From: cet1@cus.cam.ac.uk (Chris Thompson) Newsgroups: sci.math Subject: 19-year cycles (was: Re: The Largest Versatile Number) Date: 4 Jul 1996 20:04:09 GMT I will try and keep enough mathematical content in this to justify it being in sci.math, rather than sci.astro. But please be aware that there is an FAQ on calendars which is posted to that newsgroup, among others. In article <4rfj1d$ef4@gap.cco.caltech.edu>, toby@ugcs.caltech.edu (Toby Bartels) writes: |> Matthew Hudelson wrote: |> |> >I believe that there is some arcane use of the number 19 in determining the |> >date of Easter in the Christian calendar. |> |> This is a holdover from the ancient Semitic lunar calendars |> which used a 19 year cycle of lunar months. In a sense. It is an attempt to reproduce a feature of the lunar-solar calendar in use at the time and place of the historical events involved [specifically, that Passover is celebrated at the time of the full moon]. It appears intrusive in the Roman/Christian calendar only because their are no other true lunar cycle features in the latter, the "months" having become periods only vaguely related to the lunar cycle. |> I'm pretty sure the modern Hebrew calendar still uses this cycle. Yes, of course. Not that Passover in the modern Jewish calendar is always at the same full moon as the Gregorian "Paschal Full Moon": in 3 years out of the 19 it is a month later. After 2199 that will become 4 out of 19. |> Does anyone know about the modern Muslim calendar? The Islamic calendar is based on the lunar month, either determined by the astronomical moon or a pretty accurate fictitious moon with a period of 29d 12h 44m. The "year" consists of 12 lunar months, and so is only vaguely related to the true solar year. Compare and contrast with "months" in the Roman/Christian calendar. For those who use the fictitious moon, the month length pattern repeats after 30 years. 19's don't come into it. |> Also, how inaccurate is this 19 year cycle? How do you want to measure it? The difference between 19 tropical years and 235 synodic months is a tad over 2 hours. Maybe more to the point, the ratio year/month is 12+ 1/2+ 1/1+ 1/2+ 1/1+ 1/1+ 1/17+ ... as a continued fraction, and truncating before the large partial quotient 17 gives the Metonic approximation 235/19. Chris Thompson Email: cet1@cam.ac.uk