5041/5040: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
comma splits 7/5 in two |
||
| Line 7: | Line 7: | ||
== Theory == | == Theory == | ||
5041/5040 represents the difference between 72/71 and 71/70. It is also the answer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - [[25/24]], [[121/120]], and this. | 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 the answer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - [[25/24]], [[121/120]], and this. | ||
== References == | == References == | ||
Revision as of 06:32, 5 February 2025
| 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 the answer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - 25/24, 121/120, and this.
References
- Wikipedia Contributors, Brocard's problem.