Jean-Jacques Dupas
107 articles published in Tangente
Math for everyoneN°81Feb 14, 2022Points on the sphere
How can points be distributed "as well as possible" on a sphere? The idea is to place them "as far apart as possible." With two, three or four points, one might think that the vertices of a regular polyhedron inscribed in the sphere would do the trick. And yet…
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Math for everyoneN°81Feb 14, 2022Distances on a sphere
Pioneered by Menelaus of Alexandria in the first century CE, spherical geometry can be a little disconcerting. It is two-dimensional: for example, longitude and latitude are enough to locate any point on the sphere's surface.
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History and CultureN°203Dec 21, 2021Exceptional documentaries on Arte.tv
Arte.tv recently released a series of documentaries about mathematics. Not to be missed.
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History and CultureN°203Dec 20, 2021What makes us human: geometric intuition
Humans have possessed geometric intuition since the dawn of time—but do other primates share it? To find out, Mathias Sablé-Meyer proposes an experiment: identify the odd one out in a series of six quadrilaterals.
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History and CultureN°203Dec 20, 2021Doing maths is good for the brain... it’s proven!
A brain trained in maths during youth is better equipped to reason correctly and guard against misinformation and stereotypes.
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Math for everyoneN°203Dec 16, 2021φ is irrational
Let's see how to prove that φ is irrational.
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Math for everyoneN°80Nov 18, 2021The Cayley diagram
How can we grasp the structure of a finite group at a glance? The Cayley diagram provides the answer!
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Math for everyoneN°79Aug 26, 2021Polyhedra: from Euler's formula to Poincaré's characterization
What is a polyhedron? Throughout history, several characterizations have been proposed, only to be repeatedly undermined by the appearance of "monsters" serving as counterexamples. We look back at this epic story, which reaches its conclusion in Poincaré's work.
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Math for everyoneN°200Jun 14, 2021The magic ring of tetrahedra
Details on how to build the ring of tetrahedra that you can cut out from the pull-out section of Tangente 200. An explanation of how the numbers on its forty faces were chosen, using a rule that generalizes the concept of a magic square.
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Math for everyoneN°78May 18, 2021The parabola in all its finery
A common exercise in the days of descriptive geometry was to construct a point on a curve and its tangent. Following the ellipse, here is a short survival guide offering a handful of constructions for solving the same problem for the parabola.
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Math for everyoneN°78May 18, 2021The ellipse and its many features
Although descriptive geometry provides laborious methods for constructing an ellipse with straightedge and compass (see the article "Albrecht Dürer and technical drawing"), other, more conventional methods also exist. A point on the curve, the center, foci, axes and tangents: let's take a quick tour of the available techniques!
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Math for everyoneN°78May 18, 2021When the compass won't follow the ruler
A famous result in geometry, still surprising when first encountered, states that any point in the plane constructible with straightedge and compass can be constructed with a compass alone. But how is this actually done?
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