FRANCOIS LAVALLOU
64 articles published in Tangente
Math for everyoneN°74Apr 16, 2020Triangle cubics
Beyond the centroid, the orthocenter and the centers of the two circles familiar from school geometry, thousands of points can be associated with the three vertices of a triangle. These myriad points lie on hundreds of cubics with remarkable properties.
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Math for everyoneN°74Apr 16, 2020Elliptic curves
An elliptic curve is an algebraic curve of genus 1, defined by a polynomial equation in Cartesian coordinates with real coefficients.
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Math for everyoneN°193Mar 20, 2020The foundations of signal processing
Harmonic analysis, born of functional analysis, studies how functions can be represented as superpositions of basis functions. In signal theory, these basis functions, often polynomials, lie at the heart of sound and image processing in our digital world.
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Math for everyoneSep 18, 201910-adic numbers
Some mathematicians, tired of manipulating objects according to established procedures, begin to play with the rules themselves. What seems to be nothing more than pure intellectual pleasure often finds unexpected applications. Such is the case with 10-adic numbers...
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Math for everyoneN°71Jul 10, 2019Erwin Schrödinger's cat
In its century of existence, quantum physics has proved extraordinarily effective and has never been found wanting. Yet many difficulties remain when it comes to interpreting it. One emblematic example of its strangeness is a famous feline thought experiment.
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Math for everyoneN°188May 13, 2019A cross-ratio from another world
During the 19th century, the search for quantities invariant under a particular group of transformations became the main focus of the various branches of geometry. The cross-ratio, a fundamental invariant of projective geometry, also appears in non-Euclidean geometries and their models.
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KnowledgeN°70Apr 11, 2019Operations in billiards
One of the arts and pleasures of mathematics is finding different ways to represent problems. Some problems in dynamics can profitably be replaced by the study of trajectories on a billiard table, revealing hidden structures—and hence hidden logical beauty.
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Famous figuresN°70Apr 11, 2019The epic of non-Euclidean geometries
In antiquity, Euclid essentially postulated that, given a point A and a line D, there is exactly one line through A parallel to D. Two millennia later, three mathematicians share the glory of having proved that a geometry could exist without this "fifth postulate".
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Math for everyoneN°187Mar 25, 2019Envelopes by folding
Every regular curve is the envelope of all its tangent lines. For conics, these tangent lines are particularly easy to construct geometrically, making it possible to produce them by folding.
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History and CultureN°69Jan 16, 2019The geometry of measurement
The concept of measurement evolved over a long period, from concrete practice to abstraction, in a process initiated by Archimedes. This required mastering the concept of infinity.
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Math for everyoneN°185Nov 21, 2018Counting without counting
Everyday language still bears traces of certain ancient counting practices.
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Math for everyoneN°68Oct 12, 2018Go: the triumph of deep thought
Go is the quintessential game of pure strategy. Chance plays no part in it. Until very recently, it remained the preserve of human intelligence, but computers eventually established their strategic superiority here too, twenty years after their triumph at chess.
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