# #maths

Poll

If you regularly work with numbers, and are reasonably good with a spreadsheet, do still do a lot of routine calculations on your handheld calculator ?

I frequently use my casio fx 260, which I love, for routine stuff

#Excel #Calculator #Math #Maths #numbers #computers #Keyboard

Un rapport de l’Inspection générale de l'Insee, de l’Inspection générale de l'éducation, du sport et de la recherche, et de l'Inspection générale des affaires culturelles, sur "la culture statistique des Français" :

https://www.education.gouv.fr/la-culture-statistique-des-francais-constats-enjeux-et-perspectives-377984

#mathématiques #maths #math #statistique #éducation

#Maths #Mathematics. “If I have seen further than others, it is by standing upon the shoulders of giants.”

Isaac Newton

Conférence MathEnVille 2023 - Agnès Désolneux

Source : Youtube / Institut Fourier

https://www.youtube.com/watch?v=t4rsKfyoGDA

#mathématiques #maths #math #Youtube

#Maths #Mathematics. Fun with curves. Another go at the (pseudo) tetrahedron challenge. Slight improvement on the last attempt.

As a self confessed maths nut, it took much longer than it should have to see this sequence (for f-stops in photography)

Pour moi - 50% de réduction c'est égal à + 50% qu'en pensez-vous ?

#maths

One day, one decomposition

A025584: Primes p such that p-2 is not a prime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A025584.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A025584.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #PrimeNumbers #graph #threejs #webGL

"La théorie des types est aujourd'hui un outil puissant pour combiner le raisonnement logique et le calcul. Maintenant, avec les idées de la théorie homotopique des types, une nouvelle dimension est ajoutée [...]" – Vladimir Voevodsky (1966-2017)

#citation #mathématiques #maths #math

"Type theory today is a powerful device for combining logical reasoning with computation. Now, with the ideas of homotopy type theory, there is a new dimension added, which is not just combining logical reasoning and computation [...]" – Vladimir Voevodsky (1966-2017)

#quote #mathematics #math #maths

Mmm ! Ep.20 - MATHSCOLLECTION (par On fait des Maths ?)

Source : Youtube / Thomaths

https://www.youtube.com/watch?v=X5GqJc9szD0

#mathématiques #maths #math #Youtube

La somme des entiers

Source : CNRS - Images des mathématiques / Buff, Xavier

https://images.math.cnrs.fr/La-somme-des-entiers.html

#mathématiques #maths #math

"He did important work on series and in optics and was a strong supporter of Newton in his dispute with Leibniz." https://mathshistory.st-andrews.ac.uk/Biographies/Gregory_David/ #history #maths #math #mathematics #mathsodon #histodon #histodons @histodon @histodons

Source: https://twitter.com/mathshistory/status/1664925647548841984

One day, one decomposition

A025583: Composite numbers that are not the sum of 2 primes

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A025583.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A025583.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #composite #numbers #sum #primes #graph #threejs #webGL

#GeoffreyWest - Why Do #PowerLaws Work So Widely?

https://www.youtube.com/watch?v=6Gw07lDU8-Y&ab_channel=CloserToTruth

#Philosophy #PhilosophyOfScience #Math #Maths #Mathematics #Physics #UniversalLaws #LawsOfNature #LawsOfPhysics #Systems #ComplexAdaptiveSystems #Biology #Metabolism #Ageing #Aging #Emergence #ScalingLaw #ScalingLaws #PowerLaw #CloserToTruth #RobertKuhn

#Maths #Mathematics. Fun with curves. Intersecting pseudo-tetrahedrons again. Better this time.

–¿Quieres apoyar la realización del Concurso Nacional Femenil de la Olimpiada Mexicana de Matemáticas?

https://sites.google.com/im.unam.mx/concurso-femenil-omm/apoyos

"Les mathématiques sont un outil transversal aux autres sciences, car en particulier elles sont le langage de la science, mais elles sont également en grande mesure le langage de l’innovation. [...]" – Maria J. Esteban (1956–)

#citation #mathématiques #maths #math

One day, one decomposition

A025320: Numbers that are the sum of 2 distinct nonzero squares in 10 or more ways

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A025320.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A025320.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #squares #graph #threejs #webGL

Une autre saison de Voyage au pays des maths, youhouuu !

J'ai commencé par les probabilités ! https://www.youtube.com/watch?v=ZPSH6l_darY

The @WMI_research Applied Maths Seminar earlier today featured two speakers!

First talk was by Jingbang Liu (HetSys CDT, University of Warwick) presenting on "Modelling rare rupture of nanoscale liquid thin films"

Second talk was by Ioana Bouros (@WarwickSBIDER) presenting on "Warwick-Lancaster global COVID-19 model"

More information about the applied maths seminar: https://warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/applmath/

"La mathématique [...] fait partie de toute investigation, tant morale que physique. Même les règles de la logique, auxquelles elle est fermement liée, ne pourraient être déduites sans son aide." – Benjamin Peirce (1809–1880)

#citation #mathématiques #maths #math

"Mathematics [...] belongs to every inquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid." – Benjamin Peirce (1809–1880)

#quote #mathematics #math #maths

Triangular Numbers Modulo 3 (visual proof)

Source : Youtube / Mathematical Visual Proofs

https://www.youtube.com/watch?v=u8X9ymLUC38

#mathematics #math #maths #Youtube

One day, one decomposition

A025284: Numbers that are the sum of 2 nonzero squares in exactly 1 way

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A025284.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A025284.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #sum #squares #graph #threejs #webGL

"...even state-of-the-art models still produce logical mistakes, often called hallucinations. Mitigating hallucinations is a critical step towards building aligned AGI." https://openai.com/research/improving-mathematical-reasoning-with-process-supervision #AI #ArtificialIntelligence #Maths #Logic

Source: https://twitter.com/AlexKontorovich/status/1664272620370694145

#Jupiter in #3D with #CSS #trigonometry https://codepen.io/thebabydino/pen/GRYbVoe

Rotates around y axis, scroll changes x axis tilt if browser supports CSS #scroll animations.

Just one image used for sphere surface (#2). Distortion from rectangle to "dress" sphere is all CSS. If you're a patron on Patreon, then you may have seen the concept in action last month, though not with Jupiter.

Also: very impressed with #Firefox - 3D perf used to be horrendous. Now it's better than #Chrome!

#CodePen #maths #geometry

"Stop funding millions to “improving teaching of maths”, when it’s the wrong subject, whilst failing to fund a fundamentally new computer-based curriculum, one to achieve computational literacy for all." https://www.conradwolfram.com/writings/game-over-for-maths-a-level #maths #education #mathematics #math #chatgpt #ai #artificialintelligence

Source: https://twitter.com/stevenstrogatz/status/1664271388650389505

"Contrairement à un préjugé trop répandu, l'activité mathématique est donc avant tout une activité où l'on discute énormément. Séminaires, conférences, colloques sont des moments de partage, d'émotions, mais aussi de grande tension."–Cédric Villani(1973-)

#citation #mathématiques #maths #math

#Maths #Mathematics. Fun with curves. Two intersecting pseudo-tetrahedrons. It’s a start.

CNRS - Images des mathématiques : Revue de presse mai 2023

https://images.math.cnrs.fr/Revue-de-presse-mai-2023.html

#mathématiques #maths #math

Who Gives a Sheaf? Part 6: Natural Transformations

Source : Youtube / K-Theory

https://www.youtube.com/watch?v=ecGEGCfPJ_k

#mathematics #math #maths #Youtube

One day, one decomposition

A025283: Composites that use the same digits as their prime factorization

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A025283.html

2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A025283.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #composites #prime #factorization #graph #threejs #webGL

"Il est bon d'ailleurs, dans tous les cas où cela est possible, d'habituer l'élève à trouver, par une vision directe des choses et un calcul mental rapide, une valeur très grossièrement approchée de la solution. [...]" – Émile Borel (1871-1956)

#citation #mathématiques #maths #math

New Blog Post:

Use Derivative to Find the Extreme Values

In this article, you will know:

- Definition: Global Extreme Value

- Definition: Local Extreme Value

- The Extreme Value Theorem

- Fermat’s Theorem

- Definition: Critical Point

- Algorithm: Find the Global Extreme Value

Full Text: https://gapry.netlify.app/l0/2023/05/use-derivative-to-find-the-extreme-values/

#Maths #Mathematics. Fun with curves. Pseudo cube and octahedron mapped from continuous, polynomial functions. The challenge is to find whether other pseudo Platonic solids based on the tetrahedron, icosahedron and dodecahedron can be mapped in a similar manner.

Delighted to see Hello World, Issue 21 - with my #turtlestitch article and its value as a creative crosscurricular activity for the classroom, linking #maths, #computing and #textiles.

Interested in using TurtleStitch in your classroom? We're running an introduction to TurtleStitch on 14th of June at 16.30

More information and sign up: https://www.warwick.ac.uk/turtlestitch

Hello World: https://helloworld.raspberrypi.org/issues/21

#CSed #PhysicalComputing #STEMeducation #EDchat

#WMGoutreach #wmgwarwick #uniofwarwick

J'assiste à une formation où on me parle d'hyperbole alors qu'il n'y a qu'une asymptote. Les maths ont donc à ce point changé? #maths

"Quiconque connaît la notation algébrique, lit d'un clin d'œil dans une équation le résultat auquel on parvient péniblement par des règles de fausse position." – A.A. Cournot (1801–1877)

#citation #mathématiques #maths #math

Journées CPGE – ÉNS 2023 : autour des travaux des médailles Fields 2022

Source : CultureMath

https://culturemath.ens.fr/thematiques/superieur/journees-cpge-ens-2023-autour-des-travaux-des-medailles-fields-2022

#mathématiques #maths #math #FieldsMedals

The latest @WMI_research Applied Maths Seminar was by Thomas Barker (Cardiff University) presenting on "Continuum modelling of granular flow with dynamic compressibility"

Thomas's webpage: https://profiles.cardiff.ac.uk/staff/barkert1

More information about the applied maths seminar: https://warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/applmath/

"Il n'y a guère de théorie plus élémentaire [que l'algèbre linéaire], bien que des générations de professeurs et d'auteurs de manuels aient obscurci sa simplicité par d'absurdes calculs de matrices." – Jean Dieudonné (1906–1992)

#citation #mathématiques #maths #math

"There is hardly any theory which is more elementary [than linear algebra], in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices." – Jean Dieudonné (1906–1992)

#quote #mathematics #math #maths

Who gives a sheaf? Part 5: Some Categories

Source : Youtube / K-Theory

https://www.youtube.com/watch?v=fU1uaXvG0Yc

#mathematics #math #maths #Youtube

Nonstandard Area Formula for a Right Triangle (proof without words)

Source : Youtube / Mathematical Visual Proofs

https://www.youtube.com/watch?v=E-9lfVSejt4

#mathematics #math #maths #Youtube

"Schooten possessed an excellent knowledge of the mathematics of both his own time and earlier periods. Beside being an extraordinarily industrious and conscientious scholar, a skilful communicator, and an inspiring teacher, he was a man of rare unselfishness." https://mathshistory.st-andrews.ac.uk/Biographies/Schooten/ #Maths #Mathematics #Math #History #Biography #Dutch #Netherlands #histodon #histodons @histodon @histodons @mathematics @academicchatter

Source: https://twitter.com/mathshistory/status/1663113708489392131

If you're wondering how my evening is going, I just calculated the diameter of a square inscribed in a circle so I could figure out if a (square) cake I hadn't made yet would fit onto a plate I had in the cupboard #maths #totallyAGeek

Reading a book about business #Statistics and most of the first chapter is taken up with basic arithmetic. I'm transported back to days when #Arithmetic was a separate O-Grade exam from #Maths. First paper - no calculators allowed. Sweating bullets😅 😱 ➕ ➖ ✖️ ➗

"The characteristic excellence of mathematics is only to be found where the reasoning is rigidly logical : the rules of logic are to mathematics what those of structure are to architecture." – Bertrand Russell (1872-1970)

#quote #mathematics #math #maths

"L'excellence caractéristique des mathématiques ne se trouve que là où le raisonnement est rigoureusement logique : les règles de la logique sont aux mathématiques ce que celles de la construction sont à l'architecture." – Bertrand Russell (1872-1970)

#citation #mathématiques #maths #math

An interesting and original (I think) puzzle from Micky Bullock.

"Last week Negligent Neil calculated length AC. He had forgotten to switch his calculator from radians to degrees but, fortunately, he still got the answer right.

"An inky splodge has now obscured the angle at A. Negligent Neil has forgotten what his answer was for length AC, but he insists it was between 40 cm and 50 cm.

"Find length AC to 3 significant figures."

"Entre deux vérités du domaine réel, le chemin le plus facile et le plus court passe bien souvent par le domaine complexe." – Paul Painlevé (1863–1933). Ces propos sont aussi repris par Jacques Hadamard, et lui sont donc souvent attribués à tort.

#citation #mathématiques #maths #math

"An international team of researchers tested what the software could manage by providing the generative AI program with challenging graduate-level mathematics questions......" https://arstechnica.com/science/2023/05/when-it-comes-to-advanced-math-chatgpt-is-no-star-student/ #Maths #AI #ArtificialIntelligence #ChatGPT @mathst @mathematics

Source: https://twitter.com/JenLucPiquant/status/1659989673949773826

Problème de Monty Hall, paradoxe de Simpson, géométries non euclidiennes, pavages du plan et théorie des graphes : cinq nouveaux épisodes de l'excellente série "Voyages au pays des maths" disponibles depuis lundi sur arte.tv : https://www.arte.tv/fr/videos/RC-021426/voyages-au-pays-des-maths/

#maths

question for fellow mathematicians: have you ever heard of a standard name for this symbol: ¬

it's one of many symbols used to represent negation, although unlike all the alternative symbols, it has no alternative name. in Unicode, it's just called "not sign"

I want to call this symbol a "ledge" because it looks sort of like a ledge: you have a horizontal line that's folded over on the right side. but I'm curious if anyone has heard of another name for this, since I can't find anything on it

I have \( N \) identical balls and \( M \) labelled bins in which I can put them. A bin can be left empty, BUT I can only put a maximum of \( n \) in each. How many ways are there of putting the balls in the bins? If \( n=1 \) or \( n = N\), the result is standard. How about for arbitrary \( n \), assuming \( N \leq nM \)? #combinatorics #maths #math #puzzle

"Good mathematicians when they make [errors], which is not infrequent, soon perceive and correct them. As for me (and mine is the case of many mathematicians), I make many more of them than my students do [...]" – Jacques Hadamard (1865–1963)

#quote #mathematics #math #maths

Here's a tip for beginners in #AbstractAlgebra, #GroupTheory or #NumberTheory.

Sometimes it's useful to think in terms of the divisibility ordering instead of the usual ordering where 0 ≤ 1 ≤ 2 ≤ …. Divisibility gives a partial ordering on the natural numbers where we say that n ≤ m if n divides m. Or we can extend this order to all integers, in which case n and -n become equivalent in this order because they divide each other.

The main difference is that this isn't a total order. For example 7 doesn't divide 8 and 8 doesn't divide 7. The other difference is that while 0 is the least natural number in the usual ordering, it's the *greatest* number in the divisibility ordering, because everything divides 0!

Thinking this way makes several definitions make more sense:

1. The least common multiple of 12 and 10 is 60, even though 0 is also a common multiple of 12 and 10. This is because 0 is greater than 60.

2. If an element of a group never becomes the identity when you repeatedly multiply it by itself, then we say it has order 0. This is because the order of an element is the least power of the element that equals the identity, under the divisibility ordering.

3. Likewise we say that a ring has characteristic 0 if 1 + … + 1 is never 0. Again we can use the divisibility ordering to say that the characteristic is the least integer for which adding together that number of 1s gives 0.

Oh this is very cool: A Number System Invented by Inuit Schoolchildren Will Make Its Silicon Valley Debut - https://www.scientificamerican.com/article/a-number-system-invented-by-inuit-schoolchildren-will-make-its-silicon-valley-debut/

'The “Kaktovik numerals,” named after the Alaskan village where they were created, looked utterly different from decimal system numerals and functioned differently, too. But they were uniquely suited for quick, visual arithmetic using the traditional Inuit oral counting system, and they swiftly spread throughout the region. Now, with support from Silicon Valley, they will soon be available on smartphones and computers—creating a bridge for the Kaktovik numerals to cross into the digital realm.'

Theorem:

replacing math in the K12 curriculum with psychology would be a net benefit

Because in the real world, there are more real life problems related to psychology then to math

Mathstodon.xyz is a server for people who love maths. We have LaTeX rendering in the web interface!

:Fediverse: https://mathstodon.xyz

We hope there’ll be lots of maths chat, but any topic of conversation following the code of conduct and the principle of getting along together is OK.

If you have any questions, contact the admin at @christianp

#FeaturedServer #Maths #Math #Mathematics #Mathematical #Mathematicians #Mathematician #LaTeX #Science #Mastodon #Fediverse

Oh, and now I've seen someone else ❤️ed this 🌈 logarithmic spiral from a couple of years back https://codepen.io/thebabydino/pen/powNvqB

This could also really benefit from getting a pure #CSS exp() remake!

#CodePen #mathematics #maths #cssTricks #cssGrid #coding #frontend #webDev #webDevelopment

Someone ❤️ed a #CodePen ▦ animation https://codepen.io/thebabydino/pen/KJddbK I made half a decade ago and when I saw it, it hit me how having sqrt() in #CSS can help us with creating a triangular grid in CSS without setting row & col indices on each item and without shape-outside/ float tricks. 💡

Really need to code some use cases for the mathematical functions. The MDN examples are so bad at illustrating how useful they are...😭

#mathematics #maths #cssTricks #cssGrid #coding #frontend #webDev #webDevelopment

@aethelshane #haiku #575prompt

tonight's call, mentioned

a short figure like Yoda

once influenced me

#humblebrag behind the #micropoetry:

I had the pleasure of being in the company of Dr. L.F. Cheung, a #maths lecturer at the Chinese University of Hong Kong when I was an undergraduate student there.

I solved an open problem he raised and my write-up is on this #math paper here: https://web.archive.org/web/20180320161442/http://www.pumj.org/docs/Issue3/Article_1.pdf

https://leeyieng.files.wordpress.com/2020/03/46cad-issue_3.pdf

Incidentally, he is also physically short, like Master Yoda. I mentioned him to a friend whose major was linguistics on our Google Meet call tonight the moment she mentioned computational linguistics, which Dr Cheung introduced to me.

John Last (past Chair of the UK Arts & Design Institutions Association) once wrote:

'There is a flaw in the logic that says to count is become productive but to create is not' (quoted in Art Newspaper).

There is a crisis in #arts education in the UK, which a philistine Govt. cares little about.

Certainly better #maths #education is required, but this is not an either/or proposition; we need to reinvigorate our treatment of #art & the arts in #schools!

Having a bit of a #maths day trying to work out how to uncross self intersecting shapes for #inkscape's shape builder tool. The problem is, these enclosed shapes sometimes go forwards and sometimes go backwards and i can tell what i have is a chain which switches at each crossing.

Do you have any ideas?

I am writing something, and I want to refer to the isoceles triangle formed in a regular n-gon by two adjacent vertices and the center. Surely there is a simple name for it…isn’t there?

Any ideas?

Things my brain thinks up when I'm trying to sleep:

It's possible to raise a number to a positive integer such as 2^2, it's also possible to raise a number to a positive fraction such as 2^(1/2) but what is the result of raising a number to a negative integer or fraction such as: 2^(-2) or 2^(-1/2)?

I'd really love to know the answer to this.

Discovery about Book Embedding of Graphs - Numberphile

Source : Youtube / Numberphile

https://www.youtube.com/watch?v=qw2Pl_Nk3CA

#mathematics #math #maths #Youtube

I can now have stuff like this in #CSS!

If you're wondering what in Satan's name is that supposed to be doing... well, creating a sphere like in the second image.

Does it work? Not with that formula, as it would need division with units in calc() to get an angle from a triangle where I know the hypotenuse & opposing edge.

But smth like asin(3vw/5vw) doesn't work!

So I have to use asin(3/5), then multiply with 1vw to set lengths.

Related https://twitter.com/anatudor/status/1537881090223853568

Chrome 114 now passes all tests in the demo too!

Firefox 114 is very close, only failing abs() and sign()... which can be easily emulated using other functions, as I explained in this article from a couple of years back https://css-tricks.com/using-absolute-value-sign-rounding-and-modulo-in-css-today/

We have Maths in CSS, people! 🥳🎉

Thanks @aperiodical for the opportunity to host @carnivalofmaths again! I'm the host for CoM #172 and #215. #maths #math #mtbos

https://leeyieng.wordpress.com/2023/05/01/carnival-of-mathematics-215-april-2023/

@christianp Thanks! Hopefully some other #math #maths #science #computerscience folks will chime if there are other servers out there that support rendering LaTeX.

#JacobYatsko - A New Way To Look At #Fibonacci #Numbers

A look at how #PisanoPeriods and the #Modulo #Function can turn the #FibonacciSequence into strange and fun visual designs.

I would appreciate it if people could help me get more federated on my new instance. Please boost this post if any of the following tags apply to you so I can follow!

#actuallyautistic

#adhd

#disabilityrights

#auspol

#trans

#lgbtqia

#socialism

#communism

#leftist

#maths

#computerscience

#science

#sciencefiction

#books

#philosophy

#plushies

#calckey

This is giving me ideas... https://atlasofplaces.com/cartography/dymaxion-world-map/

#CSS #geometry #maths #3D

Sounds a bit like Gödel's incompleteness theorem… "there are true propositions about the natural numbers that can be neither proved nor disproved from the axioms."

https://en.wikipedia.org/wiki/Kurt_Gödel #Math #Maths #Logic #Godel

Just published a new #maths toy/game. A new interpretation of the trending aperiodic monotile.

This time playing with the "turtle" tile. And it has a new companion fish to help it tile the plane aperiodically.

The files are here:

https://www.printables.com/model/454334-turtle-and-fish-aperiodic-monotile-puzzle

#math #mathematics #geometry #science #3dprinting #stem #printables #toy #game #games #aperiodic #monotile

@lurker

OK, I've just thought of a better one:

-7515

#matchsticks #maths

"The proof of self-evident propositions may seem, to the uninitiated, a somewhat frivolous occupation. [...] Self-evidence is often a mere will-o'-the-wisp, which is sure to lead us astray if we take it as our guide." – Bertrand Russell (1872-1970)

#quote #mathematics #math #maths

"La démonstration de propositions évidentes peut sembler [...] une occupation quelque peu frivole. [...] L'évidence n'est souvent qu'un simple feu follet, qui ne peut que nous égarer si nous le prenons pour guide." – Bertrand Russell (1872-1970)

#citation #mathématiques #maths #math

Oh, I totally forgot but I have to mark the French mathematics Olympiads, and the deadline is... this weekend.

So here we go! ✏️

Kids these days... Are amazing!

> New Orleans teens’ Pythagorean proof gains compelling evidence

Stuff I've been doing lately: support* tests for mathematical functions.

Confused about what browser supports what mathematical functions or constants?

https://codepen.io/thebabydino/pen/yLRBJXP tells you what your browser supports.

*not only support, but more about that/ use cases another time

#css #maths #mathematics #coding #trigonometry #webDev #webDevelopment #frontend #CodePen

Lemniscate of Bernoulli has the equations:

x = (a·cos(t))/(1 + sin²(t))

y = (a·sin(t)·cos(t))/(1 + sin²(t))

where a is the lemniscate half width and 0 ≤ t ≤ 2·π 😊

A couple of years back, I made a canvas lemniscate of Gerono animation 😼 https://codepen.io/thebabydino/pen/yLyxgVQ

Feel free to guess as to why I've posted this stuff 🤭😈

#canvas #maths #geometry #trigonometry #js #JavaScript #CSS #coding

J'adore la géométrie en général, et encore plus quand elle nous parvient d'un autre monde, d'un autre univers ! :shibahearteyes:

(C'est du "coded loop art" réalisé par des "coded loop artists" : c'est l'association de la #art, #codage en #informatique et #maths pour réaliser des boucles codées artistiques.)

"Before Turing, things were done to numbers. After Turing, numbers began doing things." —George Dyson, Turing's Cathedral #computing #maths #Turing

Aperiodic monotile!

I thought Penrose tiles would never be beaten! There's now a single tile which fills the plane aperiodically!

My first #lasercutter project. Created in #inkscape

Wow!! What a breathe of fresh air this paper is in the midst of suffocating levels of "AI solves everything" hype cycle.

https://arxiv.org/abs/2303.10798

They have found at long last, a single tile, an "einstein", which they call a "hat"/polykite that tiles the entire plane aperiodically.

Previously the best known aperiodic tiling of the plane required at the least two different tiles, the most famous ones being the Penrose tiles, and those that adorn Alhambra.

It is all the more wonderful that the first two authors don't have any academic/research affiliations. They write somewhere in the paper, how it all started, so wonderful:

"One of the authors (Smith) began investigating the hat polykite as part of his open-ended visual exploration of shapes and their tiling properties. Working largely by hand, with the assistance of Scherphuis’s PolyForm Puzzle Solver software (www.jaapsch.net/puzzles/polysolver.htm), he could find no obvious barriers to the construction of large patches, and yet no clear cluster of tiles that filled the plane periodically."

Why is the study of tilings such a big deal? Well, it hints at and tries to formalize various physics concepts that are of immense interest to many of us (and dare I say, even neuroscientists): quasi crystals!, possible new states of matter, emergent structures from simple units, how symmetries and asymmetries arise, stability of heterogenous media, soft matter physics, order without periodicity, criticality etc., etc.,

On quasi-crystals and their search, applications, uses etc., I recommend the wonderful Paul Steinhardt's book: "The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter"

#Physics #Maths #Combinatorics #AperiodicTiling #PenroseTiles #Einstein #Emergence #condensedmatter

"Le symbolisme est utile parce qu'il rend les choses difficiles (ceci n'est pas vrai pour les parties avancées des mathématiques, mais seulement pour les débuts). Ce que nous voulons savoir, c'est ce qui peut être déduit de quoi. [...]" – Bertrand Russell (1872-1970)

#citation #mathématiques #maths #math