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Science memes
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this post was submitted on 23 Jun 2024
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Science Memes
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That depends on the decay factor of one centaur to the next. If the centaurs shrink by anything more than a factor of two, then no. The creature will converge onto a single length.
What? If it's geometric it needs to be less than 1, that's all. 9/10 + 81/100 + 729/1000 + ... = 10
C•(1-r)^-1^ = C•x
Where r is the ratio between successive terms.
Should be anything less than a harmonic decrease (that is, the nth centaur is 1/n the size of the original).
The harmonic series is the slowest-diverging series.
The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can't just say "less than harmonic" though, I mean 1/(2n) is "slower".
Eh, that's just 1/2 of the harmonic sum, which diverges.
Yes, but it proves that termwise comparison with the harmonic series isn't sufficient to tell if a series diverges.
Very well, today I accede to your superior pedantry.
But one day I shall return!
Judging by the image the centaura shrink with about a factor of two so the entire creature should be either infinitely long or just very very long.