#Maths

My latest: is mathematics really all about counting things? https://joshs-newsletter-a4b32f.beehiiv.com/p/mathematics-counting #math #maths

"After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic."

Florio, Salvatore, and Øystein Linnebo, The Many and the One: A Philosophical Study of Plural Logic (Oxford, 2021; online edn, Oxford Academic, 23 Sept. 2021), https://doi.org/10.1093/oso/9780198791522.001.0001, accessed 4 Dec. 2023. #OpenAccess #OA #Philosophy #Language #Maths #Math #Mathematics #Logic #NonFiction #Academic #Book #Books #Ebook #Ebooks #Bookstodon @philosophy @bookstodon (67)

"Mathematics has beauties of its own – a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable [...]" – Jacob William Albert Young (1865-1948)
#quote #mathematics #maths #math

"Les mathématiques ont leurs propres beautés – une symétrie et une proportion dans leurs résultats, une absence de superflu, une adaptation exacte des moyens aux fins, ce qui est extrêmement remarquable [...]." – Jacob William Albert Young (1865--1948)
#citation #mathématiques #maths #math

FACT CHECKED: Every ant, in fact, cannot have his day. With an estimated current population of 20 quadrillion and only 5 trillion days since the big bang, every ant currently alive would have to share their day with nearly 4000 ants. And that's without factoring in every ant that has ever lived.

:ms_cross: MISINFORMATION

#misinformation #factcheck #antz #ants #maths

Carnival of mathematics 222
Source : The Aperiodical / John D. Cook blog

https://www.johndcook.com/blog/2023/12/02/222nd-carnival-of-mathematics/
#mathematics #maths #math

Le « problème du logarithme discret » en cryptographie
Source : CNRS - Images des Mathématiques / Delaunay, Christophe

https://images.math.cnrs.fr/Le-probleme-du-logarithme-discret-en-cryptographie.html
#mathématiques #maths #math #cryptographie

🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #4🎄

L'université de Sheffield (Grande-Bretagne) a mis au point un modèle mathématique pour réaliser le parfait sapin de Noël en terme de décoration. Deux étudiants en mathématiques âgés de 20 ans se sont penchés sur la question, à la demande d'une chaîne britannique de grands magasins.

* nombre de boules de Noël : diviser par 20 la racine carrée de 17, puis multiplier le résultat par la taille du sapin en centimètres.

* longueur des guirlandes : multiplier 13 par π, puis diviser le résultat par 8, et multiplier par la hauteur de l'arbre.

* longueur des guirlandes électriques : multiplier π par la taille du sapin.

* diamètre de l'étoile : diviser la hauteur du sapin par 10.

Exemple :
Pour un sapin de 1,80 m, il faudra compter :
37 boules.
919 cm de guirlandes décoratives.
565 cm de guirlandes lumineuses.
une étoile ou un ange de 18 cm de haut.

Voilà !

À vous de tester et juger votre sapin.

⚠️Please boost si vous avez aimé.

#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques

Tiens, @ClaireLomme à l'instant sur France Inter pour parler de l'enseignement des #maths en ULIS.
Edit : le lien vers la chronique 👉 https://www.radiofrance.fr/franceinter/podcasts/le-zoom-de-la-redaction/le-zoom-de-la-redaction-du-lundi-04-decembre-2023-5234831

One day, one decomposition
A050936: Sum of two or more consecutive prime numbers

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A050936.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A050936.html

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

@Dunstable
Actually, you'd still only get to eat one chocolate per day and be left with 552 chocolates on the 25th.
:-)
#maths

@Dunstable Or better still, each one of the sub-advent calendars also had another one for every day all the way down. Then you'd have infinitely many chocolates (but wouldn't have time to reach any of them).
#maths #recursion #fractal

#Maths #Mathematics To understand the infinities, perhaps we should listen to the likes of Gauss who argued against “the use of infinite magnitude as something completed, which is never allowed in mathematics. Infinity is simply a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction.”

Any mathematician who invokes God in an attempt to explain the infinite has truly lost the plot.

@SinclairSpeccy That reminds me of the free chocolate generator:
https://www.youtube.com/shorts/NdUAU6MLLEg
#maths #chocolate

I've been experimenting with different ways to draw the relationships among some objects of interest from functional analysis.

In this figure the ellipses are supposed to be sets of sets (e.g., IPS, the set of all inner product spaces). The shaded circles are the subsets created by the induced {norm, metric, topological space}. I want to add some of the flow the other direction (than set inclusion), like the fact that a complete normed vector space is a Banach space, or that a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space. Both require that Cauchy sequences in (X,d), where d is the induced metric that came from the inner product space, are complete (this is part of the "otherwayness").

Not sure I like this but this is the latest thing I've tried...

#math #maths #functionalanalysis #texlatex #tikz

"Once a model has been satisfactorily worked out, the generativity of mathematics comes into play. Once this happens, it becomes possible to feel as though you're doing physics, when what you're really doing is studying the model [...]" – Alain Connes (1947-)
#quote #mathematics #math #maths

"Dès qu'un modèle de la physique est suffisamment élaboré, la générativité des mathématiques entre en jeu : on peut alors avoir l'impression de faire de la physique en étudiant ce modèle d'un point de vue strictement mathématique." – Alain Connes (1947-)
#citation #mathématiques #maths #math

In 1683 the Swiss mathematician Jacob Bernoulli discovered this beautiful expression for the constant e while studying continuous compound interest.

See https://en.wikipedia.org/wiki/Jacob_Bernoulli for more on Bernoulli's work and life.

#math #maths #eulersnumber #compoundinterest #jacobbernoulli

@atoponce @phonner
Why do you think that the set of reals has a different size from the set of squared reals?
#maths #math #infinity #yawn

@atoponce
(1) That's not what is meant by "infinities come in different sizes",
(2) By attaching "∞" (which I assume you are re-defining as a special new number which is greater than all the other reals) to the 'end' of the reals you have invented a new algebra with new rules. That's not the one we normally use to do #maths :-)
(3) I see nothing there asserting differing magnitudes of "infinity" (unless that's in the secret axioms of your new algebra).
(4) Read up on Cantor's work.

I've been studying quantum fields a bit, and if you back up (all the way to Hooke's Law [1]) you wind up studying simple harmonic oscillators. Simple Harmonic Motion (SHM) is apparently very common in nature and there many familiar examples, including:

(i). A mass on a spring that doesn't experience any other forces (Hooke's law),

(ii). A pendulum, as long as the angle it travels through is small. In particular, you need sin θ ≈ θ, that is, θ, close to zero, to be able to solve the equation of motion. This is why this only works if θ is small, and perhaps not surprisingly the error grows as θ grows [2], and

(iii). RLC circuits [3]. In general, these systems have angular frequency ω = √k/m (and so ω² = k/m), and assuming θ is small we have this equation of motion:

x'' + ω²x = 0

The solution to this differential equation is

x(t) = c1*cos(ωt) + c2*sin(ωt)

If you stay with the math and logic eventually you can see that a wave is a bunch of coupled simple harmonic oscillators. It is really quite amazing.

A few of my notes on these topics are here: https://davidmeyer.github.io/qc/oscillators.pdf. The LaTeX source is here: https://www.overleaf.com/read/xjmyvksvtztb. As always, questions/comments/corrections/* greatly appreciated.

#hookslaw #newtonslaw #simpleharmonicoscillators #quantumfields #math #maths #ordinarydifferentialequations #texlatex #tikz #circuittikz

References
---------------
[1] "Hooke's law", https://en.wikipedia.org/wiki/Hooke's_law

[2] "Oscillation of a Simple Pendulum", https://www.acs.psu.edu/drussell/Demos/Pendulum/Pendulum.html

[3] "Oscillations in Electrical Circuits", https://math24.net/oscillations-electrical-circuits.html

An Amazing way to Sum Squares (visual proof V using cuboids)
Source : Youtube / Mathematical Visual Proofs

https://www.youtube.com/watch?v=VYaEGvClg7Q
#mathematics #maths #math

🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #3🎄

Comme j'adore les Simpson ...

Dans un des épisodes des Simpson (épisode 6 saison 7, 1995), on peut voir Homer Simpson se promener nonchalamment, et en 3D, devant une égalité qui rappelle un fameux théorème du mathématicien Pierre Fermat :

Il est écrit : 1782¹² + 1841¹² = 1922¹²

Le théorème de Fermat, ou depuis sa démonstration partielle Théorème de Fermat-Wiles, s'énonce comme suit

« Il n'existe pas de nombres entiers strictement positifs x, y et z tels que : x^n + y^n = z^n dès que n est un entier strictement supérieur à 2. »

Chose savoureuse, cet épisode des Simpson a été diffusé seulement quelques semaines après la publication des quelques 100 pages de la démonstration d’Andrew Wiles en 1995.

Homer aurait-il démontré le contraire ?

Cette égalité est due à David X. Cohen, matheux et co-scénariste de cette série pleine de références scientifiques.

Si on la vérifie sur une calculatrice standard, on trouve que le terme de gauche vaut 2.541210259e+39 et que celui de droite vaut… 2.541210259e+39 !
Tout simplement les nombres sont tellement grands que la calculatrice va les arrondir…

Puis, en y regardant de plus près, on voit tout de suite que l’égalité est fausse car comme 1782 est pair, 1782¹² l’est aussi et comme 1841¹² est impair pour les mêmes raisons, la somme 1782¹² + 1841¹² est impaire. Or 1922¹² est pair !

Informé de cette dernière objection, David X. Cohen a fait apparaître dans un autre épisode (épisode 2 saison 10, 1998) un tableau noir (voir Figure #2), sur lequel se trouve un autre faux contre-exemple : 3987¹² + 4365¹² = 4472¹². 😂

Voilà !

⚠️Please boost si vous avez aimé.

#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques

3 décembre 1616 : #CeJourLà naissance de John Wallis (†8/11/1703), mathématicien anglais dont les travaux sur le calcul infinitésimal (cf. intégrales de Wallis) ont ouvert la voie à ceux de Newton et Leibniz. On lui doit le symbole ∞ pour l'infini.
https://fr.wikipedia.org/wiki/John_Wallis
#mathématiques #maths #math

One day, one decomposition
A050931: Numbers having a prime factor congruent to 1 mod 6

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A050931.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A050931.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #factor #congruent #graph #threejs #webGL

After 32 years of searching, and with some assistance from a Supercomputer, Mathematicians have finally discovered a new Example of a special Integer called a Dedekind Number, the 9th one #Maths #Research https://www.sciencealert.com/mathematicians-have-found-the-ninth-dedekind-number-after-32-years-of-searching

"Chess combines the beauty of mathematical structure with the recreational delights of a competitive game. Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick." – Martin Gardner (1914-2010)
#quote #mathematics #maths #math

"Les échecs combinent la beauté d'une structure mathématique avec les plaisirs récréatifs d'un jeu compétitif. La magie mathématique combine la beauté d'une structure mathématique avec la valeur divertissante d'un tour." – Martin Gardner (1914-2010)
#citation #mathématiques #maths #math #échecs

@matj1
Only 99%? Really?
154476802108746166441951315019919837485664325669565431700026634898253202035277999,

36875131794129999827197811565225474825492979968971970996283137471637224634055579,

4373612677928697257861252602371390152816537558161613618621437993378423467772036
#maths #math #elliptic
https://math.berkeley.edu/~tb65536/AG_Final_Project.pdf

Did you know that 276,951,438 is the smallest 9-digit number that, when written in three rows of 3, forms a 3×3 magic square?

It is also the only 3x3 normal magic square, excluding rotations and reflections.

Interestingly, a normal magic square of order n, that is, a magic square which contains the integers 1,2,...,n², has magic constant M given by

M = n · (n² + 1)/2

For example, the magic square in the image contains integers 1,2,..,3² and so

M = 3 · (3² + 1)/2 = 3 · 10/2 = 15

#math #maths #magicsquare #magicconstant #numbertheory

[Image credit: https://fermatslibrary.com]

References
--------------
[1] "Magic constant", https://en.wikipedia.org/wiki/Magic_constant

[2] "A006003", https://oeis.org/A006003

[3] "Notes on Magic Squares and Cubes", https://www.trump.de/magic-squares

[4] "Magic Square", https://mathworld.wolfram.com/MagicSquare.html

The unreasonable effectiveness of linear algebra.
Source : Youtube / Michael Penn

https://www.youtube.com/watch?v=Rqv3cXt8ZNU
#mathematics #maths #math #Youtube

Studying ML maths be like.

#AI #MachineLearning #Maths #Engineering #Math #Mathematics #ML #DL #DeepLearning

🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #2🎄

Cette magnifique peinture de 1895 de Nikolai Bogdanov-Belsky est exposée à la Galerie Tretiakov, à Moscou.

Elle montre des calculs mentaux à l'école publique de Sergei Rachinsky. Des garçons dans une école de village russe tentent de calculer (10²+11²+12²+13²+14²)/365 de tête.

Le titre même de cette peinture est « Calcul mental à l'école populaire de S. A. Rachinsky », et donc, pas de doute, son auteur l'a réalisée en hommage au calcul mental.

On ne sait pas si ces écoliers avaient réussi ou pas, et avec quelle méthode.

Nous allons prendre ici leur place, d'une certaine manière.

Une des méthodes possibles consiste à s'appuyer sur cette égalité :

10²+11²+12² = 13²+14²
(Ce sont les seuls 5 entiers naturels consécutifs qui présentent une telle propriété. Voir explication en fin du pouète)
=
2(13²+14²)/365 =
2(169+196)/365 =
2(365)/365 =
2

Le résultat est donc 2.

Voilà !

Et n'hésitez pas à la partager votre méthode.

*** Complément explicatif concernant l'égalité 10²+11²+12² = 13²+14²

On cherche n entier naturel tel que
(n-2)² + (n-1)² + n² = (n+1)² + (n+2)²
3n² - 6n + 5 = 2n² + 6n + 5
n² = 12n
n(n - 12) = 0
n = 12

De même, on démontre que l'égalité suivante n'est possible que pour ces 3 entiers consécutifs :
3² + 4² = 5²

⚠️Please boost si vous avez aimé.

#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques

One day, one decomposition
A050813: Numbers n not palindromic in any base b, 2 <= b <= 10

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A050813.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A050813.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #palindromic #base #graph #threejs #webGL

Another great video by #Veritasium.
From the SAT question everyone got wrong to #Earth's solar and sidereal day
https://youtube.com/watch?v=FUHkTs-Ipfg
#space #science #maths

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Bartholomaeus Keckermann's Systema compendiosum totius mathematices," Convergence (September 2020) https://maa.org/press/periodicals/convergence/mathematical-treasure-bartholomaeus-keckermanns-systema-compendiosum-totius-mathematices #Maths #Math #Mathematics #Book #STEM

Came across this cool #CSS pattern https://codepen.io/josetxu/pen/mdvzaQZ?editors=0100 - uses 35 gradients, so I instantly knew I could simplify it and make it easily customisable.

So here it is my version on #CodePen https://codepen.io/thebabydino/pen/WNPamBB?editors=0100 - 9 gradients with n set to 4. Because yes, you can change n! 😎

#coding #pattern #cssPattern #cssGradient #frontend #code #maths #blending #blendMode #xor #logic #trigonometry #geometry #webDev #webDevelopment

#Maths #Mathematics. Apropos of nothing. A light history of the number zero, a number which is definitely something.

https://www.bbc.com/future/article/20161206-we-couldnt-live-without-zero-but-we-once-had-to

🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #1🎄

La géométrie fourmille d'étonnantes pépites et le théorème suivant en fait partie, tant il peut être contre-intuitif pour beaucoup de gens.

Le THÉORÈME DU PAIN BOULE TRANCHÉ affirme que toutes les tranches de même largeur ont autant de croûte les unes que les autres.

Dit autrement, certes la tranche du guignon est entièrement recouverte de croûte, mais elle est plus petite que les tranches centrales et les deux effets se compensent exactement.

En termes plus géométriques, si une sphère est partagée en sections de largeurs égales, alors toutes les sections ont la même aire.
On démontre d'une manière générale qu'une tranche de largeur h dans une sphère de rayon R a une aire A égale à :

A = 2 π R h

On voit bien que ce résultat ne dépend absolument pas de l'endroit de la sphère qu'on choisit de couper. La quantité de croûte ne dépend que de la taille du pain et de l'épaisseur de la tranche.

Donc pas la peine de se disputer à table pour avoir la tranche du guignon!😉

Voilà !

⚠️Please boost si vous avez aimé.

#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques

#BOTD: Nikolai Ivanovich Lobachevsky.

"Nikolai Lobachevsky published his work on non-Euclidean geometry, the first account of the subject to appear in print." https://mathshistory.st-andrews.ac.uk/Biographies/Lobachevsky/ #OTD #History #Maths #Math #Mathematics #STEM #Geometry @science

"Quand je travaille sur un problème, je ne pense jamais à l'esthétique. Je ne pense qu'à la façon de résoudre le problème. Mais quand j'ai fini, si la solution n'est pas belle, je sais qu'elle est mauvaise." – Buckminster Fuller (1895-1983)
#citation #mathématiques #maths #math #problème

"When I am working on a problem, I never think about beauty. I think only of how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." – Buckminster Fuller (1895-1983)
#quote #mathematics #maths #math #problem

@petitbridgechallenge @scollectif
Nous avons bien réfléchi et voici notre réponse.
#petitbridge #teampe #maths #logique

Last year, I arranged a series of ten talks by disabled mathematicians, aimed at a general audience.
Presenters included @solderandchaos, @sophiemacmaths, @matthras, and me, roped in at short notice.
The recordings are all still online: https://www.ncl.ac.uk/maths-physics/engagement/outreach/what-can-mathematicians-do-/

If you're starting to put up christmas decorations, my quick explanation of how to fold and cut a Christmas star might inspire you: https://www.youtube.com/watch?v=S90WPkgxvas

#math #maths #WhatCanMathematiciansDo

Accessible proofs of the transcendence of e and pi:
https://www.youtube.com/watch?v=WyoH_vgiqXM
#maths #e #pi #transcendental #polynomial #number #numbertheory #Mathologer #math

7 of the hardest math problems that have yet to be solved
Source : Interesting Engineering / Tejasri Gururaj

https://interestingengineering.com/lists/math-problems-unsolved-hardest-part1
#mathematics #maths #math #problems

#decompwlj
The decomposition into weight × level + jump of natural numbers is the fundamental theorem of arithmetic ; applied to prime numbers, it leads to a new classification of primes

1000 sequences decomposed with 3D graphs (threejs webGL), 2D graphs - CSV, dump, img to download
⬇️ ⬇️
https://decompwlj.com

➡️ OEISWiki page: Decomposition into weight × level + jump : https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump
➡️ arXiv:0711.0865 [math.NT]: Decomposition into weight * level + jump and application to a new classification of primes: https://arxiv.org/abs/0711.0865

#FundamentalTheoremOfArithmetic #math #maths #mathematics #sequences #OEIS #NumberTheory #PrimeNumbers #JavaScript #php #graph #3D #classification #primes #threejs #webGL #integer #decomposition #arithmetic #numbers #theory #equation #graphs #sieve #fundamental #theorem #arithmetic

Et si on se faisait un CALENDRIER DE L'AVANT des mathématiques insolites & amusantes ?🎄

Si 70+ boosts de ce pouète alors je m'y engagerai y compris pour aujourd'hui.
À vous de jouer.

*** Édition : du coup c'est lancé : je viens de poster celle du Jour #1.

#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques

Moment of truth.. we've got workmen in to lay the flooring in our attic extension.. only *I* did the #maths working out how much we needed.

I'm sure I've got more than enough. I squared off the awkward area into two larger rectangular areas, I added a 10% excess AND when it came to ordering had to round up to the nearest pack size...

... Still, "confident" as I am in my calculations I'm still worried I haven't got enough.

Will find out later XD

The Most Wanted #Prime #Number
https://www.youtube.com/watch?v=vKlVNFOHJ9I
#maths #math #numbers #PrimeNumber #PrimeNumbers

Run up against a #maths problem for which my search fu is failing me.

Given a closed polyline path and a drawn line of width 2×𝑟, which line traces said path as its midline, is there an algorithmic method for finding the paths defined by the outer and inner edges of that line, respectively?

Suspect the hurdle am hitting is that this is problem with known solution and more importantly, a jargony name, which name would readily search up result if only such jargon were known to me.

#mathematics

Quand la géométrie rencontre la sorcellerie.😉

#maths #mathematics #mathematiques #geometry #geometrie

Fixed points and strike mandats - nice and short #maths blog post about finding better fixed points https://pvk.ca/Blog/2012/02/19/fixed-points-and-strike-mandates

1/6
#MathsMonday
This past week I ran a #Mathematics poll https://dotnet.social/@SmartmanApps/111434764484267476 which was inspired by a comment about people having more intelligent conversation here than Twitter, and having seen a similar poll there I thought I'd see what results we'd get here - if people were better at #Maths here. But once I started I realised there were some other factors which weren't going to help the result (more later), and in the end we saw about the same level of #Math ability here as there....

67 1 43
13 37 61
31 73 7
is the smallest #MagicSquare composed of #primes .
I notice a few #Heegner numbers in there. Wouldn't it be fun if just the Heegner numbers could form a magic square.
#maths #primenumber #primenumbers

@Colinvparker @lambdatotoro
In other news, the smallest sequence of *consecutive* primes which can form a 3x3 magic square is:
1480028129
1480028141
1480028153
1480028159
1480028171
1480028183
1480028189
1480028201
1480028213
(Exercise for the student to arrange them correctly :-) ) #maths #fun #primes #MagicSquare

@Colinvparker @lambdatotoro
Yes, 210 makes complete sense.
I recently became curious about magic squares of primes and wondered if a run of nine existed and realised if so then they'd be *quite* large. Did a search up to like a gazillion with no luck and so looked to see if anyone else had done so, hence why I happened to have a note of that number. I've resisted looking for a proof of arbitrary length progressions so far as I want to think about it myself for a bit. :-) #fun #maths #primes

Secrecy must never be introduced into the Computational Sciences.

Mathematics is typically where we keep Secrets, and we aren't doing so any longer because Ethics.

#Maths #Ethics #ComputerScience #Computation #TheMoreYouKnow #TheMoreYouUnderstand #TheMoreYouGrok #TheMoreYouAre

#Maths #Mathematics What Cantor omitted to mention was that each subset of the power set of ℕ (except ∅) encodes for a unique natural number in binary form. For example, {5,4,1} → 11001 and {8,6,4,2} → 10101010. Now, if the subsets of P(ℕ) are assembled in strict order and numbered, we find that 25 → {5,4,1} → 11001 → 25 and 170 → {8,6,4,2} → 10101010 → 170. But then cantor ‘proved’ that there is no bijective function from ℕ to P(ℕ) so this must all be nonsense.

Recourir à la géométrie pour poser parfaitement une moquette.

#maths #mathematics #mathematiques #geometry #geometrie

@lambdatotoro
Many, I would imagine. But here's a very minor #fun one.
p=100996972469714247637786655587969840329509324689190041803603417758904341703348882159067229719 is the first of TEN consecutive #primes in #arithmetic #progression. The first or last nine of these may form a magic square, e.g....
#maths

Hey #mathematics bubble!
I keep running into open problems that have been exhaustively checked up to a ridiculously large number but we don't know if it's true everywhere.
Today it was "Are there any Wieferich primes other than 1093 and 3511?" and if there are the next one has to be ≥2^64, everything until then has been checked.

Question: are there any examples where that actually happened? Like an open problem where there actually was an example after a large™ gap like that?
#math #maths

Since a while now, I regularly times out in the evening on #IRC (only there for some reason). Since the server I'm on doesn't support a sane auth mechanism, I end up with "<nick>1" instead of "<nick>" (because I timeout and reconnect faster than what the server considers a timeout). Since it happens every evening, the even days it's restored to "<nick>".

There is a poetic beauty to the clockwork repetition of the bug fixing itself. It almost has the elegance of a double negation in #maths

#onthisday in 1915: Albert Einstein submitted a paper to the journal "Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin" that would fundamentally alter our understanding of the universe [1]. The four page paper contained what became known as the Einstein field equations, which relate the geometry of spacetime to the distribution of matter within it [2].

Einstein's field equations were presented in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor) [3].

#einstein #generalrelativity #einsteinfieldequations #physics #maths #maths

[Image credit: https://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/echo/einstein/sitzungsberichte/6E3MAXK4/index.meta]

References
--------------
[1] "Die Feldgleichungen der Gravitation", https://einsteinpapers.press.princeton.edu/vol6-doc/273

[2] "Einstein field equations", https://en.wikipedia.org/wiki/Einstein_field_equations

3] "Einstein tensor", https://en.wikipedia.org/wiki/Einstein_tensor

(1/2)

Dans la série « les chats sont très à l'aise en maths » : 😻

Photo 1 : séquence de Fibonacci (et c'est ma photo de profil)
Photo 2 : tangente d'une courbe
Photo 3 : droites perpendiculaires
Photo 4 : triangle isocèle

#catsofmastodon #caturday #caturdayeveryday #chatsdemastodon #catsoffediverse  #cats #chats #maths #mathematics #mathematiques #fibonacci

Any four numbers are the x-coordinates of the vertices of a regular tetrahedron.

(by Akira Weinberger: https://twitter.com/akivaw/status/1727850817489891702)

#geometry #desmos #math #maths #mathematics #mathviz #MathVisualization

#Fibonacciday #jourdefibonacci #maths mathématiques

You can't beat a good blackboard.
https://www.youtube.com/watch?v=Yi0cxiJ17tI
#maths

I've just fitted a polynomial to my scores out of ten for each actor's effort at playing #DoctorWho over the years and it predicts a score of 4229013373370/10 for number fifteen.
So that's nice.
#maths #statistics

Functional Analysis is a very cool topic which sits between infinite dimensional linear algebra and real and complex analysis (a couple of mind-blowing topics in their own right...).

A few of my (very nascent) notes are here: https://davidmeyer.github.io/qc/functional_analysis.pdf. The LaTeX source is here: https://www.overleaf.com/read/fgrrxmkycvry. As always, questions/comments/corrections/* greatly appreciated.

Happy Thanksgiving everyone!

#math #maths #mathematics #functionalanalysis

I have now been waiting twenty minutes for something that should have happened in ten minutes. Do I leave and come back via a detour another day to collect it, or hope that I get it in less time than the detour? I feel like a game theory exam question.

#maths #gameTheory

#CSSchallenge2023

An easy one this time. Code this with:

⚠️only CSS (just styles set on the root, nothing more)
❌no JS
❌no SVG
⚠️no images in general save for at most 2 CSS gradients
⚠️under 200 bytes of CSS

#css #coding #pattern #tiling #tessellation #maths #mathematics #geometry #frontend #webDev #webDevelopment

Next best thing.

https://arxiv.org/pdf/2106.11285.pdf

#mathematics #maths #math

An exact solution for the goat problem:
https://www.youtube.com/watch?v=ZdQFN2XKeKI
#Numberphile #maths #math #goats

Toying with using #SVG lighting filters for #CSS 3D shapes... 🤔

(not happy with it, perf sucks huge donkey dicks, 3D rotation is choppy as fuck...)

#coding #frontend #3D #maths #mathematics #geometry #svgFilter #webDev #webDevelopment

Think of a number:
https://www.youtube.com/watch?v=KdZrxkix9Mk
#maths #numbers #math

Berlin.

Polyhedra & fluffy toys.

But what first got my attention in that shopping complex were the anti-suicide nets. Seeing the prices though... they make total sense.

That big snow leopard costs as much as I make in a fucking year before taxes, ffs! Not that I want/ need it.

#berlin #inflation #polyhedra #geometry #3D #toys #maths #mathematics #fml #ffs #decoherence

1/7
Last week for #MathsMonday we showed that Terms are separated by any operators, not just + and -, contrary to the impression one might get from this #Maths textbook. This week we'll again #DoTheMaths but on binary and unary #Math operators, and deduce for ourselves the #Mathematics properties of them. As far as I'm aware, they don't have a name, so I'm gonna call them TerAnds - the group of an operator and associated operand(s) 🙂

First note what the textbook says about an invisible + ...

Whenever I see this guy on #BlackPenRedPen I think...
#DoctorWho #maths #YouTube #math

#Maths #Mathematics. When a mathematician invokes God in an attempt to understand the infinities, they have left the path of wisdom.

This is one of my favorite cartoons illustrating quantum superposition [1].

#math #maths #quantumsuperposition #schrodingerscat #physics

References
--------------
[1] "Quantum superposition", https://en.wikipedia.org/wiki/Quantum_superposition

As we know, the demographics on #Mastodon are different to the other places, and I'd like to try a little #Mathematics experiment with this #Maths #poll and see what difference there might be in the results here vs. there, just out of curiosity.

Thank you to everyone who participated in this poll. Discussion of the results and the answer at https://dotnet.social/@SmartmanApps/111479903041615089

What is 8÷2(1+3)=?

@SasquatcherGeneral
"waiting for somebody to respond citation needed or demanding proof"
As a #Maths #teacher I've had people (especially at the other place) refuse to believe me even after I've presented them with #Mathematics textbook references, then they'll quote a ChatGPT #Math answer that "proves" I'm wrong. 😂