5041/5040: Difference between revisions
Jump to navigation
Jump to search
m Added color name |
Tags: Mobile edit Mobile web edit Advanced mobile edit |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 7: | Line 7: | ||
== Theory == | == Theory == | ||
5041/5040 represents the difference between 72/71 and 71/70. It is also | 5041/5040 represents the difference between [[72/71]] and [[71/70]]; therefore tempering this comma out splits their product, [[36/35]], in two; as 36/35 is the ratio of [[6/5]] to [[7/6]], tempering out this comma also splits [[7/5]] in two, by equating [[84/71]] to [[71/60]]. It is also a solution to Brocard's problem, n! + 1 = m^2, for which there are only three known answers: [[25/24]], [[121/120]], and this. | ||
== References == | == References == | ||
* Wikipedia Contributors, [[Wikipedia:Brocard's problem|Brocard's problem]]. | * Wikipedia Contributors, [[Wikipedia:Brocard's problem|Brocard's problem]]. | ||
[[Category:Commas referencing a famous use of a number]] | |||
Latest revision as of 23:46, 2 March 2026
| Interval information |
19th highly compositema
reduced
5041/5040, the third brown pair comma, or the 19th highly compositema is a 71-limit superparticular interval measuring about 343 millicents.
Theory
5041/5040 represents the difference between 72/71 and 71/70; therefore tempering this comma out splits their product, 36/35, in two; as 36/35 is the ratio of 6/5 to 7/6, tempering out this comma also splits 7/5 in two, by equating 84/71 to 71/60. It is also a solution to Brocard's problem, n! + 1 = m^2, for which there are only three known answers: 25/24, 121/120, and this.
References
- Wikipedia Contributors, Brocard's problem.