#tetration — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #tetration, aggregated by home.social.
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#TIL: #Tetration - I never learned that in school, not even in high school.
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#TIL: #Tetration - I never learned that in school, not even in high school.
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Whenever I see the number 288 I always think «288 is special. Where have I seen it before?»
Then I remember that 288=1¹+2²+3³+4⁴. The general sequence of the sums of the first \(n\) «hypersquares» is https://oeis.org/A001923, and it seems that it's hard to say too much about it. Feels kind of surprising, given that we have https://en.wikipedia.org/wiki/Faulhaber%27s_formula for \(\sum_{k=1}^nk^p\), the sum of the first \(n\) of the \(p^\text{th}\) powers.
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Whenever I see the number 288 I always think «288 is special. Where have I seen it before?»
Then I remember that 288=1¹+2²+3³+4⁴. The general sequence of the sums of the first \(n\) «hypersquares» is https://oeis.org/A001923, and it seems that it's hard to say too much about it. Feels kind of surprising, given that we have https://en.wikipedia.org/wiki/Faulhaber%27s_formula for \(\sum_{k=1}^nk^p\), the sum of the first \(n\) of the \(p^\text{th}\) powers.
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I keep on thinking about tetration; it is fascinating! Today I was wondering if you could make a number system that is based on tetration. I think it would be able to handle really large numbers. I played around with it briefly but didn't find something that made sense to me. So I looked it up. I didn't find a tetration number system, but I did find a cool website on tetration by Daniel Geisler, https://tetration.org/original/index.html
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I keep on thinking about tetration; it is fascinating! Today I was wondering if you could make a number system that is based on tetration. I think it would be able to handle really large numbers. I played around with it briefly but didn't find something that made sense to me. So I looked it up. I didn't find a tetration number system, but I did find a cool website on tetration by Daniel Geisler, https://tetration.org/original/index.html
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This train of thought naturally led me to start thinking about hyperoperations, https://en.wikipedia.org/wiki/Hyperoperation. For data visualization I like making log plots. Is there a similar kind of plot based on inverse tetration instead of inverse exponentiation? I think it might be useful for visualizing really large numbers, perhaps from something like combinatorics.
#hyperoperations
#tetration -
This train of thought naturally led me to start thinking about hyperoperations, https://en.wikipedia.org/wiki/Hyperoperation. For data visualization I like making log plots. Is there a similar kind of plot based on inverse tetration instead of inverse exponentiation? I think it might be useful for visualizing really large numbers, perhaps from something like combinatorics.
#hyperoperations
#tetration -
Basic #tetration introduction (an operation they never taught you in school)
https://www.youtube.com/watch?v=oyjDTAjpYig
#math #²hyperpower
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Basic #tetration introduction (an operation they never taught you in school)
https://www.youtube.com/watch?v=oyjDTAjpYig
#math #²hyperpower
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Can't believe I just found the #tetration button on my keyboard!
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Can't believe I just found the #tetration button on my keyboard!
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New CatSynth TV! #Tetration (aka iterated exponential, power towers) 😺📈 📺 https://youtu.be/OEWuyutJ8eo (includes demo programs in #Haskell and #Swift) #Mathematics
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New CatSynth TV! #Tetration (aka iterated exponential, power towers) 😺📈 📺 https://youtu.be/OEWuyutJ8eo (includes demo programs in #Haskell and #Swift)
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I always hated \( \log \) for being clunky. Why don't we use the #tetration (and probably other things) #notation for \( \log \) instead?
So \[ ^{2} 32=5 \] and the #prime #number #theorem says the odds of \[ n \in \mathbb P \sim {^{e} n^{-1}}. \]
Way less clunky, nice and #symmetrical to exponentiation.
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Check out my blog post about solving a tetration problem using code!
https://karmanyaah.malhotra.cc/puzzles/2022/06/tetration/ -
https://www.youtube.com/watch?v=elQVZLLiod4
This was fun. Really appreciated the use of cobweb graphs -- I remember seeing them on my TI-84 calculator and never quite understanding what they're for.#math #tetration #threeblueonebrown
(aside: I managed to find that "switchover" point by poking around and then doing a binary search (followed by a Google search because the decimal number didn't ring any bells) which, although it lacked the real mathematical insight, was also fun in itself)
