Re: Why not 13 months? (Was La Systeme Metrique)
Kai Henningsen (kai@khms.westfalen.de)
12 Jul 1995 21:32:00 +0200
mls@panix.com wrote on 11.07.95 in <mls-1107950024110001@mls.dialup.access.net>:
> solar calendars. To be pedantic, the mean tropical year of 365.24189...
> days and mean synodic month of 29.05309... days have a ratio of
> 12.36826..., with a minor (over the historical period) secular vari-
Umm ... 365.24189.../29.05309...=12.57152...12.57153. Obviously, one of
these numbers must be wrong.
Assuming your .36826 figure is correct ...
> mations in larger spans of years -- but it may surprise you just HOW
> much larger than 19 years you have to allow to get a better value of
> the solar/lunar ratio!
... just for fun, I just threw this at my "find nice ratios" program for
0.36826 and 0.36827 (as lower and upper bounds):
Lower bound:
1/ 2= 0.5000000000 (Fehler= -0.3577363819)
1/ 3= 0.3333333333 (Fehler= 0.0948424121)
2/ 5= 0.4000000000 (Fehler= -0.0861891055)
3/ 8= 0.3750000000 (Fehler= -0.0183022864)
4/ 11= 0.3636363636 (Fehler= 0.0125553586)
7/ 19= 0.3684210526 (Fehler= -0.0004373340)
67/ 182= 0.3681318681 (Fehler= 0.0003479386)
74/ 201= 0.3681592040 (Fehler= 0.0002737088)
81/ 220= 0.3681818182 (Fehler= 0.0002123006)
88/ 239= 0.3682008368 (Fehler= 0.0001606560)
95/ 258= 0.3682170543 (Fehler= 0.0001166180)
102/ 277= 0.3682310469 (Fehler= 0.0000786213)
109/ 296= 0.3682432432 (Fehler= 0.0000455025)
116/ 315= 0.3682539683 (Fehler= 0.0000163790)
123/ 334= 0.3682634731 (Fehler= -0.0000094310)
239/ 649= 0.3682588598 (Fehler= 0.0000030962)
Upper bound:
1/ 2= 0.5000000000 (Fehler= -0.3576995139)
1/ 3= 0.3333333333 (Fehler= 0.0948669907)
2/ 5= 0.4000000000 (Fehler= -0.0861596112)
3/ 8= 0.3750000000 (Fehler= -0.0182746355)
4/ 11= 0.3636363636 (Fehler= 0.0125821717)
7/ 19= 0.3684210526 (Fehler= -0.0004101682)
67/ 182= 0.3681318681 (Fehler= 0.0003750831)
74/ 201= 0.3681592040 (Fehler= 0.0003008554)
81/ 220= 0.3681818182 (Fehler= 0.0002394488)
88/ 239= 0.3682008368 (Fehler= 0.0001878056)
95/ 258= 0.3682170543 (Fehler= 0.0001437688)
102/ 277= 0.3682310469 (Fehler= 0.0001057731)
109/ 296= 0.3682432432 (Fehler= 0.0000726553)
116/ 315= 0.3682539683 (Fehler= 0.0000435326)
123/ 334= 0.3682634731 (Fehler= 0.0000177233)
130/ 353= 0.3682719547 (Fehler= -0.0000053077)
So, to get any better, you need nearly a factor of ten; to get
significantly better, even more.
Kai
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