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When I was 8 I would sometimes watch a Disney VHS tape that had Donald Duck exploring stuff like this. The golden ratio, octaves of sound/music, pythagorean theorem etc. I loved it.
Donald Duck in Mathmagic Land. You can find the whole thing on youtube
> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation. Just out of curiosity, which equations are considered the top three “most beautiful?”
This seems to be the original source https://physicsworld.com/a/the-greatest-equations-ever/ but it doesn't actually rank the equations. The other source commenting on that does, but only the sample is available on Google Scholar. From that, first is Euler's identity, second is Maxwell's four electromagnetic field equations, and third isn't in the sample. The NYT article also commenting on it https://archive.ph/H7ujx…
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> Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.
Ancient Mesopotamian laws sometimes flayed people alive for incompetent or corrupt work. Those types of mild punishments are good incentive to use the right angles. Pun intended.
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> they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry. Culture of free thinking? Socrates, the most iconic free thinker of all time was forced to commit suicide by the greeks. So much for a culture of free thinking. > They also sentenced some of their free thinkers to death for not worshipping the gods but that’s a separate issue. It isn't. It directly contradicts and refu…
> Socrates, the most iconic free thinker of all time was forced to commit suicide by the greeks. See my last sentence. > It directly contradicts and refutes your assertion. Maybe Greek society was not a homogeneous mass, and some parts of it nurtured free thinking while others reacted against it?
So then your assertion was incorrect: 'they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry.' They didn't start anything? Some of them did? What are you even saying then?
It's idiot's logic to claim that greeks nurtured free thinkers while admitting they killed free thinkers.
Instead of digging yourself a bigger hole, just admit you were wrong.
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> Socrates, the most iconic free thinker of all time was forced to commit suicide by the greeks. See my last sentence. > It directly contradicts and refutes your assertion. Maybe Greek society was not a homogeneous mass, and some parts of it nurtured free thinking while others reacted against it?
> Maybe Greek society was not a homogeneous mass, and some parts of it nurtured free thinking while others reacted against it? So then your assertion was incorrect: 'they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry.' They didn't start anything? Some of them did? What are you even saying then? It's idiot's logic to claim that greeks nurtured free thinkers while admitting…
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There are fully general and valid geometric proofs, eg http://mathandmultimedia.com/wp-content/uploads/2010/02/pyth...
Despite labels $a$, $b$, $c$, I don't see how it's fully general. At best you could say it works for similar triangles, if you have that concept. But I don't see how it proves anything if $a$ were say doubled, and $b$ kept the same.
* For any real positive values $a$ and $b$
* let $T$ be the (unique) right-angled triangle with non-hypotenuse sides of length $a$ and $b$
* then $a$^2 = $b$^2 = $c$^2
* where $c$ is the (unique) length of the hypotenuse of $T$.
You could give me the instance
$a$ = 2, $b$ = 3
$a$ = 4, $b$ = 3