Lmst

A049097: Primes p such that p+1 is squarefree

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A049097.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A049097.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A049097.html

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

Decomposition into weight × level + jump of A049097 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A049097 in 2D (log(weight), log(level))

We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

#decompwlj #math #mathematics #maths #sequence #OEIS #graph #natural #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of natural numbers: the fundamental theorem of arithmetic and the sieve of Eratosthenes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of natural numbers

Decomposition into weight × level + jump of prime numbers: in 2D with sequences on the OEIS: a new classification of primes

Graph in 2D (log(weight), log(level)) of the decomposition into weight × level + jump of prime numbers

A049096: Numbers k such that 2^k + 1 is divisible by a square > 1

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A049096.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A049096.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A049096.html

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

Decomposition into weight × level + jump of A049096 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A049096 in 2D (log(weight), log(level))

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers by Joseph Mazur, 2024

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today?

#books
#nonfiction
#maths
#mathematics
#history
#notation

In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us, how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics From words to abbreviations to symbols, this entertaining history shows how math evolved to the familiar forms we use today. "An enjoyable read.

" — Science "If you enjoy reading about history, languages and science, then you'll enjoy this book. . . . you don't have to be a mathematician to enjoy this informative book.
" — Guardian.com's, GrrlScientist "Fascinating."

Y should I Sine the contract by myself when my X can Cosine and pay the Tan grand on my car loan

Stolen from a friend, who knows who they stole it from. Mnumonic to remember that sin gives the Y coord, cos gives the X coord, of points on the unit circle.
#precalc #teaching #maths #trig

I've tried several sources to find a proof of Bezout's Identity that is clear and simple.

This one is my favourite so far.

(I'm revisiting, before I do an exercise to prove that \[ax \equiv b \pmod n
\] has g=gcd(a,n) incongruent solutions, provided g divides b )

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

#maths #numbertheory

Ooh, someone's added a review for The Mathematicians' Library on @thestorygraph.com@bsky.brid.gy . I'm really interested in hearing about books that I didn't include but people think I should have! app.thestorygraph.com/reviews/fe38... #Maths #MathsToday #Books

Review by peterdonelan - The M...

Ooh, someone's added a review for The Mathematicians' Library on @thestorygraph

I'm really interested in hearing about books that I didn't include but people think I should have!

https://app.thestorygraph.com/reviews/fe385221-d1a0-4da8-8d2c-c5c7dc106ec9

#Maths #MathsToday #bookstodon

"The considerations, which led up to the construction of the rational domain, were the first steps in a historical process called the arithmetization of mathematics. This movement, which began with Weierstrass [...], had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics."–Tobias Dantzig (1884–1956)
#quote #mathematics #maths #math

Quote from Tobias Dantzig : "The considerations, which led up to the construction of the rational domain, were the first steps in a historical process called the arithmetization of mathematics. This movement, which began with Weierstrass [...], had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics."

"Les considérations qui ont conduit à la construction des corps ont été les premières étapes d'un processus historique appelé arithmétisation des mathématiques. Ce mouvement, qui a commencé avec Weierstrass [...], avait pour objet la séparation de concepts purement mathématiques, tels que nombre, relation, et ensemble, des idées intuitives que les mathématiques avaient acquises par une longue association avec la géométrie [...]"– Tobias Dantzig (1884–1956)
#citation #mathématiques #maths #math

Citation de Tobias Dantzig : "Les considérations qui ont conduit à la construction des corps ont été les premières étapes d'un processus historique appelé arithmétisation des mathématiques. Ce mouvement, qui a commencé avec Weierstrass [...], avait pour objet la séparation de concepts purement mathématiques, tels que nombre, relation, et ensemble, des idées intuitives que les mathématiques avaient acquises par une longue association avec la géométrie et la mécanique."

Retrouvez nos conseils didactiques et un nouveau jeu pour la maternelle ! La balayette de Josette inspirée de la scopa ou des oiseaux compteurs ♣️❤️
Associer différentes représentations du nombre et décomposition 😉
➡️ https://www.mathebdo.fr/
#mathebdo #maths #teampe #maths #Pédagogie #Numérique #Classe #TeamProf
@scollectif

Theorem of the Day (November 24, 2025) : The Wedderburn-Artin Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/Algebra/Wedderburn/TotDWedderburn.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#123

#mathematics #maths #math #theorem @Theoremoftheday

Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem.

The Wedderburn-Artin Theorem : Any finite dimensional semisimple algebra is isomorphic to a direct product of matrix algebras over division algebras.

Now this animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com
A little more work on axis sizing and controls.

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

4: The palindromes in base 10 (A002113) ➡️ https://decompwlj.com/3DgraphGen/Palindromes.html

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

3: The triangular numbers (A000217) ➡️ https://decompwlj.com/3DgraphGen/Triangular_numbers.html

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

2: The prime numbers (A000040) ➡️ https://decompwlj.com/3DgraphGen/Prime_numbers.html

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

Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
🧵⬇️

1: The natural numbers (A000027) ➡️ https://decompwlj.com/3DgraphGen/Natural_numbers.html

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

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#MathsMonday
#Mathematics #Maths #Math
This week I want to come back to the "proof" that 0.(9)=1, which I debunked at https://dotnet.social/@SmartmanApps/112711027003047449. At the time, I said there was insufficient information, because it was unclear whether 1 was meant to be interpreted as the integer 1, or as a limits of accuracy 1. i.e. 1±½. People are taking it as the integer 1, in which case I can now thoroughly debunk that argument with that interpretation...