28561/28560: Difference between revisions
Named |
m Text replacement - "[[Square superparticular|S" to "[[S-expression|S" |
||
| (11 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| | | Ratio = 28561/28560 | ||
|Comma = yes | | Comma = yes | ||
|Color name = suquadtho-arugu 1sn | | Name = Pisanoisma | ||
| Color name = suquadtho-arugu 1sn | |||
}} | }} | ||
'''28561/28560''' | '''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 [[S-expression|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 == | |||
It factors into | |||
* [[37180/37179]] and [[123201/123200]] | |||
* [[31213/31212]] and [[336141/336140]] | |||