Lmst

One day, one decomposition
A156683: Integers that can occur as either leg in more than one primitive Pythagorean triple

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A156683.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A156683.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primitive #Pythagorean #triple #graph #threejs #webGL

Decomposition into weight × level + jump of A156683 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A156683 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

#USNews #Math #Science #Trigonometry
#Louisiana students who solved the #Pythagorean theorem discover nine more solutions to it.
https://www.nola.com/news/education/st-mary-students-find-extra-ways-to-solve-pythagorean-theorem/article_ef150484-9604-11ef-babc-dfee87db480d.html

Two teenagers have once again proved an ancient math rule.

From Science News: “Some people have the impression that you have to be in academia for years and years before you can actually produce some new mathematics,” says mathematician Álvaro Lozano-Robledo of the University of Connecticut in Storrs.

https://flip.it/_48RXz

#Math #Mathematics #Science #Maths #Pythagorean #Trigonometry

This level of mathematics isn't my thing, but congratulations to these two women for what they've achieved!

High school students who came up with 'impossible' proof of #Pythagorean theorem discover 9 more solutions to the problem

https://www.livescience.com/physics-mathematics/mathematics/high-school-students-who-came-up-with-impossible-proof-of-pythagorean-theorem-discover-9-more-solutions-to-the-problem

> In a new peer-reviewed study, Ne'Kiya Jackson and Calcea Johnson outlined 10 ways to solve the Pythagorean theorem using trigonometry, including a proof they discovered in high school.

#KnowledgeByte:We all know about Popular Pi Day (3/14). But do you know about rare #Pythagorean Day?

https://knowledgezone.co.in/posts/Pythagorean-Day-604e0888c23493c7af3844de

I haven't read Way of the Peaceful Warrior, but I very much value #Dan #Millman's interpretation of #Pythagorean #numerology in The Life You Were Born to Live.

I see now that original book has been made into a film.

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

Anyone here both read the book and seen this film? I'm wondering if I can get a good sense of the original book by just watching this film, which is a departure for me who traditionally would never think of "cheating" like this.

#wayofthepeacefulwarrior

One day, one decomposition
A073120: Areas of Pythagorean (or right) triangles with integer sides of the form (2mn, m^2 - n^2, m^2 + n^2)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A073120.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A073120.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #areas #Pythagorean #triangles #integer #sides #form #graph #threejs #webGL

Decomposition into weight × level + jump of A073120 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A073120 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

One day, one decomposition
A068501: Values m such that the consecutive pair parameters(m,m+1) generate Pythagorean triples whose odd terms are both prime

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A068501.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A068501.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #Pythagorean #triples #prime #primenumbers #graph #threejs #webGL

Decomposition into weight × level + jump of A068501 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A068501 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

#NASA May Pay $1 Billion to Destroy the #InternationalSpaceStation. Here’s Why : Sci Am

Here’s How Two #Teenagers Found a New Proof of the #Pythagorean Theorem : Medium

Do #MachineLearning Models #Memorize or #Generalize? : Google

Check our latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

#KnowledgeByte:We all know about Popular Pi Day (3/14). But do you know about rare #Pythagorean Day?

https://knowledgezone.co.in/posts/Pythagorean-Day-604e0888c23493c7af3844de

@AS_Katoch

#Lotus life-cycle
#Tetractys-structure and
#Pythagorean logic of
#monad (Unity - U),
#dyad (Power - P),
#triad (Harmony - H),
#tetrad (Cosmos - C):

01 Seed: U
02 Germination: P
03 Roots: H
04 Stem: C
05 Leaf: H
06 Bud: P
07 Blossoming: U
08 Full Flower: C
09 Wilt: H
10 Seed Pod: P

a^2 + b^2 = c^2

#sailing #boat #boats #math #pythagorean #photography #water #Pentax #PentaxK70 #PentaxK70_RN

Photograph of sailboats lined up at a dock with the right triangles of forestay, mast and deck aligned and visible against the blue sky.

#JamesGarfield , #theorem , #pythagorean, #president
James Garfield: Ο Αμερικανός πρόεδρος που απέδειξε το Πυθαγόρειο θεώρημα
https://eisatopon.blogspot.com/2023/06/james-garfield.html

One day, one decomposition
A009177: #Numbers that are the hypotenuses of more than one Pythagorean triangle

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A009177.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A009177.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #hypotenuses #Pythagorean #triangle #graph

Decomposition into weight × level + jump of A009177 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A009177 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

One day, one decomposition
A009112: Areas of Pythagorean triangles: numbers which can be the area of a right-angled triangle with integer sides

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A009112.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A009112.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #area #Pythagorean #triangles #graph

Decomposition into weight × level + jump of A009112 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A009112 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Euclid's proof of the Pythagorean Theorem is shown in the attached figure.

You can learn more about the Pythagorean Theorem in my recent writing: https://medium.com/illumination/learning-the-pythagorean-theorem-with-an-intuitive-approach-ecd794529cf5

#math #Pythagorean #Medium #Euclid

Another fascinating Mathologer video, about profound connections between #Fibonacci numbers and #Pythagorean triangles

https://youtu.be/94mV7Fmbx88

My #mathematics bar trick is that I can prove the #Pythagorean theorem in 30 seconds.

That for a right triangle with hypothenuse c it holds that a² + b² = c², where a and b are the two other sides.

I wonder if the Babylonians, who probably knew the theorem a thousand years before Pythagoras, also used the identity to show off after a drink or two.

What's your favourite bar trick?