#Mathematics
One day, one decomposition
A051507: Primes p such that p*q+2 is prime, where q is next prime after p
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051507.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051507.html
#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #primenumbers #graph #threejs #webGL
Some interesting architecture in Brisbane city, last night.
Let's have a look at this long-defunct Brisbane Telegraph newspaper.
Letter to the Editor, 3 Jan 1936:
'Sir.- In the paper for examination for State scholarship in mathematics on Dec 18, 1935, there appears to be an ambiguity in question 8:
'A sheepman shears 5,400 sheep...'
Mathematics both reflects and transmits a dominant culture.
I can pick a colonial invader/settler society when I see its historical maths curriculum problems.
#mathematics #colonialism
Straightforward question about derivative computations today. See my thought process and solution here:
I really like the original #lyrics for #Hallelujah. Just can't get them out of my head.
https://www.youtube.com/watch?v=NOCsdhzo6Jg
#music #song #math #maths #mathematics
t's dead! The academic world is more than 10 years behind, they'll never catch up. Math is no longer open source, it's in the hands of intelligence agencies and corporations.
#FundamentalTheoremOfArithmetic #math #maths #mathematics #sequences #OEIS #NumberTheory #PrimeNumbers #JavaScript #php #graph #3D #classification #primes #threejs #webGL #integer #decomposition #numbers #theory #equation #graphs #sieve #fundamental #theorem #arithmetic
C'est mort ! Le monde académique a plus de 10 ans de retard, ils ne pourront jamais les rattraper. Les maths ne sont plus "open source", elles sont dans les mains des agences de renseignement et des corporations.
#FundamentalTheoremOfArithmetic #math #maths #mathematics #sequences #OEIS #NumberTheory #PrimeNumbers #JavaScript #php #graph #3D #classification #primes #threejs #webGL #integer #decomposition #numbers #theory #equation #graphs #sieve #fundamental #theorem #arithmetic
"It is impossible to be a mathematician without being a poet in soul."– Sofia Kovalevskaya (1850–1891), quoting "one of the leading mathematicians of our century" (probably Karl Weierstrass).
#quote #mathematics #maths #math #poet
Without judgment:
A lot of math art involves writing, either algebraic expressions and equations (quadratic formula, Pythagorean theorem, ...), or an illustrated quote referring to doughnuts and coffee cups, or (misattributing Erdős instead of Alfréd Rényi) coffee and theorems.
To me, the power and beauty of mathematics is insight, and the older I get, the less insight feels naturally expressed in symbols (though symbols may be a particularly efficient tool to convey insight to others with suitable training).
With age as well, mathematics has come to seem a human invention and a thin veneer on reality. Mathematics may be by far the most precise and flexible description we have of physical phenomena, but fundamentally mathematics is not reality. I fear that mistaking mathematics for reality -- at levels from fundamental physics to the social sciences -- underwrites a certain disregard for Life and the Mystery of Existence.
"Imagination, Forge" is an attempt to capture this illusory reality of mathematics, with sympathy and as a cautionary reminder.
https://diffgeom.com/products/imagination-forge-wall-art-poster
Source : X-Twitter / Angel Manuel Ramos del Olmo
https://twitter.com/AMRamosDelOlmo/status/1732739806084362407
🎄Calendrier de l’avent des mathématiques insolites & amusantes🎄
Les mathématiques sont partout, il suffit de regarder. Avec ce calendrier, chaque jour, un regard, que j'espère plaisant voire amusant, sur les mathématiques.
Et pour les retrouver plus facilement, voici un index que je mettrai à jour au fur et à mesure.
Jour #7 — Plaque d'égout https://c.im/@etcetera/111538510734539729
Jour #6 — Illusion d'optique du cylindre ambigu https://c.im/@etcetera/111533140737686089
Jour #5 — Google https://c.im/@etcetera/111527179878900474
Jour #4 — Sapin de Noël https://c.im/@etcetera/111521441307267287
Jour #3 — série Les Simpson
https://c.im/@etcetera/111515923143415880
Jour #2 — Tableau de peintre https://c.im/@etcetera/111510342040574329
Jour #1 — Pain boule https://c.im/@etcetera/111506651357488741
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#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques
December's #Bletchley & #MK
@MathsJam will be *this coming Tuesday (12th December)* at the Ship Ashore in Willen, MK (https://maps.app.goo.gl/K8LwiVpTD8Ra6YWv6). There's plenty of free parking, and it shouldn't be too busy or loud.
It would be fantastic to see anyone there who has a generally positive disposition towards #Mathematics, whether you're local(ish) to Milton Keynes or just passing through.
No skills or qualifications are necessary; you just need to have a "Maths? Cool!" kinda attitude.
If you're not nearby and thinking "oh, man, why am I not nearby this cool maths thing?" then find your absolute localest #MathsJam right here: https://www.mathsjam.com/find-a-jam/
The largest #PrimeNumber (so far) was discovered five years ago today!
It’s a #MersennePrime discovered by a computer used by Patrick Laroche, an IT professional from Florida, who used the #prime-finding software Prime95 to stress-test his builds. It’s part of something called #GIMPS (Great Internet Mersenne Prime Search) that anyone can participate in and maybe discover the next largest Mersenne prime!
![Excerpt from the linked article, reading:
“GIMPS Discovers Largest Known Prime Number: 2 [raised to the power of] 82,589,933-1
BLOWING ROCK, NC, December 21, 2018 -- The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2 [raised to the power of] 82,589,933-1, having 24,862,048 digits. A computer volunteered by Patrick Laroche made the find on December 7, 2018. Patrick is one of thousands of volunteers using free GIMPS software available at www.mersenne.org/download/.
The new prime number, also known as M82589933, is calculated by multiplying together 82,589,933 twos, and then subtracting one. It is more than one and a half million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 51st known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 17 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.”](https://s3.eu-central-2.wasabisys.com/mastodonworld/cache/media_attachments/files/111/538/942/527/581/635/small/3ca4d61a60f6c5fe.jpeg)
About 2,200 years ago, the Greek geometer Apollonius of Perga wrote a book called “Tangencies” about how to construct a circle that’s tangent to any three others. This work was lost to time but can be seen here in a 9th-century Arabic translation.
Two Students Unravel a Widely Believed Math Conjecture. via @QuantaMagazine
https://www.quantamagazine.org/two-students-unravel-a-widely-believed-math-conjecture-20230810/
"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk."
"God made the integers, all the rest is the work of man."
In a lecture to the Berliner Naturforschung-Versammlung, 1886; quoted in the obituary “Leopold Kronecker”, by H[einrich] Weber, in Jahresbericht der Deutsche Mathematiker Vereinigung, 1893, page 19.
~Leopold Kronecker (December 7, 1823 – December 29, 1891)
Leopold Kronecker German mathematician was born #OTD in 1823.
In an 1853 paper on the theory of equations and Galois theory he formulated the Kronecker–Weber theorem, without however offering a definitive proof. He also introduced the structure theorem for finitely-generated abelian groups. In an 1850 paper, On the Solution of the General Equation of the Fifth Degree, Kronecker solved the quintic equation by applying group theory. via @wikipedia
🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #7🎄
Si les plaques d’égout sont rondes (voir Figure #1), ce n’est pas un hasard. Ce choix est lié à des raisons de sécurité. Imaginez une bouche d’égout carrée, ou encore en forme de triangle équilatéral. Si l’employé manipule le couvercle sans soin il peut, par inadvertance, l’échapper dans le trou, ce qu’il ne peut pas faire avec une bouche d’égout ronde.
Mais la forme ronde n’est pas la seule qui possède cette propriété. Voir Figure #2: plaque d'égout en forme de triangle de Reuleaux.
La famille des TRIANGLES DE REULEAUX (voir Figure #3) présente des propriétés similaires aux formes rondes, et dont les applications ne se limitent pas aux bouches d’égout.
On part avec un triangle équilatéral de côté R. À partir de chaque sommet on trace un arc de cercle de rayon joignant les deux autres sommets.
Mais cela suffit-il à assurer que le triangle de Reuleaux, lorsqu’on le manipule dans l’espace, ne puisse passer au travers d’un trou horizontal d’un rayon r < R ? On démontre que oui, et je vous épargne ici la démonstration !😉
Pour terminer, un mot sur monsieur Franz REULEAUX (1829 - 1905). (Voir Figure #4)
Ingénieur allemand, spécialisé dans l’analyse et la conception des mécanismes (mécanique appliquée). Sa carrière a été partagée entre l’enseignement et la recherche, d'abord à l'école polytechnique de Zurich puis à l'école industrielle de Berlin dont il fut recteur en 1890.
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#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques
One day, one decomposition
A051283: Numbers k such that if one writes k = Product p_i^e_i (p_i primes) and P = max p_i^e_i, then k/P > P
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051283.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051283.html
#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #product #primes #primenumbers #graph #threejs #webGL
The bundle Visual Category Theory by Dmitry Vostokov is on sale on Leanpub! Its suggested price is $39.95; get it for $15.00 with this coupon: https://leanpub.com/b/categories/c/socialpostsale20231204 #ComputerScience #Mathematics #FunctionalProgramming #GraphTheory
So, this obscure piece of math is going to become extremely important in figuring out what is going on with climate change.
https://en.wikipedia.org/wiki/System_identification
The innovation of relatively cheap microprocessors was a paradigm shift, completing advanced mathematical calculations using binary logic.
Today’s “innovation” is about getting expensive microprocessors to learn word problems in English so they can do math problems.
The clerical talent recruited into the British East India Company, which was the design template for our modern #education system, is rolling over with envy.
In today’s viewer submitted problem, I don’t quite get to a full answer, but I felt like I was on the right track. See my thought process and solution here:
#ukpolitics #immigration #mathematics
I propose a constructive amendment to the Immigration Bill to end another irrationality in British life. That is that henceforth pi = 3. It will disapply any foreign standard leading to the imposition of countless decimal places on our hard working people. Any illegal decimals found will be dispatched to Rwanda without any referral to the IMA.
We believe this will square the Great British Circle.
"It can be of no practical use to know that π is irrational, but if we can know, it surely would be intolerable not to know." – attributed to Edward Charles Titchmarsh (1899-1963)
#quote #mathematics #math #maths
Visualization of π being an irrational 🎵 🖼️
https://youtube.com/shorts/aUDYWYqtAR4
Keywords: #pi #mathematics #geometry #science #visualization #vulgarisation
Weierstrass's continuous, nowhere-differentiable functions are uniform limits of (smooth!) trig polynomials. In the image, virtual mountain ranges lie beneath the graphs of successive approximations to a Weierstrass function, translated horizontally (added: and vertically) for visual effect.
https://diffgeom.com/products/nowhere-differentiable-desert-mug
🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #6🎄
Le japonais Kokichi Sugihara (Figure #3), spécialisé en ingénierie mathématique, est un expert des illusions d'optique. C'est lui par exemple l'auteur de la fameuse illusion du cylindre ambigu, primée en 2016. Voir Figure #1.
Justement, on va pouvoir la reproduire assez facilement à la maison en suivant ces étapes (voir Figure #2), et en utilisant du matériel simple, comme le tube en carton du rouleau de papier de toilette 🧻 :
1) Écrasez légèrement le tube deux fois de façon orthogonale et ajoutez, sur un côté, trois points colinéaires.
2) En utilisant ces trois points comme repères, dessinez une ligne sinueuse, puis découpez le tube le long de cette ligne (les plus férus de maths calculeront la fonction sinusoïdale optimale).
3) Vous obtenez alors une forme aux bords recourbés qui se situe à mi-chemin entre un rhomboïde et un cylindre creux.
4) Placez enfin cette forme devant un petit miroir, et arrangez-la de sorte que l'illusion prenne forme. Le cerveau tendra alors à « régulariser » l'ambiguïté de la forme, et à ramener celle-ci à l'une ou à l'autre catégorie, selon le point de vue adopté par le spectateur.
Essayez, c'est facile et bluffant !
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#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques
Accelerated Windows API for Software Diagnostics by Dmitry Vostokov is on sale on Leanpub! Its suggested price is $49.00; get it for $36.75 with this coupon: https://leanpub.com/sh/zCJXXNmG #CAndCpp #OperatingSystemDevelopment #SoftwareEngineering #Apis #Software #Mathematics
Todays Task at #AdventOfCode is a slap in the face of all those who claim that school #mathematics has no real-world use 😜
One day, one decomposition
A051146: Sequence b(n) mentioned in A051145
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A051146.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A051146.html
#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #graph #threejs #webGL
Next was an amazing talk by Scott Kominers on matching algorithms at Harvard CMSA. Kominers reviews the fascinating history of matching (did you know that the AMA developed their resident matching algorithm before Gale and Shapley's paper was published?), the elegant math behind it, and more. Highly recommend https://www.youtube.com/watch?v=y6Gc0G_2Mf0 (3/8) #economics #mathematics
Why do immune responses vary depending on age?
#SFUMath Prof. Ben Ashby uses mathematical models & simulations to understand how infectious diseases evolve.
https://www.sfu.ca/research/scholarly-impacts/how-does-age-affect-immunity #SFU #SFUScience #mathematics #epidemiology #immunology
General #relativity has been wildly successful at describing how #gravity works and how it shapes the large-scale structure of the #universe.
#Space-time tells #matter how to move; matter tells space-#time how to curve.
Yet the #mathematics of general relativity is also profoundly counterintuitive.
What does a space look like if it is almost a #vacuum, having just a tiny amount of mass.
Is it necessarily almost flat?
#physics #cosmology
https://www.quantamagazine.org/a-century-later-new-math-smooths-out-general-relativity-20231130/
#GregoryChaitin - Is #Mathematics #Eternal?
https://www.youtube.com/watch?v=KEuylDsONxo
#Philosophy #PhilosophyOfScience #PhilosophyOfMathematics #Science #Math #Maths #Cantor #Ramanujan #SetTheory #God #Spirituality #Beauty #Transcendence #Numbers #Contradiction #Logic #Poincaré #Poincare #Euler #CloserToTruth #RobertKuhn
I'm looking for a subject for my master's thesis. I know I want to use #gametheory to simulate some behaviour on #social #networks. Question is, what? #Disinformation? #Voting systems? #Markets behaviour?
If you are aware of any recent #research around this area please cite it. And if you have a project in mind you'd like to see realized feel free to contact me.
#science #sociology #economy #physics #mathematics #ComputerProgramming #simulation #politicalscience #socialNetworks #graphTheory
Classement Pisa 2023 : la France chute lourdement en mathématiques, et c'est tout sauf une surprise (politiques & réformes désastreuses) 🥹🥹🥹
Today's problem took quite a bit longer than expected because of some arithmetic mistakes, but I eventually caught where I went wrong. See my thought process and solution here:
#Maths #Mathematics What happens when your graphing software can’t cope with r=2sin(nΘ+cos(nΦ)). Mathematically satisfying rendering of a nautilus shell at left, with n = 1.1. At right, with n = -2.6, something which almost (but not quite) resembles a dahlia.
"Mathematics is the door and the key to the sciences." – Roger Bacon (c. 1215-c. 1290)
#quote #mathematics #maths #math #sciences
Early in 2024 at the Differential Geometry math art shop, we anticipate introducing 3D printed pendants, earrings, and pins. (To start these will only be offered in the US.)
The plated brass pieces shown are cyclides of Dupin, flat Clifford tori in the three-sphere mapped to Euclidean three-space by stereographic projection. Each cyclide is divided into diagonal bands bounded by two "parallel" Villarçeau circles. Unlike the meridians and parallels of a torus, Villarçeau circles are images of great circles (here, Hopf circles) in the three-sphere.
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Algebraically, view the real three-sphere as the set of complex pairs \((z, w)\) satisfying \(|z|^{2} + |w|^{2} = 1\). A Clifford torus may be viewed as the set of pairs where \(|z|^{2} = |w|^{2} = \frac{1}{2}\), or may be rotated in either complex axis to arrange that the three-space image is not a circular torus. The multiplicative unit circle acts by scalar multiplication: \(\chi_{u}(z, w) = (uz, uw)\). This action preserves Clifford tori, which are unions of great circle orbits. The geometric effect, if realized, would "slide the diagonal bands along themselves," a cross between a barber pole and a smoke ring.
#Mathematics, #reading #tootsea
“Nearly 700,000 15-year-olds tested in 81 countries
1 out of 4 were low performers in maths, reading and science
#Singapore's students earned top marks in all subjects
Teen math & reading skills are in an unprecedented decline across dozens of countries.
COVID school closures are only partly to be blamed.”
An Easy-Sounding Problem Yields Numbers Too Big for Our Universe
Source : Quanta Magazine / Ben Brubaker
https://www.quantamagazine.org/an-easy-sounding-problem-yields-numbers-too-big-for-our-universe-20231204/
#mathematics #maths #math
What has caused the collapse in educational achievement in the Netherlands?
May other countries learn from our failures:
- Underpaying and overworking teachers, leading to a shortage; yes we’re that dumb
- Boring as fuck reading pedagogy (recognising transition words, topic sentences etc) so no kid learns to read
- Then, changing maths pedagogy so it becomes a reading comprehension exercise
#Education #Teachers #Reading #Mathematics #Netherlands #Nederland
🎄Calendrier de l’avent des mathématiques insolites & amusantes, Jour #5🎄
Certains nombres sont tellement grands que nous avons du mal à les imaginer. Gogol par exemple est un nombre égal à 1 suivi de 100 zéros (soit 10¹⁰⁰).
Le mot gogol est cité pour la première fois en anglais, googol, par le mathématicien américain Edward Kasner (1878 - 1955) dans son livre Mathematics and the Imagination paru en 1940. Kasner aurait demandé à son neveu alors âgé de 9 ans de baptiser le nombre qu'il venait de créer. Il lui aurait répondu simplement : « Googol ».
Le gogol est explicitement repris plus tard par les fondateurs de Google pour nommer leur entreprise : « Google a choisi ce terme pour symboliser sa mission : organiser l'immense volume d'information disponible sur le Web. »
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#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques
"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)
The image below is an experimental crossed-eyes stereogram for a poster of the chaotic attractor for the ODE system
\begin{align*}
\frac{dx}{dt} &= 10(y - x), \\
\frac{dy}{dt} &= x(28 - z) - y, \\
\frac{dz}{dt} &= xy - \tfrac{8}{3}z.
\end{align*}
If you're willing to comment, it would be helpful to know whether the stereo effect is difficult to achieve and/or maintain.
Episode 2 of “it’s not just numbers” is out!
In this episode we meet Alef Sterk and Henk van Waarde. We discuss our experiences transitioning from high school and how they needed to adjust to study mathematics at university.
In our chat we touch upon getting used to the extra freedom and compare how we studied and what made the difference for us.
Are we giving the wrong incentives in how learning is evaluated, challenging instead a good attitude to learn? You won’t find an answer to this, but I hope there will be enough food for thoughts and a good preparation on the next episode where we will discuss what goes into teaching a course and all the unseen background work.
You can listen to us on https://podcasters.spotify.com/pod/show/not-just-numbers/episodes/S1E02---Studying-mathematics--with-Alef-Sterk-and-Henk-van-Waarde-e2bs7f3 and on all major platforms
An open disk and a radially-slit open disk are conformally equivalent: There is an invertible holomorphic mapping from one to the other. The grid lines are the images of concentric circles and rays from the origin.
Omar Khayyam Persian mathematician, astronomer, and poet died #OTD in 1131. As a mathematician, he is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics. As an astronomer, he calculated the duration of the solar year and designed the Jalali calendar. via @wikipedia
Books by Omar Khayyam at PG:
https://www.gutenberg.org/ebooks/author/1787
#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.
🎄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 !
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#calendrierdelavent #adventcalendar #maths #mathematics #mathematiques
"Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language.""
Can Programming...
~John W. Backus
American Mathematician John Warner Backus was born #OTD in 1924.
He directed the team that invented and implemented FORTRAN, the first widely used high-level programming language, and was the inventor of the Backus–Naur form (BNF), a widely used notation to define formal language syntax. He later did research into the function-level programming paradigm, presenting his findings in his influential 1977 Turing Award lecture "Can Programming Be Liberated from the von Neumann Style?"
@monsoon0
' "Most curious," Horowitz said, like a mathematician pondering a problem.'
(From a detective novel of the flight-readage type)
#mathematics #mathematicians
The output from my latest simulation showing that John Clauser is a nincompoop and so is the Nobel committee.
3,700-year-old Babylonian stone tablet gets translated, changes history
They were doing trigonometry 1500 years before the Greeks.
Most historians have credited the Greeks with creating the study of triangles' sides and angles, but this tablet presents indisputable evidence that the Babylonians were using the technique 1,500 years before the Greeks ever were.
Mansfield and his team are, understandably, incredibly proud. What they discovered is that the tablet is actually an ancient trigonometry table.
#History #Mathematics #Babylon #Trigonometry #Archeology #Amazing
upworthy.com/3700-year-old-bab…
🎄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
Due to very long habit that is proving hard to break, I use dollar signs to enter and leave inline math mode in LaTeX and MathJax. It would be convenient to have emacs convert opening and closing dollar signs to \\( and \\) automatically on the fly.
A bit of web searching on how to accomplish this hasn't turned up anything except man pages on writing emacs lisp functions (which I can presumably figure out/learn eventually) and other composition software (which is less convenient than continued habit-breaking).
I'd be grateful if you, dear reader, could point to an existing snippet of emacs lisp to do this intelligently: Able from context to distinguish an "opening $" and a "closing $", and both from an "intentional \$". TIA!
🎄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
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
"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."
A Mathematician's Apology
~Godfrey Harold Hardy (7 February 1877 – 1 December 1947)
Hardy had a long collaboration with John Edensor Littlewood, and he discovered and supported the work of Srinivasa Ramanujan. via @wikipedia
English mathematician, known for his achievements in number theory & mathematical analysis G. H. Hardy died #OTD in 1947.
In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics. Hardy is usually known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology, often considered one of the best insights into the mind of a working mathematician written for the layperson.
G. H. Hardy @ PG:
https://www.gutenberg.org/ebooks/author/39236
"There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world."
As quoted in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane
~Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856)
Russian mathematician and geometer Nikolai Lobachevsky was born #OTD in 1792.
He is known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula.
Another of his achievements was developing a method for the approximation of the roots of algebraic equations (Lobachevsky method). via @wikipedia
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
Infinity or division by zero error?
JavaScript or PHP? Pick your side 😜
This is the best mathematical explanation of the "division by zero" problem I've seen, explained by #EddieWoo, watch this: https://www.youtube.com/watch?v=J2z5uzqxJNU
"That the study of mathematics and their application to astronomy are full of interest will be allowed by all who have devoted their time and attention to these pursuits; and they only can estimate the delight of arriving at truth, whether it be in the discovery of a world, or of a new property of numbers."
Mechanism of the Heavens, Preliminary Dissertation (p. 2), John Murray. 1831
~Mary Somerville (26 December 1780 – 29 November 1872)
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.
... and an animation loop where the values of the fields rotate counterclockwise through a full turn.
A plane vector field assigns a vector to each point of a plane region. Near an isolated zero, a vector field is characterized qualitatively by an integer, the index, which counts how many times the value rotates upon tracing a small circle about the zero.
The formula \(e^{i\theta} = \cos\theta + i\sin\theta\) gives a pleasant explanation of the shapes in the poster. If \(k\) is an integer and \(r\) a positive real number, the field whose value is \(re^{ikt}\) at the unit complex number \(e^{it}\) models a field of index \(k\) along the unit circle. The tips of the arrows are the vector sum,
\[
e^{it} + re^{ikt} = e^{it}(1 + re^{i(k-1)t}),
\]
a path having \(|k - 1|\)-fold rotational symmetry about the origin.
https://diffgeom.com/products/topological-index-wall-art-poster
Quand la géométrie rencontre la sorcellerie.😉
Abraham de Moivre French mathematician who was a pioneer in the development of analytic trigonometry & in the theory of probability died #OTD in 1754.
He wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers. He 1st discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the nth power of the golden ratio φ to the nth Fibonacci number. He also was the 1st to postulate the central limit theorem. via @wikipedia
![The doctrine of chances: or, a method of calculating the probabilities of events in play, by A. de Moivre .... - London : printed for A. Millar, in the Strand, 1761. - [4], xi, [1], 348 p. ; 4º .](https://assets.toot.cafe/cache/media_attachments/files/111/482/211/697/117/684/small/df24d9cffb48c9af.jpg)
"[The Analytical Engine] might act upon other things besides number … the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent."
(Notes on the Analytical Engine invented by Charles Babbage)
~Augusta Ada King, Countess of Lovelace (10 December 1815 – 27 November 1852)
Ada Lovelace's notes were labelled alphabetically from A to G. In Note G, she describes an algorithm for the Analytical Engine to compute Bernoulli numbers. It is considered to be the first published algorithm ever specifically tailored for implementation on a computer, and Ada Lovelace has often been cited as the first computer programmer for this reason. The engine was never completed and so her program was never tested. via @wikipedia
British Mathematician also called the first computer programmer Ada Lovelace died #OTD in 1852. She is known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine. She was the first to recognise that the machine had applications beyond pure calculation.
Babbage's friend Charles Wheatstone commissioned Ada Lovelace to translate Menabrea's paper into English. She then augmented the paper with notes, which were added to the translation.
#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.
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
Sperm movement and math. Yes there is a relationship. Great article.
#Mathematics #Sperm #Flagella #ReproSci #Reproduction #Science #scicomm
Newton's own annotated copy of Principia Mathematica.
The Cambridge papers of Sir Isaac Newton, including early drafts and Newton’s annotated copies of Principia Mathematica have been added to UNESCO’s International Memory of the World Register. The chief attractions in the Cambridge collection are Newton’s own copies of the first edition of the Principia (1687), covered with his corrections, revisions and additions for the second edition.
via Cambridge University Library
My nautilus with golden rectangle print for Fibonacci Day. November 23 if written in MM/DD format recalls the #mathematician Leonardo Bonaccio of Pisa (c. 1170 - c. 1240 or 50) aka Fibonacci’s sequence (1,1,2,3…) where each number is the sum of the previous two. He used it to describe rabbit populations, but the sequence is commonly observed in nature, 🧵1/2
#linocut #printmaking #mathematics #mathart #sciart #nautilus #GoldenRatio #Fibonacci #fibonacciday2023 #FibonacciDay #MastoArt
English Mathematician John Wallis was born #OTD in 1616.
He is credited with introducing the symbol ∞ to represent the concept of infinity. He similarly used 1/∞ for an infinitesimal. John Wallis was a contemporary of Newton and one of the greatest intellectuals of the early renaissance of mathematics. via @wikipedia
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