Daniel Lignon
91 articles published in Tangente
History and CultureN°80Nov 17, 2021The Monster
The Monster is a group with more elements than there are atoms on Earth. Let’s meet it...
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Math for everyoneN°80Nov 17, 2021The classification of finite simple groups
Are finite groups simple? Not so fast: although the classification of finite simple groups began more than a century ago, a complete proof is still being written! Work on this proof began in the late 1980s and should be completed in 2025. But the task is daunting…
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History and CultureN°80Nov 16, 2021Galois's brilliant contribution
Following his work on solving fourth-degree equations, Lagrange turned to the fifth-degree case. It was not until Abel that these equations were shown not to be solvable by radicals. Galois would provide a necessary and sufficient condition for an equation of any degree to be so solvable. In doing so, he founded group theory.
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Math for everyoneN°79Aug 26, 2021The Poincaré conjecture
By the end of the 19th century, following the work of Poincaré and many other mathematicians, including Bernhard Riemann (1826–1866) and Enrico Betti (1823–1892), the topology of surfaces in our ordinary space was well understood.
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Math for everyoneN°201Aug 23, 2021Discovering barycentric curves
Barycentric curves do exist!
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Math for everyoneN°201Aug 23, 2021Convex sets and line segments
It is fairly easy to tell whether or not a subset of the plane is convex.
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Math for everyoneN°200Jun 14, 2021Friendship among numbers
In mathematics, being amicable is not the same as having friends...
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Math for everyoneN°200Jun 14, 2021200, a number like no other!
It can be written as a numeral, 200, or in words, two hundred. Even so, at first glance, the number does not seem particularly interesting. Admittedly, it is not perfect, unlike the eponymous issue of Tangente, but, like Achilles, it is powerful... and therefore fascinating. Here is a brief survey of its arithmetic properties.
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Math for everyoneN°78May 18, 2021From geometry to algebra: constructing numbers
Starting with two distinct points in the plane and performing only finitely many ruler-and-compass constructions, can we obtain any point in the plane? If not, which points can we obtain in this way?
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Math for everyoneN°76Nov 05, 2020News from the Collatz conjecture
Syracuse... For some, the name evokes a classic song performed by the late Henri Salvador (1917–2008); for mathematics enthusiasts, however, it refers to the Collatz conjecture, whose statement is very simple but which remains unproved to this day. A recent result lends further support to the conjecture.
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Math for everyoneN°76Nov 05, 2020Iterative methods for solving equations
Sequences, including recursively defined sequences, arise in many areas of mathematics. This is true of numerical methods for solving equations, which are in fact iterative methods—hence the presence of sequences.
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Math for everyoneN°196Oct 13, 2020Numbers in computers
Many kinds of software, from scientific computing to video games, need numbers to perform their tasks. These numbers may be integers or real numbers. Despite the enormous power of computers, approximations are inevitable; as they accumulate, they can be harmful and sometimes even catastrophic.
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