One day, one decomposition
A039004: Numbers whose base-4 representation has the same number of 1's and 2's

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A039004.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A039004.html

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

It's a funny thing, but the actual #mathematics of a Bell test, which I am writing in a paper now (for direct distribution, not publication in the failed journal system), is quite beautiful.

It is a pair of wheels that, when they turn in unison, produce a wave-like effect in the detectors. (One has to imagine PBS that can do a whole 360.) With INVARIANT correlation coefficient.

Yet those incompetent #quantum #physics dunderheads cannot see it, because they are unqualified cultists.

✨ Joint Max Planck-Weizmann Postdoctoral Programme ✨

The Max Planck Society (@maxplanckgesellschaft) and the Weizmann Institute of Science jointly offer outstanding postdoctoral researchers in the fields of #physics, #chemistry, #mathematics, #ComputerScience and #EarthSciences a prestigious four-year appointment in a unique research environment.

🚨 Application dealine: 1 November 2023

☑️ Get more info: https://www.mpg.de/20566192/max-planck-weizmann-postdoc-programm

The best A – A ≠ 0 paradox
Source : Youtube / Mathologer

https://www.youtube.com/watch?v=VO2A6I3Woos
#mathematics #math #maths

1/4
#MathsMonday
1917 (iii) - Terms included in denominator
My investigation into (alleged) changes in #Mathematics rules in 1917 started with claims that the number of terms included in the denominator of a #Math expression was changed in 1917 (though I've yet to find any actual evidence of this - let me know if you have a reference for it). Some mentioned Lennes' letter, yet his letter says nothing at all about this! For now, let's assume it's true and see what that would mean for #Maths...

"A mathematical problem at its heart, cake cutting connects rigorous reasoning to questions of human preferences and real-world issues, and so attracts not only mathematicians, but also computer scientists, economists, social scientists and legal experts. Questions of fairness (and unfairness) are decidedly universal"

https://www.sciencenews.org/article/cake-cutting-math-problem-fairness-envy

#Mathematics #Resources #Sharing #Fairness

Some useful inequalities:

1. Cauchy–Schwarz inequality

\[\displaystyle\sum_{k=1}^na_kb_k\leq\sqrt{\sum_{k=1}^na_k^2}\sqrt{\sum_{k=1}^nb_k^2\]

2. Hölder's inequality

\[\displaystyle\sum_{k=1}^n\left|a_kb_k\right|\leq\left(\sum_{k=1}^n|a_k|^p\right)^{1/p}\left(\sum_{k=1}^n|b_k|^q\right)^{1/q}\]

3. Minkowski's inequality

\[\displaystyle\left(\sum_{k=1}^n\left|a_k+b_k\right|^p\right)^{1/p}\leq\left(\sum_{k=1}^n|a_k|^p\right)^{1/p}+\left(\sum_{k=1}^n|b_k|^p\right)^{1/p}\]

4. Hardy's inequality

\[\displaystyle\sum_{k=1}^\infty\left(\dfrac{a_1+a_2+\cdots+a_k}{k}\right)^p\leq\left(\dfrac{p}{p-1}\right)^p\sum_{k=1}^\infty a_k^p\]

#Inequality #Cauchy #Schwarz #Hölder #Minkowski #Hardy #Maths #Mathstodon #Mastodon #Mathematics

"The chemist smiles at the childish efforts of alchemists, but the mathematician finds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any research of today." – Florian Cajori (1859-1930)
#quote #mathematics #math #maths

#puzzle #énigme #logical #logique #maths #mathematics
Ce collier de perles est formé de 25 cercles de même taille. La ficelle passe par le centre de chaque cercle. La zone délimitée par la chaîne à l'intérieur de chaque cercle est ombrée en bleu et les zones restantes des cercles sont ombrées en orange. Quelle est l'aire la zone orange moins la zone bleue ?

Note: on peut répondre en faisant des calculs géométriques. Mais il y a une autre manière 😘 !

Merci de BOOSTER + répondre en mode CW.

Carnival of Mathematics 219
Source : The Aperiodical / Reflections and Tangents

https://karendcampe.wordpress.com/2023/09/09/carnival-of-mathematics/
#mathematics #math #maths

@Mnaudin
As a #Mathematics teacher who uses the #Maths method on the left, I can tell you I would never write out all those steps of working out. In fact I wouldn't even write it out. I do that one in my head as 310+2*31=310+62=372. Only takes 2-3 seconds. Not sure if there's a similar mental technique for the #Math method on the right(?), but as far as I can see method on the left is actually the far quicker of the two.

J'adore :shibahearteyes:
Les agriculteurs peuvent être de grands inventeurs de ce qui est nécessaire !

Ici, on trouve des mathématiques, de la physique, de l'ingénierie, du low-tech, et ... des vaches. 🐮

On peut apprécier l'utilisation d'une circonférence (C = 2πr) et la fuite de particules / nourriture par une ouverture, pour encourager un espacement équidistant des vaches essayant de manger. Tout est parfait !
#engineering #mathematics #physics #lowtech #agriculture #cows

#maths #math #mathematics #mathematiques #mathstodon
Dans ce match Chine vs. Japon, on retrouve la « distributivité » chez les deux, chacun à sa manière.

Explication de la méthode japonaise :
Voir pouète suivant.

"It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the sciences." – Eric Temple Bell (1883-1960)
#quote #mathematics #math #maths

The Biggest Smallest Triangle Just Got Smaller
Source : Quanta Magazine / Leila Sloman

https://www.quantamagazine.org/the-biggest-smallest-triangle-just-got-smaller-20230908/
#mathematics #maths #math #triangle

Decomposition into weight × level + jump of prime numbers:

in 3D, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Prime_numbers.html

a new classification of primes ➡️ https://decompwlj.com/primedecomp.php

#decompwlj ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump

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

One day, one decomposition
A038772: Numbers not divisible by any of their digits

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A038772.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A038772.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #divisible #digits #graph #threejs #webGL

Join @EUCYS on 13-15 September in Brussels 🇧🇪
➡️Over 130 young scientists aged 14 to 20, from 36 countries🌍will present their scientific projects in #Mathematics #Biology #Chemistry #Engineering and more. Come & meet these young talents!
https://eucys2023.eu

🐦🔗: https://n.respublicae.eu/REA_research/status/1700039386190991718

Dans cette vidéo, le célèbre professeur de mathématiques Howie Hua dit qu'il lui a fallu beaucoup trop de temps pour réaliser que la différence entre les carrés signifie littéralement « quelle est la différence entre ces deux carrés ? » Voici comment visualiser x² - y² = (x+y) (x-y).
#mathematics #maths #mathstodon #mathematiques #math

"Most of the time, conceptualizing means making models. A model in our mind of an external object [...]. When we need to communicate this model from one person to another, we need to do it accurately. [...]" – Jean-Marie Souriau (1922-2012)
#quote #mathematics #maths #math