ancient meme prototype

#Pythagoras really hated beans 🫘

Greek mathematics, the study of numbers and their properties, patterns, structure, space, apparent change, and measurement, is said to have originated with Thales of Miletus (l. c. 585 BCE) but was clearly understood during the periods of the Minoan civilization (2000-1450 BCE) and the Mycenaean Civilization (c. 1700-1100 BCE) and was derived from older Mesopotamian and Egyptian mathematical sy... #History #Science #Pythagoras #GreekScience #HistoryFacts https://www.worldhistory.org/article/606/greek-mathematics/

Another #manim video, this time #math stuff. One of my favorite "proof without words" #proof of the #Pythagoras theorem.

This version of this proof has a square of side length equal to the hypotenuse inside 4 triangles. At some point, I also want to do the other version of this proof where the triangles go inside a square with side=hypotenuse. Same principle, except the algebra uses the square of a difference (𝑎−𝑏)² instead of the square of a sum used in this proof. In both cases a 2𝑎𝑏 term cancels out to reveal the Pythagoras theorem.

As is usual with learning a new thing I'm realizing that my earlier animation of the Master theorem could've been made much better if I had bothered to read up some other sections of the reference manual.

Ah, nu heeft hij ontdekt dat per tien cm van de gelijkbenige driehoek de schuine kant veertien cm is. Nog even en hij vindt de stelling van Matthijs uit. Jammer joh, die Griek was je nét voor.
#millenniatelaatgeboren #Pythagoras

#pythagoras was not just in to the triangles, they also knew wine and punish greedy

https://youtu.be/ISfIT3B4y6E
#science

New Orleans teens’ Pythagorean proof gains compelling evidence

'Calcea Rujean Johnson and Ne’Kiya Jackson’s achievement was not the first time trigonometry has been used to prove the theorem'

#mathematics #geometry #trigonomety #Pythagoras

https://www.theguardian.com/us-news/2023/apr/07/new-orleans-teens-pythagorean-theory

In the news: two students create a new proof for #Pythagoras. That reminded me of a really elegant and beautiful pure-geometrical proof for Pythagoras' theorem by Andrew Pimlott. It and he seem to be forgotten. The proof isn't even mentioned on the Wikipedia page. Who would have known that in this day and age information can still so seriously get lost? #mathematics #fediverse / #mastodon to the rescue. Here are the two pages from my — 1990's, unfinished — book.

Very interesting read and good work by the teens.
https://www.theguardian.com/us-news/2023/apr/07/new-orleans-teens-pythagorean-theory

If the video which tried to deconstruct the proof is to be relied upon , I love the use of geometric progression and similar triangles to arrive at this result. I was not able to understand why this should hold. Someone please explain.

\[
\frac{\sin 2\alpha}{2a} = \frac{\sin \beta}{c}
\]

https://www.youtube.com/watch?v=nQD6lDwFmCc&t=324

#math #Pythagoras

@AndriusKulikauskas
#Fermat has a point. The #Pythagoras trick uses a right angle triangle, a square relationship so the formula is basically taking a shortcut, the trick, therefore can only work squared.

The #math relationship (in rads) appears to be

a^sin(π/(2(n-1)) = b^n + c^n

or there about.

@AndriusKulikauskas Another #Maths question please.

We know a^2 +b^2=c^2 because it draws out a triangle. Why do people expect ^3 to work? It seems like it’s human pattern recognition being applied to the words rather than the shape.

Going up a power is going up a dimension so it needs to draw out a volume, so the formula is
aaa = abb = acc
Or
a^3 = ab^2 + ac^2

Up a dimension again is
aaaa = aabb + aacc
then
aaaaa = aaabb + aaacc

So the formula is
a^x.a^2 = a^x.b^2 + a^x.c^2

Increasing all the powers is just breaking the laws of physics.

Thanks

#Pythagoras #Fermat

"US teens say they have new proof for 2,000-year-old mathematical theorem - New Orleans students Calcea Johnson and Ne’Kiya Jackson recently presented their findings on the Pythagorean theorem

Two New Orleans high school seniors who say they have proven Pythagoras’s theorem by using trigonometry – which academics for two millennia have thought to be impossible – are being encouraged by a prominent US mathematical research organization to submit their work to a peer-reviewed journal.

Calcea Johnson and Ne’Kiya Jackson, who are students of St Mary’s Academy, recently gave a presentation of their findings at the American Mathematical Society south-eastern chapter’s semi-annual meeting in Georgia.

They were reportedly the only two high schoolers to give presentations at the meeting attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech. And they spoke about how they had discovered a new proof for the Pythagorean theorem."

https://www.theguardian.com/us-news/2023/mar/24/new-orleans-pythagoras-theorem-trigonometry-prove

#Maths #Mathematics #Pythagoras #PythagoreanTheorem #BIPOC #US

Picture: tetraktys figures on Neolithic pottery, Los Millares, Andalucia

Yod, the tenth letter of the Hebrew alphabet, has the numeric value of 10. It is the letter that symbolises God and the first letter in the Tetragrammaton (YHWH), often inscribed within an upward-pointing equilateral triangle with the yod at the apex, a symbol derived, via the kabbalists, from the Pythagorean tetraktys, a triangular figure consisting of ten points. https://www.mdpi.com/2077-1444/9/11/375

#Neolithic #Kabbalah #Pythagoras

Leseempfehlung für die Matheblase im #FediLZ: "Der Satz des #Pythagoras in 365 Beweisen".

Vieles sicherlich eher für die Lehrer als für die Schüler verständlich, aber auf jeden Fall spannend und den Blick weitend. Kann man bestimmt auch alles mit #geogebra nachbauen... 😉

#schule

https://link.springer.com/book/10.1007/978-3-662-62886-7

Why is it impossible?

1) The square of the length of any segment between two lattice points is an integer. #Pythagoras

2) The area of an equilateral triangle is \( \frac{\sqrt{3}}{4} s^2 \), thus it must be irrational. https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/advanced-area-with-triangles/v/area-of-an-equilateral-triangle

3) Pick's Theorem, which is easy to prove for triangles, shows the area of a polygon with vertices on a square lattice must be a rational number. In the image above, the area is 11.5. https://nrich.maths.org/5441

Sometime love is easy! #geometry #pythagoras #love #humor

Here's a list of what I've been working on/thinking about for the last week. https://clerestory.netlify.app/work/?utm_source=mastodon&utm_medium=social&utm_campaign=20221129

Featuring #duBoisReymond #Kant #Graeber #Lucretius #Hesiod #Spinoza #Bacon #McGilchrist #Arendt #Geertz #Piaget #Einstein #Wertheimer #Solon #Confucius #Buddhism #complexity #Logos #Althusser #Nietzsche #Spinoza #Marx #Schopenhauer #Montaigne #Kuhn #Nagel #Pythagoras #Popper #Gödel and more!

Here's a maths fact that I find surprisingly useful in everyday life.

Suppose you have a long thin right-angled triangle, say with sides 1 and ε. Then Taylor expanding Pythagoras' Theorem gives that the hypotenuse is approximately 1 + ε²/2. Since ε is small, ε²/2 is tiny. So the hypotenuse is basically the same length as the side!

I'll give some examples of places where this comes up. Would love to hear others! (1/2)

#Math #Mathematics #Maths #Geometry #Pythagoras

“As long as Man continues to be the ruthless destroyer of lower living beings, he will never know health or peace. For as long as men massacre animals, they will kill each other. Indeed, he who sows the seed of murder and pain cannot reap joy and love…” #Pythagoras

#DruidInnen hatten auch ausgezeichnete mathematische Kenntnisse und erwarben Kenntnisse von griechischen Gelehrten wie #Pythagoras von Samos. Ein Beweis dafür ist das steinerne Becken in #Bibracte, einem Oppidum der #Aeduer. Dieses ist genau nach dem Sonnenstand zur Tag- und Nachtgleiche im Frühjahr und Herbst ausgerichtet. Quelle: https://www.zdf.de/dokumentation/zdfinfo-doku/die-druiden-geheimnisvolle-priester-der-kelten-102.html

A lovely post showing how you can generalise from the initial values to come up with the values via geometry that would be harder to achieve by algebraic methods.

https://www.forbes.com/sites/startswithabang/2020/03/06/the-bizarre-math-of-why-10%C2%B2-11%C2%B2-12%C2%B2-13%C2%B2-14%C2%B2/

#Mathematics #Geometry #Algebra #Pythagoras