#mathematics #mathsmanuelacasasoli #maths
Not only pure mathematics
Symmetric entanglements of tangled Platonic polyhedra via assemblies of multistrand helices wound around edges of the conventional polyhedra.
Symmetric tangled Platonic polyhedra

Symmetric tangled Platonic polyhedra

Tangled tetrahedra, octahedra, cubes, icosahedra, and dodecahedra are generalizations of classical—untangled—Platonic polyhedra. Like the Platonic polyhedra, all vertices, edges, and faces are symmetrically equivalent. However, the edges of...

#mathematics #mathsmanuelacasasoli #maths
Difficult questions about prime numbers.
Expander graphs and the Chowla conjecture, a question about the relationships between integers.

Mathematicians Outwit Hidden Number Conspiracy
1-https://www.quantamagazine.org/mathematicians-outwit-hidden-number-conspiracy-20220103/
2-https://arxiv.org/abs/2103.06853

Mathematicians Outwit Hidden Number Conspiracy | Quanta Magazine

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

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Truncated Temari
Five creative truncated Platonic solids projected onto the sphere.

Imagination encircles the world.
Albert Einstein

Carolyn Yackel
1-http://gallery.bridgesmathart.org/exhibitions/2012-bridges-conference/cyackel
2-http://faculty.mercer.edu/yackel_ca/
3-http://faculty.mercer.edu/yackel_ca/images/temariballs.html

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Origami helps in the study of mathematics and science in many ways. … Using origami anyone can become a scientific experimenter with no fuss.

Martin David Kruskal

The Complete Book of Origami Polyhedra
Tomoko Fuse: https://en.wikipedia.org/wiki/Tomoko_Fuse

Témoignage

J'aurais beaucoup de choses à dire sur l' #école. Je vais me concentrer ici sur un point particulier : l' #apprentissage des maths.

Toute ma #scolarité durant, j'ai été une brèle en #math. J'ai des souvenirs précis. Vous voyez les "calculs écrits", qu'on apprend en CM1 ou CM2 ? Je ne sais toujours pas résoudre une division de cette manière, mais je fais encore des cauchemars de leur apprentissage. Les premières #équations en 6ème... la torture. J'ai eu besoin de cours de rattrapage tellement je n'y pigeais rien. J'étais le seul dans ce cas dans ma classe ! Et même avec ces derniers, et bien, au final, je n'y pigeais toujours rien.

Bref, vous voyez le genre du gusse. J'arrivais à passer à trav' dans les autres matières sans trop d'effort. Mais les maths... FFS.

Toute ma scolarité durant, donc... sauf UNE année. En seconde, on a eu un prof de math formidable. Concret. Pratique. Physique dans ses explications, gestuel, vivant, et proposant pleins de moyens mnémotechniques pour se rappeler comment appréhender tel ou tel élément. Révélation totale. Immédiatement, je ne tapais plus que des 18, des 20 (en Belgique on a des contrôles d'évaluation continue). Je me suis retrouvé à être celui à qui les autres demandaient de leur expliquer certains points. Je faisais plus que comprendre les #maths : je les ressentais en moi. Et la cerise sur le gâteau, c'est que j'adorais ça. J'étais tellement stimulé ! Bon, ça a duré un an. Puis vint la première. On nous assigna alors un autre prof, un type barbant, académique comme la plupart des autres. Retour à la case départ. Moyenne de 5 en #math. Ça a eu beaucoup d'impact sur mon moral et ça a été un des nombreux facteurs qui m'ont fait quitter le lycée en milieu d'année (avant quelques années de galère), mais ça, ce sera pour une autre fois.

Aujourd'hui encore, je me dis que si ça trouve je suis un #mathématicien raté faute d'un apprentissage adapté. Sans doute pas, hein, mais qui le saura jamais à coup sûr ?

La conclusion c'est que, bordel, si on pouvait avoir un enseignement plus adapté aux spécificités intellectuelles de chaque gamin·e, qui sait quels trésors cachés on trouverait dans chacun·e d'entre-elleux ?

#mathématique #école #autisme #tdah​ #éducation #enseignement #pédagogie

caml :vegan: (@caml@toot.moi.lc)

Content warning: Souvenirs d'école. De l'importance d'un apprentissage adapté à chacun·e

#mathematics #mathsmanuelacasasoli #maths
Mathematics is beautiful, and for thousands of years, so many great minds have been studying mathematics to make our world a better place for everyone.
30+ Brilliant Mathematicians Who Unlocked the Modern World

30+ Brilliant Mathematicians Who Unlocked the Modern World | Abakcus

Mathematics is beautiful. We have curated 30+ brilliant mathematicians whose work continues to help shape our modern world.

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Knot theorists proved the validity of a mathematical formula about knots after using machine learning to guess what the formula should be.
DeepMind’s AI helps untangle the mathematics of knots

DeepMind’s AI helps untangle the mathematics of knots

The machine-learning techniques could benefit other areas of maths that involve large data sets.

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The Euler equations reveal one of the difficulties of understanding fluid dynamics – non-linearity.
Fluid dynamics and the Euler equations
Euler original paper-1757

Maths in a Minute: Fluid dynamics and the Euler equations

The motion of water, air, or indeed any fluid, is weird when you think about it. It moves as a continuous mass, and can move with great force, yet it is made up of tiny individually moving molecules. We know from personal experience that external...

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Everyone used at least once the visual representation of sets called Venn diagrams.
But who was John Venn? And how did he come to create such an iconic tool that’s used so broadly today?
On the cover: Vhat? Vhere? Venn

On the cover: Vhat? Vhere? Venn - Chalkdust

Madeleine Hall takes a brief dive into the world’s favourite set-relationship-representation diagram.

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Mathematics and rainbows
Stokes' phenomenon, a problem which originated nearly 200 years ago with a question about rainbows, and has generated an entire field of mathematics.
Stokes's phenomenon: An asymptotic adventure

Stokes's phenomenon: An asymptotic adventure

Life is the art of approximation. If we took into account all the details of every aspect of the things we experience, we'd never get anywhere. We need to be careful about which things to ignore, though, because if those details contain a...

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Kevin Hartnett (https://twitter.com/KSHartnett) about one of the biggest recent results in topology. The Smale conjecture, manifolds, diffeomorphism...
How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

#mathematics #mathsmanuelacasasoli #maths
The equation of a lemon...
The equation x^2 + z^2 = y^3 (1−y)^3 of Citrus appears as simple as the figure itself.

Many ideas for teachers
Imaginary - Open Mathematics
1-https://www.imaginary.org/gallery/herwig-hauser-classic
2-https://www.imaginary.org/

#maths #think

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A discovery about soap films helped mathematicians understand how the boundary between melting ice and water evolves.
Mathematicians Prove Melting Ice Stays Smooth
The singular set in the Stefan problem

Mathematicians Prove Melting Ice Stays Smooth | Quanta Magazine

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

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Another way to love Mathematics
A very special Möbius strip, the simplest non-orientable surface.
Mathematical Imagery
Infinite Loop, Thread on Mobius Frame

Mathematical Imagery

Advancing research. Creating connections.

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As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.
In Topology, When Are Two Shapes the Same?

In Topology, When Are Two Shapes the Same? | Quanta Magazine

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

#mathematics #mathsmanuelacasasoli #maths

Twirls, based on polyhedral structures and constructed with small parts.
By Krystyna Burczyk
http://www.origami.edu.pl/

Here
At the Gate of the Hell / À Porta do Inferno
Mathematical Art Galleries
http://gallery.bridgesmathart.org/exhibitions/2021-joint-mathematics-meetings/burczyk

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Mathematicians have expanded category theory into infinite dimensions, revealing new connections among mathematical concepts.
Infinity Category Theory Offers a Bird’s-Eye View of Mathematics

Infinity Category Theory Offers a Bird’s-Eye View of Mathematics

Mathematicians have expanded category theory into infinite dimensions, revealing new connections among mathematical concepts

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New Math Book Rescues Landmark Topology Proof
One of the most important pieces of mathematical knowledge was on the verge of being lost, maybe forever. Now, a new book hopes to save it.
The Disc Embedding Theorem

New Math Book Rescues Landmark Topology Proof | Quanta Magazine

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.

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When Maths and Art are so close...
12 perfectly reflective spheres arranged in an icosahedron and the chaos...

https://www.imaginary.org/

1-Fractal Icosahedron
https://www.imaginary.org/gallery/fractal-polyhedra
2-The Lorenz attractor
https://www.imaginary.org/gallery/the-lorenz-attractor