physics, forces and velocities are usually represented by vectors, mathematical objects with both magnitude and direction. Yet their behavior under a change of frame reveals two types of vectors, depending on the orientation of space: polar and axial.
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Math for everyoneN°206Jun 21, 2022Mathematics points the way
We encounter broken symmetries every day, allowing us to distinguish up from down and right from left. Likewise, when objects in our mathematical spaces can be oriented, their orientation inevitably rests on an arbitrary definition.
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History and CultureN°206Jun 21, 2022A man of letters and numbers
At 78, too old for a Fields Medal, and with no prize specifically devoted to philosophy, the mathematician and philosopher Bertrand Russell was awarded the 1950 Nobel Prize in Literature, much to his surprise.
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History and CultureN°82May 18, 2022Cauchy, a forgotten pioneer
Because Augustin-Louis Cauchy did not take a direct interest in solving algebraic equations, he is an overlooked figure in the history of group theory. Yet his research on permutations provided valuable tools for those who worked on Galois theory.
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Math for everyoneN°205Apr 20, 2022Voronoi cells
How a London doctor used Voronoi diagrams to combat cholera.
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CuriosityN°202Oct 13, 2021The Chinese remainder theorem
The periodic nature of planetary revolutions naturally gives rise to the notion of congruence. The earliest surviving written problem on this theme is known as the Chinese remainder theorem. Its universality has led to many fundamental applications in the theory of numbers and polynomials.
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Math for everyoneN°78May 18, 2021Origami and folds for geometric constructions
Greek geometers regarded only straightedge-and-compass constructions as acceptable. Some problems that defeated their ingenuity—for reasons that would not be understood until the advent of algebra—can nevertheless be solved using origami.
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Math for everyoneN°198Feb 01, 2021Dazzling Penrose tilings
Sir Roger Penrose is renowned for his remarkable and foundational work in geometry and cosmology, and for the applications of that work to black holes. It is puzzling, however, that he is famous to the general public for the tiling that bears his name, with its many remarkable properties.
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