28561/28560: Difference between revisions

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'''28561/28560''', is an [[Unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] of about 0.06{{cent}}. It is a superparticular with a fourth power as its numerator, in this case 134 = 1692 so that this comma is expressible as [[Square superparticular|S]]169 and as the difference between [[169/168]] and [[170/169]]. Its denominator decomposes as (132 - 1)(132 + 1), which, as 13 is a member of the Fibonacci sequence, by a property of that sequence is equal to 5*8*21*34, the product of the four nearest members of the sequence to 13. This is responsible for the comma belonging to a relatively low [[prime limit]] for the size of its numerator and denominator, though the same Fibonacci property also applies to the [[scintillisma]], S441 = S(212). Therefore, this comma has been given the name of the '''pisanoisma''', in reference to Leonardo Pisano, the discoverer of the Fibonacci sequence.

'''28561/28560''' is an [[Unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] of about 0.06{{cent}}. It is a superparticular with a fourth power as its numerator, in this case 134 = 1692 so that this comma is expressible as [[Square superparticular|S]]169 and as the difference between [[169/168]] and [[170/169]]. Its denominator decomposes as (132 - 1)(132 + 1), which, as 13 is a member of the Fibonacci sequence, by a property of that sequence is equal to 5*8*21*34, the product of the four nearest members of the sequence to 13. This is responsible for the comma belonging to a relatively low [[prime limit]] for the size of its numerator and denominator, though the same Fibonacci property also applies to the [[scintillisma]], S441 = S(212). Therefore, this comma has been given the name of the '''pisanoisma''', in reference to Leonardo Pisano, the discoverer of the Fibonacci sequence.

== Commatic relations ==

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-'''28561/28560''', is an [[Unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] of about 0.06{{cent}}. It is a superparticular with a fourth power as its numerator, in this case 13<sup>4</sup> = 169<sup>2</sup> so that this comma is expressible as [[Square superparticular|S]]169 and as the difference between [[169/168]] and [[170/169]]. Its denominator decomposes as (13<sup>2</sup> - 1)(13<sup>2</sup> + 1), which, as 13 is a member of the Fibonacci sequence, by a property of that sequence is equal to 5*8*21*34, the product of the four nearest members of the sequence to 13. This is responsible for the comma belonging to a relatively low [[prime limit]] for the size of its numerator and denominator, though the same Fibonacci property also applies to the [[scintillisma]], S441 = S(21<sup>2</sup>). Therefore, this comma has been given the name of the '''pisanoisma''', in reference to Leonardo Pisano, the discoverer of the Fibonacci sequence.
+'''28561/28560''' is an [[Unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] of about 0.06{{cent}}. It is a superparticular with a fourth power as its numerator, in this case 13<sup>4</sup> = 169<sup>2</sup> so that this comma is expressible as [[Square superparticular|S]]169 and as the difference between [[169/168]] and [[170/169]]. Its denominator decomposes as (13<sup>2</sup> - 1)(13<sup>2</sup> + 1), which, as 13 is a member of the Fibonacci sequence, by a property of that sequence is equal to 5*8*21*34, the product of the four nearest members of the sequence to 13. This is responsible for the comma belonging to a relatively low [[prime limit]] for the size of its numerator and denominator, though the same Fibonacci property also applies to the [[scintillisma]], S441 = S(21<sup>2</sup>). Therefore, this comma has been given the name of the '''pisanoisma''', in reference to Leonardo Pisano, the discoverer of the Fibonacci sequence.
 == Commatic relations ==