#pythagorean — Public Fediverse posts

Garfield's Proof of the Pythagorean Theorem

https://en.wikipedia.org/wiki/Garfield%27s_proof_of_the_Pythagorean_theorem

#HackerNews #Proof #of #the #Pythagorean #Theorem #mathematics #geometry #education #theorem #proof

The deep mathematics of why 10² + 11² + 12² = 13² + 14² Pythagorean theorem? Tired. Pythagorean runs? Wired! Learn why 10² + 11² + 12² = 13² + 14², plus a whole lot more! bigthink.com/starts-with-... #math #science #pythagoras #pythagorean

The deep mathematics of why 10...

One day, one decomposition
A002144: Pythagorean primes: primes of the form 4*k + 1

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

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

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

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

#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

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

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

#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

a^2 + b^2 = c^2

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

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?

#Pythagorean #Harp #demo

https://yewtu.be/watch?v=4cUy13R5SC4

Alt. link.:

https://www.youtube.com/embed/4cUy13R5SC4

#LatestMusicPurchase

#Goatchrist - Pythagoras

#avantgarde | #progressive #blackmetal from #england. It's actually not often that an avantgarde band is just weird enough to fit my taste - this one does. The album's lyrics quite literally cover #pythagorean #philosophy and #metaphysics.

#nameyourprice on #bandcamp

https://goatchrist.bandcamp.com/album/pythagoras

Time for #ProofInAToot! (Well, okay, in two toots.)

Let's generate #Pythagorean triplets \(a^2 + b^2 = c^2\). Dividing by \(c^2\), this is equivalent to finding rational points on the unit circle, \(x^2 + y^2 = 1\).

Consider the line of rational slope \(t\) going through \((-1,0)\), which results in the following system:
\[
\begin{align*}
y &= tx + t\\
x^2 + y^2 &=1
\end{align*}
\]
Its nontrivial solution is
\[
\begin{align*}
x &= \frac{1 - t^2}{1+t^2}\\
y &= \frac{2t}{1+t^2}.
\end{align*}
\]

I just found something interesting about #Pythagorean triples. You can systematically enumerate them in a tree using some magical-looking matrices!

https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples

The proof that the matrices work is a boring calculation and gives no insight into how the matrices were derived in the first place. I think I'm going to be reading some papers to figure out where those matrices came from.