Fabien Aoustin
140 articles published in Tangente
History and CultureN°197Dec 04, 2020Vaughan Jones, the knot magician
The mathematician Vaughan Jones, who died on September 6, 2020, profoundly influenced several areas of mathematics, including topology and functional analysis, as well as physics, particularly quantum theory. His name remains associated with powerful invariants in knot theory.
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Math for everyoneN°76Nov 05, 2020The challenges of computational geometry
It is easy to overlook, but many geometric problems can be solved by iterative methods or, more broadly, algorithms. These questions are the subject of computational geometry! This is a vibrant, highly active field in which many seemingly elementary questions still await solutions.
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Math for everyoneN°76Nov 05, 2020The remarkably rich Prouhet–Thue–Morse sequence
The Morse word, or Prouhet–Thue–Morse sequence, is an easy-to-construct mathematical object with plenty of surprises in store. Join us in exploring a combinatorial sequence that would certainly deserve to be every bit as famous as Fibonacci's!
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Math for everyoneN°76Nov 05, 2020Fractals: the aesthetics of iteration
Repeating a geometric transformation at different scales produces fascinating figures whose aesthetic appeal is far from their only attraction. Let's (re)discover the most iconic fractals!
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Math for everyoneN°76Nov 05, 2020Heron's algorithm
Heron of Alexandria is known for a famous formula that gives the area of a triangle without requiring its height. He also devised highly sophisticated mechanisms and an extraordinarily efficient recursive method for approximating the square root of a positive number.
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Math for everyoneN°76Nov 04, 2020Blaise Pascal takes on induction
Although specialists still debate the origins of proof by induction, they often agree that Blaise Pascal's Traité du triangle arithmétique (Treatise on the Arithmetical Triangle) was the first work to set it out explicitly. A guided tour of a landmark in the history of proof.
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Math for everyoneN°76Nov 04, 2020The many faces of mathematical induction
Mathematical induction is both a classic and an indispensable tool, and its principle is easily stated.
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Math for everyoneN°76Nov 04, 2020Happy is one who, like a number...
Starting with an integer, apply a simple rule to obtain a new number. Repeat the process with the result, and so on... Depending on the pattern followed by this sequence—cyclic, constant from some point onward, and so on—the starting number is described as happy, perfect... But sometimes the pattern is still unknown.
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Math for everyoneN°76Nov 04, 2020Iterative processes at the heart of mathematical activity
Repeating computational or logical procedures is one of the defining features of mathematical activity. The advent of computing gave fresh impetus to this technique, which has been used since antiquity.
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Math for everyoneN°76Nov 04, 2020A sequence of ideas
Algorithms for constructing integer sequences from a given number are diverse. Many were devised in the 20th century by well-known mathematicians (Ulam, Kaprekar, Sloane...) and sometimes produce surprising results, some of which remain conjectures.
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Math for everyoneN°76Nov 03, 2020Editorial
Iterate, iterate... As the Shadoks proclaimed in their day, only by trying again and again do we eventually succeed. In other words, the more often it fails, the greater the chance that it will work. This may raise a smile, yet iterative processes prove to be as simple as they are effective.
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History and CultureN°196Oct 14, 2020Marvelous logarithms
Logarithms emerged at the very beginning of the 17th century, thanks to the eccentric Scottish mathematician and theologian John Napier. By dramatically speeding up calculations, they paved the way for extraordinary scientific advances, particularly in astronomy.
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