81–90 of 248 posts
I sometimes wonder how people will remember the invention of computers, smartphones, and the internet in a few centuries. People will most probably learn that either Bill Gates or Elon Musk invented it all in one evening when an apple fell from a tree.
It's a parody but I wonder how close to the truth it is...
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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.
A "you" can, and many individual "you"s presumably did that, to general satisfaction. But the implicit assumption you made is that eyeballing and cutting is easy, while triangles are hard, even though it's the other way around, especially with stone age tools. But we're talking about groups of people, "they", who all build a lot. Such groups tend to have a few people who make these observations, and then the observat…
Earlier quoted context omitted.
A "you" can, and many individual "you"s presumably did that, to general satisfaction. But the implicit assumption you made is that eyeballing and cutting is easy, while triangles are hard, even though it's the other way around, especially with stone age tools. But we're talking about groups of people, "they", who all build a lot. Such groups tend to have a few people who make these observations, and then the observat…
>A "you" can, and many individual "you"s presumably did that, to general satisfaction I was chatting with the person that was in charge of marking the fields for the local youth soccer league. I volunteered to help one weekend, and one of the first things he asked was if I knew what a 3/4/5 triangle was since it was the only way to know you'll be squared. I never did figure out to what level he was dead panning his j…
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Agree it's closer but still an instance.
depends on the method they used to come up with the formula. It's not obvious that the sum of a "more complicated than you can do in your head" series of fractions would be either the square root of two or the the diagonal of a square, let alone both. This is a fragment of a single clay tablet. If they had a systematic method of coming up with this convergent series, there might have been a stack of tablets showing s…
Is there a theorem or conjecture like this ?
"For any irrational number, like square root of 2, we can always find the approximation of at most 3 rational numbers with just +,-,* and /" ?
This challenges the idea that ancient Greek mathematicians were always ahead of others.
It's interesting that Pythagoras gets credit for a theorem he may not have discovered, especially when there's proof that Babylonians knew it 1000 years earlier. This challenges the idea that ancient Greek mathematicians were always ahead of others.
I have a curiousity. Is there a theorem or conjecture like this ? "For any irrational number, like square root of 2, we can always find the approximation of at most 3 rational numbers with just +,-,* and /" ?
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I know the top one is generally considered to be Euler's Equation. e^(i * pi) + 1 = 0 It's considered incredibly elegant because it manages to combine multiple fundamental mathematical concepts into a single equation. 1 is the multiplicative identity, 0 is the additive identity, pi is the circle constant, e is euler's number, i is the square root of -1, the basic building block of complex numbers.
IMO, it’s better with tau. e^(i * tau) = 1 You lose the 0, but isn’t it a bit odd the 0 is there in the first place? Normally we’d reduce it to: e^(i * pi) = -1 Which obviously isn’t as nice in this case. And hey, if we’re allowed to break the conventions, you can have the 0 back easily. e^(i * tau) = 1 + 0