Amazing Math
Surprising or counterintuitive mathematical results and proofs
Welcome to 2020! | Tangente
As usual, the new year inspired the Tangente team and their friends, who all vied with one another to tease out the number 2020's astonishing properties.
When works speak for themselves | Tangente
Advertising regularly makes use of it, as do graphic designers and artists. Self-reference has become a genre in its own right, appealing not only to our eyes but to all our senses! Let's take a wild tour of this seemingly limitless creativity.
Disputes and paradoxes | Tangente
Even the greatest mathematicians have fallen into the traps laid by logic and its paradoxes.
The paradoxes that shook mathematics
What a devilish theory Georg Cantor created with set theory! So thought some mathematicians at the turn of the 20th century, when a series of paradoxes seemed to threaten the foundations of mathematics. This prompted a reassessment of the role of logic.
Discontinuities of all kinds
They have been called "pathological"; Henri Poincaré spoke of "monsters," accusing them of being "strange functions that strive to resemble as little as possible the respectable functions that serve some purpose." Yet some discontinuous functions have left their mark on history.
Images: unexpected applications | Tangente
When we think of the mathematics behind image processing, compression, transmission, denoising and the restoration of digital files naturally come to mind. Its other applications are less familiar—for example, its use in art to help restore frescoes.
Blockchain in all its mathematical forms | Tangente
Blockchain technology is among the technologies to watch in the years ahead, as it could revolutionize several sectors of the economy. It draws on recent mathematical developments through increasingly sophisticated processes.
Stories of successful maths–industry collaborations | Tangente
On November 26, 2019, AMIES invited a number of speakers to describe successful collaborations between companies and mathematical research laboratories. It was an opportunity to discover sometimes unexpected partnerships, suggesting that mathematics will play an increasingly prominent role in business operations.
Heilbronn triangles
How should points be placed in a region of the plane to maximize the smallest area determined by any three of them? Despite the elementary nature of this geometry problem, no general solution is known even today!
On persistence
Apply the same algorithm to the digits of a number, then repeat the process with the digits of the result, and you encounter the notion of persistence… and the questions it raises.
Kissing numbers: kisses in geometry | Tangente
Kiss anyone you like...
Optimal packing of squares in a larger square | Tangente
You'll never arrange your boxes the same way again!
The moving sofa problem
Moving house always brings a host of problems... including mathematical puzzles! One of them was formalized by Leo Moser in 1966.
Kurt Hensel, the father of p-adic numbers
Kurt Hensel is best known for his research on p-adic numbers.
Number theorist Christian Mauduit has died
The number theorist was an expert on representing integers in different bases.
A dive into a strange world of numbers
At the beginning of the 20th century, the German mathematician Kurt Hensel "invented" new numbers, written with infinitely many digits, as in the decimal system, but based on a very different notion of proximity. This curious theory proved very fruitful in arithmetic!
10-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...
Shuffling an infinite deck of cards
Shuffling a fifty-two-card deck is easy enough. But suppose the deck contained infinitely many cards: could it still be "shuffled"? The answer is entirely up to you! Welcome to the world of paradoxes that play with infinity…
Cosmology and polyhedra: Plato to Kepler | Tangente
Regular polyhedra appear in many theories. These five solids fascinate us with their remarkable symmetries.
Oumupo: The workshop of potential music | Tangente
In 1960, François Le Lionnais and Raymond Queneau founded a collective dedicated to renewing literary forms: Oulipo (the Workshop of Potential Literature). From the outset, Le Lionnais considered extending this approach to other forms of expression.