S-expression: Difference between revisions
m →Table of pentaparticulars: *relation |
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</pre> | </pre> | ||
...as expected. In fact, if you look at the expressions in the table, it becomes obvious why we have the central element squared (via a 2 and -2 in the S-factorization), as it follows from the general algebraic form of {{nowrap| ''n''<sup>2</sup> / (''n''<sup>2</sup> - 1) {{=}} ( ''n''/(''n'' - 1) )/( (''n'' + 1)/''n'' ) }}. | ...as expected. In fact, if you look at the expressions in the table, it becomes obvious why we have the central element squared (via a 2 and -2 in the S-factorization), as it follows from the general algebraic form of {{nowrap| ''n''<sup>2</sup> / (''n''<sup>2</sup> - 1) {{=}} ( ''n''/(''n'' - 1) )/( (''n'' + 1)/''n'' ) }}. | ||
'''It should be noted:''' The same derivation above can be observed as not depending on the number of 0's in the S-factorization of the expressions of <code>F(k + 1)</code> and <code>F(k + 2)</code>, and that therefore we have S''a''/S''b'' being an equidistance relation of intervals, where the generalized versions of the terms <code>F(k + 1)</code> and <code>F(k + 2)</code> correspond to the two differences of intervals of the form (''n'' + ''k'')/''n'', where ''k'' = 3 corresponds to one zero in the monzo, and where the terms <code>F(k + 1)</code> and <code>F(k + 2)</code> therefore correspond to the two differences used to make three intervals of the form (''n'' + ''k'')/''n'' equidistant. "Which three intervals" is thus answered as those of 3 consecutive/adjacent values of ''n''. | |||
=== Table of three-particulars === | === Table of three-particulars === | ||