Talk:S-expression: Difference between revisions

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== What is So supposed to stand for? ==

<math>So(k) = \frac{ 4k^2 + 4k + 1 }{ 4k^2 - 4k - 3 }</math> simplifies to <math>\frac{2 k + 1}{2 k - 3}</math> so it doesn't feel very "square". --[[User:Frostburn|Frostburn]] ([[User talk:Frostburn|talk]]) 12:08, 5 July 2024 (UTC)

: From [[Square superparticular#Abstraction]]: "A suggestion is to use the notation Sok, if this is not unambiguous, with the letter "o" standing for "odd"."

: Specifically, it's "square" w.r.t. the "odd harmonic series" (as opposed to the natural harmonic series); with respect to odds it's technically only one off of the odd analogue of superparticular.

: If that still doesn't make sense to you, think of <math> {\rm So}(k) = h_k^2 h_{k-1}^{-1} h_{k+1}^{-1} </math> as the "source" of its squareness (as h<sub>k</sub> is the harmonic series analogue so this is the direct analogue of k<sup>2</sup>/(k+1)/(k-1)). Ideally, for the analogy to be perfect, So''k'' would be odd-particulars (as it'd be impossible to have them be superparticular when they are defined entirely in terms of ratios between odd numbers), but quodd-particular is thus the next best thing.

: Hope that clarifies. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:31, 5 July 2024 (UTC)

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 == What is So supposed to stand for? ==
 <math>So(k) = \frac{ 4k^2 + 4k + 1 }{ 4k^2 - 4k - 3 }</math> simplifies to <math>\frac{2 k + 1}{2 k - 3}</math> so it doesn't feel very "square". --[[User:Frostburn|Frostburn]] ([[User talk:Frostburn|talk]]) 12:08, 5 July 2024 (UTC)
+: From [[Square superparticular#Abstraction]]: "A suggestion is to use the notation Sok, if this is not unambiguous, with the letter "o" standing for "odd"."
+: Specifically, it's "square" w.r.t. the "odd harmonic series" (as opposed to the natural harmonic series); with respect to odds it's technically only one off of the odd analogue of superparticular.
+: If that still doesn't make sense to you, think of <math> {\rm So}(k) = h_k^2 h_{k-1}^{-1} h_{k+1}^{-1} </math> as the "source" of its squareness (as h<sub>k</sub> is the harmonic series analogue so this is the direct analogue of k<sup>2</sup>/(k+1)/(k-1)). Ideally, for the analogy to be perfect, So''k'' would be odd-particulars (as it'd be impossible to have them be superparticular when they are defined entirely in terms of ratios between odd numbers), but quodd-particular is thus the next best thing.
+: Hope that clarifies. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:31, 5 July 2024 (UTC)