# Talk:Eclipse cycle

## syzygia

I've been trying to find the original Greek word "syzygia" (from which syzygy comes), but I haven't yet found it. All I've come up with is the Roman transliteration. I'm guessing it's συζυγια—can someone verify this, please? Ortonmc 04:30, 9 Nov 2003 (UTC)

It indeed comes from the Greek word συζυγία, which means "union", itself originating from the prefix συν- ("with") and the noun ζυγός ("yoke"). — Poulpy 11:52, 15 December 2005 (UTC)

It appears to me that this page and Saros cycle are very redundant and cover nearly the same topic. Could someone please explain the rationale for having two separate entries? I'm am leaning towards a proposed merge of these two pages, though it is not clear what the merged topic should be called. Lunokhod 20:48, 2 January 2007 (UTC)

This page is about all possible eclipse cycles, whereas the saros page is only about the saros cycle. Since it is the most important one I suppose that one deserves its own page. I see very little overlap between the pages; for instance the elaborate example of saros seeries 131 would be out of place here. Tom Peters 00:37, 3 January 2007 (UTC)

I would like to reiterate the question that Lunokhod asked at the beginning of this section: What is the difference between this and Saros cycle? This could be discussed in a formal merge debate if necessary. Dr. Submillimeter 16:07, 4 January 2007 (UTC)

I would have to answer along the same lines as before: the saros is AN eclipse cycle, while this page is about eclipse cycles in general, and gives a list of well-known examples. The best-known have gotten their own pages which give more details (not all of those have been started by me). I think Wikipedia will be poorer if everything but the saros is thrown out. Tom Peters 00:03, 5 January 2007 (UTC)
The saros is the best-known and historically most important of the eclipse cycles. Considering most people's background, it's probably better to say that eclipse cycles represent a generalization of the concept behind the saros. One can construct different rational-number combinations of the different flavors of months and get recurrence cycle times of different lengths. It makes sense to me, and I see the difference. I note, though, that the only two cycles (longer than the lunar year) I had encountered before reading the article are saros and Metonic cycle, and the Metonic cycle is much more often thought about strictly in the context of calendation, but since both of them represent approximate integer relationships between lunar and annual cycles the two ideas have to be related. Merging the two articles would either result in cutting out all but the mention of more general eclipse cycles, or give a long two-pointed article that would probably be designated as in need of splitting. This is pretty esoteric stuff, though, and I wouldn't expect a university undergraduate to be able to grasp the subject in a reasonable amount of time. BSVulturis 21:23, 4 January 2007 (UTC)
Tom, I think that you are taking this a bit personally, which you shouldn't. We are all here to help improve the quality of this page. From my reading of the responses above and below, it appears that all of us here are experts in related fields and understand what is trying to be said. Unfortunately, the article is poorly written, and this makes it difficult to grasp the first time around without doing some mental exercises. When I say that the rationale for the table of continued fractions is not clear, this does not mean that I do not understand what a continued fraction is; this is an editorial comment, such as would be encountered in a review of any article before being published, scientific or otherwise. Lunokhod 10:46, 5 January 2007 (UTC)
Appreciated. However I do take this personally because I've put a lot of time in many of the pages that are now being adopted in the WikiProject Moon. I believe that all of the information that I collected and contributed is accurate and valuable (although not for everybody), and often not easily available elsewhere on the Internet. On Wikipedia we're in a constant struggle to defend our contributions and information we think valuable against all kinds of people who want to change or remove it for various reasons (benevolant or malicious). Wikipedia is not in fact in all cases a collaborative effort. Even disregarding edit wars, politics, and propaganda (which are not the issue here), there are conflicting opinions on what Wikipedia is, should, or could be, and for whom. We have governance and policies, but as you have noticed there remain different interpretations.
Anyway, I think at the heart of the matter lies the vision of the intended audience. We have to assume some level of background knowledge and skills. If we put the level low then advanced topics go out of scope and Wikipedia becomes trivial and uninteresting for the knowledgeable people who are competent to actually write high quality articles. If we put in more advanced or specialized stuff then we must assume a higher level of knowledge and skills, or explain all the jargon and methods in tedious detail: i.e. write a tutorial instead of an encyclopedia. In fact I already went that way in my writings, giving frequent hints on how to obtain certain results: but your critique has prompted me to elaborate in detail that becomes painful. A line must be drawn somewhere.
As for the continued fractions: as already explained repeatedly in the article, to find an eclipse cycle you need to find a fraction approximation to the ratio of synodic and draconitic months. Continued fractions are the way to obtain this. Most books and articles just give the cycles without explaining where they come from, assuming that the readers can figure it out themselves. If I just give a list you would complain about references and verifiability (even though it is trivial to check whether a cycle fits or not). Newcomb, and IIRC van den Bergh, do show continued fractions progressions: but these original sources are very inaccesible (I read that the journal that contains Newcomb's article from over a century ago was purged last year from the library of the Naval Observatory that originally published them). Continued fractions used to be a common (and not very difficult) technique taught at school (also mandatory for anything with gears), but not anymore. So I think it is helpful to show the detailed progression for the uninitiated: but for an explanation of what a continued fraction is and how to compute with it, they should follow the link (incidentally, I find that article too mathematical, totally ignoring practical applications: what is the audience for THAT?). Generally, I suppose I do have an egocentric attitude when writing for Wikipedia: I write what I know, for the person who I was before I knew it and had to find it all out by myself, adding the details that I would have loved someone explain to me when I wanted to find out. Mind that I do have a teaching license, have taught, and have written tutorials. But for lack of a more clearly defined intended audience I think my attitude is not unreasonable. Tom Peters 13:39, 5 January 2007 (UTC)
I have a Ph.D. in astronomy, I work as a professional astronomer, and I think this page is filled with esoteric jargon that is not even meaningful to the average astronomer (professional or amateur). I would direct other astronomers and astronomy students away from this page and towards something written in plain English. Worse, I think it could confuse my students if they ever found it. If I have problems with this page, then who is the intended audience (besides Tom Peters and his friends)? Dr. Submillimeter 19:58, 5 January 2007 (UTC)
Dr. Submillimeter, can you please cite an example of what you are talking about and propose a fix to the situation? Victor Engel 20:24, 5 January 2007 (UTC)
So prof. Submillimeter, what and how would YOU teach your students about eclipses? Tom Peters 21:49, 5 January 2007 (UTC)
I teach my students concepts, not vocabulary. When I teach, I try to use little jargon unless it is central to the concept. The term "node", for example, cannot be avoided here. However, the terms "synodic month", "draconitic month", "anomalistic month", "syzygy", and virtually all the terminology in the Eclipse cycles section should be removed in favor of short, descriptive phrases that describe the concepts in plain English if and when possible. The flood of vocabulary will simply distract readers from the concepts being taught.
I would focus on the basic concepts. First, I would state that eclipses occur when the nodes line up with the Full Moon or the New Moon. Next, I would bring forth the periodicity for the movement of the nodes and the phases. I would then demonstrate that the moon eclipses the Earth or is eclipsed every six months or so, and that the periodicity can be divided up into larger periods.
I also further reviewed the "continuing fractions" part of the text and found that it could be written much more succinctly and with only a brief mention to continuing fractions rather than a demonstration. (Continuing fractions needs a Wikipedia article.) People understand that the Moon does not orbit the Earth in exactly one month or that the Earth does not orbit the Sun in exactly 365 days. The cycles described here follow a similar concept. It can just be stated straightforwardly without the esoteric calculations (or at least with a minimum number of esoteric calculations).
Continued fractions has a Wikepedia article, and it is linked from the article under discussion. There is even a section in the article that speaks directly to the issue at hand, how it can be used to find "Best rational approximations". Victor Engel 02:21, 6 January 2007 (UTC)
These are my the beginnings of my thoughts on the articles. However, I really do not feel like investing more time in explaining my position, especially if I am going to receive continued statements from people saying, "Real astronomers would write pages with complex equations and vocabulary. Explaining things in simple English and a minimal amount of arithmatic is bemeaning to the subject." I honestly have the impression that the obsession with all of these calculations about lunar cycles is driven more by some type of infatuation with numbers and periodicity; it certainly does not look like it is written to teach people about astronomy. Dr. Submillimeter 00:24, 6 January 2007 (UTC)
This last point, that "it certainly does not look like it is written to teach people about astronomy" is something I alluded to elsewhere in this discussion. Eclipse cycles are not just about astronomy. An article about eclipse cycles is just as valid for calendrics and history as it is for astronomy. If the calculations don't interest your particular field, just ignore them. They may well be very important to another field. Victor Engel 02:21, 6 January 2007 (UTC)
Dear Dr.Submillimeter, thanx for your explanation. It does show that we do have a fundamental difference in attitude towards technical terms ("jargon"). I find it very odd that you want to teach concepts, but prefer to keep using descriptic phrases for them instead of giving proper names. That becomes tedious VERY fast when used repeatedly in a text. People working on any subject tend to create jargon quickly, not to be secretive but because they need it. See for instance the huge production of abbreviations and acronyms in business-speak. If you want to be active in any field, the first thing to do is to learn understand the language. I do not find it improper for an encyclopedia article to introduce people to the jargon of the subject. The Wikipedia is full of articles that have descriptive phrases as lemmata, which actually makes them hard to find. For example, there used to be Computing the date of Easter, for which I could never remember the capitalization, and I managed to get it renamed to Computus which has been the unique proper name for this particular procedure for 17 centuries. And surely you remember the controversy over the Fumocy - a concept in need of a name.
As for the continued fractions: obviously there are several ways to find the proper fractions. But historically the continued fractions technique has been used for this kind of problem, and it is an elegant method to obtain these results. Whether it is beyond the intended audience depends on what this audience is and what their skills are. As always, I suppose we should keep it "as simple as possible, but not simpler". You write that you reviewed it and found a better way to explain, so please be a Wikipedian and start editing; I think we should at least mention the continued fraction method and list its resulting series (being the historical, and an elegant method giving comprehensive results), and I believed that the explicit example would be helpful for those who are not familiar with the technique. Tom Peters 02:47, 6 January 2007 (UTC)

## Confusing?

Lunokhod and other interested readers: I elaborated on the method to find eclipse cycles. How do you like it now? I disagree that the overview should be presented in prose: each cycle can be assessed by the same characteristics, which are best presented next to one another in a table; as is customary in the quoted literature and websites. Are there more people who still find all this confusing? Tom Peters 00:23, 4 January 2007 (UTC)

Most of the article is understandable; it's just the last two sections that I am having a hard time figuring out. I suspsect that a non-expert will be more confused than I. Here's my rationale for flagging these, as well as some ideas on how to fix this.
Thanx for your detailed critique, but I am getting desperate on how to satisfy you. replies indented below. Tom Peters 13:00, 4 January 2007 (UTC)
• These two sections present lots of data and numbers, but nowhere do these sections try to explain what these numbers actually mean.
well actually, all that is in the sections above. Those two sections show how to obtain the various cycles using the actual numbers, and lists the results.
• The first sentence says "These are the lengths of the various types of months as discussed above". The reason for listing the lenghts of the various months needs to be explained before doing so.
How else can you actually compute the numeric values of their beat periods?!
• The first equation after "Note that:". Where does this come from, and what do the symbols in the eqation mean? The reason for presenting an equation should always be described in text form before giving the equation. As an example "Newton's law of gravitation is given by..."
Hello?? The symbols are given immediately above that and are obvious abbreviations of the various month names!
• I can not understand at all what is trying to be done in these sentences: "We obtain these relations from approximations of the ratio of the synodic and draconitic months. They can be found by the method of continued fractions: this arithmetic technique provides ever better approximations of a decimal number by common fractions. The target ratio is 29.53059 / (27.21222/2) = 2.170391..."
As already explained in detail in the article, eclipses can occur only at New and Full Moons, i.e. when the Moon returns to the Sun or directly opposite to it. These "syzygies" recur every synodic month (29.53... days). Also eclipses can only occur when the Moon and Sun are near one of the nodes of the Moon's orbit on the ecliptic. The Moon returns to a node after a draconitic month, and the Sun after an eclipse year. So in the rare occasion that an eclipse has occurred, we must wait an integer number of synodic months AND an integer number of draconitic months before another eclipse can occur. As all explained in the first sections. So how can one find that S synodic months match D draconitic monts? Compute the ratio S/D, and approximate that number by common fractions of integers. The numerators and denominators give you the number of draconitic and synodic months respectively. The "continued fractions" technique provides successive better fractions that approximate the exact decimal value. Because those numbers become bigger, the length of the corresponding eclipse cycle is longer too. We use the synodic month as unit, so put an eclipse cycle at S synodic months exactly. Then that's D draconitic months plus or minus a (hopefully small) mismatch, and A anomalistic months which is not an integer either, and so many eclipse years, and days. All those numbers are given in the table in the second section. All that is old news, from Newcomb to Meeus in the References; also see the table of Rob van Gent in the Links.
• Even though I don't understand the above sentences, I really doubt that the following two tables are necessary. In any case, the algorithm used to calculate these is not clear, nor is the meaning of the obtained ratios.
Not clear to you, because apparently you don't understand continued fractions. Those tables are there for people who do, or care to learn about it by following the link.
• The organization of the second section does not help the reader understand the origin of the various cycles. Instead of saying "This table summarizes the characteristics of various eclipse cycles. More details are given in the comments below, and several notable cycles have their own pages." I think that it would be better to say something like. "There are various eclipse cycles, whose origin is related to xxx." Then, in paragraphy form (not glossary index form) these should be explained. The table should most likely be an infobox on the side or bottom of the text, and not at the start of the section.
That is a matter of presentation. Because we need to repeat the same kind of information for each eclipse cycle, a table is the preferred format.
• The descriptions of the cycles do not contain enough information for a non-expert to understand. As an example "Lunar year: Twelve (synodic) months. A little longer than an eclipse year: the Sun has returned to the node, so more eclipses may occur." While this might be factually correct, a few more sentences describing why this causes more eclipses, and why the periodicity is a year (and not 18 years) would be helpful.
Hello, may we assume that the reader has read the page thusfar and understands by now how things work??
The same goes for "Octaeteris: An old calendar cycle rather than an eclipse cycle, 8 years equals 99 lunations to within 1.5 days." What does this mean?
What do you mean "what does this mean"? 8 years are equal to 99 lunations with an error of no more than 1.5 days. What is possibly unclear about that??
• What is the persistence, and why isn't it given in the table?
I never got to fill that in. It should tell how long a series of eclipses recurring at the interval with the length of the pertinent eclipse cycle lasts. It has not been documented for most cycles anyway, although an approximate theoretical duration can easily be computed.
• The headings of the table are not too clear. It should be explicitly mentioned, perhaps in a table caption, that "days", and "draconian" refer to the periodicity in terms of these variables.
Lunokhod 10:18, 4 January 2007 (UTC)
I'll advertise on WP:Moon for additional objective opinions, as I still find these sections confusing. As someone who is familar with the lunar orbit, ephemerides, etc., I can intuit what is probably trying to be said here. Nevertheless, we should keep in mind that many people will not have either the patience or background to figure this out for themselves. Lunokhod 15:28, 4 January 2007 (UTC)

## Third opinion on confusing items

Lunokhod asked for a third opinion on the confusing sections. Here are my thoughts:

• Numerical values - The first section uses a lot of jargon that is explained in the above text but that is difficult to follow. The second section contains some esoteric calculations that are not needed here. It would confuse the average reader, and it is not clear what purpose these calculations serve.
• Eclipse cycles uses a lot of terminology that is explained, but the explanations are very poor and unenlightening. Moreover, it is so technically-oriented and so esoteric that it does not look like it would be of interest to the average reader. Removing it would strengthen the article.

In general, I suggest rewriting the article while avoiding jargon (or introducing jargon carefully). This article is simply not written for a general audience. Dr. Submillimeter 16:03, 4 January 2007 (UTC)

## Fourth opinion on confusing items

"Eclipse cycle" is one page that I have surfed to and relied upon quite often, including recently on my "Length of the Lunar Cycle" project, and obtained a lot of useful information from it. I never found fault with its contents, organization, or layout. It always had the answers that I needed, easy and quick to find! Kalendis 12:50, 5 January 2007 (UTC)

Eclipses have been studies and documented for thousands of years. While they are esoteric to some, they are very important for reasons I won't discuss here. Suffice it to say that the remaining discussion should be taken in the context of having an interest in eclipses.

Eclipses, from a purely physical perspective, are well defined and easily described given the right language. Given the wrong language, such a discussion can be very confusing. For example, we need to be very clear what we mean by one orbit of the moon, since one orbit can mean different things.

All this NECESSARILY requires a certain amount of jargon. The jargon is required for clarity. I find that it is presented in this article in a very clear and logical progression. If a term, like "node" is unfamiliar to the reader, they can follow the included link to familiarize themselves with the terms. If the link does not provide the needed information, that should not adversely impact the quality of the article under consideration. In other words, we should not consider the Eclipse Cycle article to be poorly written because the link to "node" is poorly written.

As to the difference between Saros cycle and eclipse cycle, that's like asking for the difference between a zebra and a horse. There's no issue in having separate articles for zebra and horse, is there?

Regarding the numbers used and whether there should be further explanation of where they come from, if you follow the included links, appropriate explantion is included. The only change I would suggest is that if a table is to be given that lists the values to be used, then just use those values, rather than using elipses, ("29.53059... / (27.21222.../2) = 2.170391..." would be better rendered as "29.53059/(27.21222/2)=2.170391". Perhaps a note about the inverse would be appropriate, too, but that would seem to be a bit pedantic.

I note that the continued fractions expansion using these 7-digit approximations excludes the saros cycle, being (2;5,1,6,1,1,1,2,126,...) rather than (2;5,1,6,1,1,1,1,1,11,1) as listed in the article. So I must assume higher precision numbers were used in the continued fractions calculations, rather than the numbers listed. Victor Engel 21:00, 5 January 2007 (UTC)
That is correct. For the continud fractions I used the full (10 decimals or so) values from the ELP; hence the ellipses. I'll provide the accurate values with reference tomorrow. —The preceding unsigned comment was added by Tom Peters (talkcontribs) 21:51, 5 January 2007 (UTC).

Regarding the continued fractions, if you don't understand continued fractions, learn about them. They look unwieldy at first, but their use is appropriate here. You could also use numerical techniques to discover the same values, but why, when continued fractions suffices? Perhaps a shorthand version of noting the continued fractions would be appropriate here to save space. But that would be even more confusing to those not familiar with continued fractions. Frankly, I think that is fine. For those interested in the derivation of the numbers, they can learn about continued fractions, plug in numbers and test the results, or look up the numbers in some reference. In any case, the presentation here is very clear, in my opinion.

Regarding persistence, that probably should be taken out unless it can be completed. I suspect persistence is related to how close the rational number approximates the intended ratio.

Finally, with regard to projects such as project Moon, people working on those projects must be cognizant of the fact that the scope of an article INTERSECTS with the project. Because it's an interesection, there likely is interest germane to the article that is beyond the scope of the project. That should NOT result in expulsion of the material not germane to the project.

Victor Engel 18:57, 5 January 2007 (UTC)

## draconic or Draconic?

(I moved this discussion from my personal page Talk:Tom Peters to this more public place. Tom Peters 13:03, 9 February 2007 (UTC))

Hi Tom. I didn't know this before (and as there is no refernce I'm not sure if it is true), but it appears that the draconic month is named after the constellation Draco (constellation). If this is true, wouldn't Draco be a proper noun, and wouldn't the adjective be capitalized (as is Martian, but not lunar)? Google shows that both are common, but Google is not a reliable source. Lunokhod 19:22, 10 January 2007 (UTC)

(best answer here?) That's a new theory for me; I don't see what that constellation can possibly have to do with eclipses, considering that it is sitting around the ecliptic pole and nowhere near the ecliptic plane. The story I know is that it refers to the dragon that lives in the nodes and eats the Sun and Moon at eclipses. Tom Peters 22:55, 10 January 2007 (UTC)
I'm the one who just capitalized it, and you reverted. ( I hadn't seen this page, by the way.) Draconic is derived from a mythological figure, presumably the same one the constellation is named after. So some capitalize it. It seems the association has been lost to many, and now both are used by reputable sources. I'm not changing it back.
by the way, the work of you two is great. Saros136 11:39, 9 February 2007 (UTC)
Thanx. But which mythological figure (person?) you are referring to? There have been historical persons called Draco, most notably the law-giver: for him the proper adjective is draconian. For all I know draconic refers to a dragon living in the nodes and eating the Sun or Moon at an eclipse; it may or more likely may not be associated with the constellation of the dragon. In either case it should not be capitalized. Tom Peters 13:03, 9 February 2007 (UTC)
Just as an update, I did look into my original question, and draconic has nothing to do with the constellation (not much of a surprise here, I removed the offending material from the wiki page). Still have no idea as to the capitalization problem though. Lunokhod 16:28, 9 February 2007 (UTC)
Thanks for moving this to the Eclipse Cycle page, where more people can see I'm wrong. Well, partly. I shouldn't have been so sure there is a mythological origin here. I'm not sure. I was influenced party by the fact that Meeus capitalized it in Astronomical Algorithms. When he writes with Espanak it's lowercased though. But I'd still rather capitalize Draconian month if it turned out to be derived from a mythological figure...I think there are examples supporting it. Saros136 03:31, 11 February 2007 (UTC)
Uh, but what is a Draconian month supposed to mean? "{D|d}raconian usually means something like "drastic", derived from the name of the harsh law-giver. Tom Peters 19:24, 13 February 2007 (UTC)

I wanted to gather some information on solar and lunar eclips as it would be occurring in india on 19/03/2007. But when i read this article i lost interest in eclips. The reason being it is so very much difficult to understand the words. The jargons used is not understood by a layman like me or for that matter by anyone. It should be in plain simple english with more diagrams in it so that it could be universally understood. There are some mathematical terms used which is tangent to my understanding. A person who dosent understand math will not understand this article at all. Please improve this article before people like me start to loose interest.

Thank you

## removed confuse tag

This section summarizes concepts discussed previously in the article, while it may be confusing on it's own it is not confusing in the context of the article.--TimL (talk) 05:19, 12 June 2011 (UTC)

In the list of continued fractions, why do only some of the ratios have names? Also seems a calculation of the fraction several digits to show the increasing precision might be nice.
In the chart of eclipse cycles, what is the significance of "number of anomalistic months" column and "number of eclipse years columns"? I know the answer to the former, but that is not explained in the article. The list of fractions looks like an exercise of some sort that's not totally necessary for the article. Not the whole list anyway, too technical. It's also unfortunate terminology such that a draconic year is not 12 draconic months. I guess 12 draconic months is just, well, 12 draconic months. --TimL (talk) 17:33, 22 July 2011 (UTC)

About the names, I have no answer. I suspect that if there is an answer, though, it is beyond the scope of this article. For those fractions that do have a name, though, it is useful to have the name. If significant enough, it has its own article, that could go into more detail.
About the number of anomalistic months and eclipse years columns, if you're suggesting adding text explaining the relevance of these columns or what characteristics of eclipses one might glean from those numbers, I think that's a good idea. But we also don't want to add too much information to the article.
What's so technical about continued fractions? Anyone who is not familiar with them can follow the link provided to see how they work. Successive entries in a continued factions table show increased accuracy in rational approximations. I think that's the whole point.
And what does draconic year have to do with anything? Do you think there is something about the word "month" that implies there must be a year?Victor Engel (talk) 20:08, 22 July 2011 (UTC)
On the 3rd point, the continued fractions, list the decimal value I think would help the reader see what is going on. We are increasing precision towards the magic number. The more precise, the longer the series, I think that is missing from the article. Again it also is confounding why only some of these ratios are significant and not others. That's what makes it seem, well, kind of random. Hopefully it's not beyond the scope of the article.
I agree, decimal representations would be a good idea.
As to the 4th point, if you have a draconic year and a draconic month, one might expect them to be related somehow, even referring to the same phenomenon. It's taught to us in pre-school that 12 months equals a year. Kind of hard to dissociate that relation. I think dropping the term "draconic year" for the term "eclipse year" would avoid confusion. --TimL (talk) 20:26, 22 July 2011 (UTC)
I hadn't realized "draconic year" was in the article. Anyway, there are all sorts of years. A year is simply a period of revolution of Earth with respect to something. The length of the year depends on what that something is. The pre-school definitions likely come from the Gregorian calendar, which formulates month and year based upon an approximation to the northern spring equinox year. Other kinds of months an years are just as accurate, and, in the case of this article, more germane. Probably dropping "eclipse year" from the article is not a good idea, since it's relevant to eclipse cycles.Victor Engel (talk) 21:05, 22 July 2011 (UTC)

## My removal of the octaeteris

While a unique lunisolar cycle, the octaeteris is not an eclipse cycle. Per discussions with User talk: Victor Engel an I, there is only a 33% chance of another eclipse occurring in 8 years, 1 day. This is because an octaeteris is 8.434 eclipse years, which is too far from a half integer to make it a reliable cycle. If by chance there is another eclipse it is the only other eclipse in the series, again because of the deviation from the half-integer eclipse year. Also nowhere on the Internet could I find a article or reference to a book that discusses the octaeteris as an eclipse cycle. Moreover the original article stated it was not an eclipse cycle, so I'm not sure what the motivation was for listing it in the 1st place. It is an effective lunisolar cycle, but not eclipse cycle. Perhaps a note could be added as to why it is not an eclipse cycle. I'm not sure I can do that without treading the waters of WP:OR. --TimL (talk) 00:47, 23 July 2011 (UTC)

I cannot recall but since I am one of the main original authors I suppose I put it in. Presumably because it is an astronomical cycle like the others, and there is no other place in Wikipedia where such cycles are collected. But in principle you are correct that it is not an eclipse cycle and therefore should not be in the list. Tom Peters (talk) 10:07, 25 July 2011 (UTC)

## More on the continued fractions charts

What is the point? On the last two lines we get 9031/4161 and 9808/4519. What good are these ratios? What is the meaning of them? Who cares about them? That's why is call this an "exercise of some sort" and I question it's relevance. It could simply b shown that the ratios of the common cycles approximate the desired "magic number" and that the process of continued fractions can be used , we don't need to see the whole process. I'm leaning towards moving both of these with a simpler representation. Also, could someone possibly be kind enough to explain to me what is going on in this chart? I read the Wikipedia entry on continued fractions and the notation here makes no sense. I think it is making he article stink. Why does it go 2+1 then 5+1 the 1+1 than back to 6+1, then 1+1 add infinitum? Not only that after looking at the [[continued fractions[[ discussion it looks like this is being done is reverse. Look, math may not be my strong point but there is something wrong with this chart. --TimL (talk) 09:39, 23 July 2011 (UTC)

If you look at the Continued Fractions page, read under the heading "Best rational approximations". That is the point of the continued fractions. We have a decimal number here, and we have a listing of the best possible rational approximations to that decimal number. I agree the format is rather unwieldy, and, in fact, doesn't display properly with long lines and/or parentheses. Perhaps another format, like that used in the continued fractions page should be used instead. Victor Engel (talk) 03:51, 24 July 2011 (UTC)
P.S. If you navigate to http://www.wolframalpha.com/ and enter a decimal number, it will calculate the continued fractions representation. The format used there would probably be a better presentation for this article. Victor Engel (talk) 03:56, 24 July 2011 (UTC)
Thanks for the link. That site can do some amazing things. Hopefully it will help me wrap my head around the problem. One thing I'm still missing is the link between the numbers on the left and the months on the right and how they are related. Thanks for your reply. (now I'm wondering what an eclipse year sounds like, ha) 346 Hz if I please I suppose. --TimL (talk) 17:50, 24 July 2011 (UTC)

More on continued fractions: There are repeated complaints that this is incomprehensible. Personally I think the continued fractions page is fine, clear, and understandable, but for some it apparently is not. I don´t care to try repair that page. Maybe we can improve the representation on this page. I do not favour the standard notation (2;5,1,6,...) here because I think it is important to list the successive approximations to show where the various eclipse cycles come from. Is this format clearer?

```   2.170391682 =                       half draconic months/synodic months:
1
2 + --------------------------------------------       2/1
1
5 + ----------------------------------------      11/5
1
1 + ------------------------------------      13/6        semester
1
6 + --------------------------------      89/41
1
1 + ----------------------------     102/47       octon
1
1 + ------------------------     191/88
1
1 + --------------------     293/135      tritos
1
1 + ----------------     484/223      saros
1
1 + ------------     777/358      inex
1
11 + -------    9031/4161
1
1 + ---    9808/4519
...
```

Tom Peters (talk) 12:34, 25 July 2011 (UTC)

Well take row 4, the 1st three rows I get (I think). How did we get from 13/6 to 89/41? Are these the "fractional parts" in the iterative process of computing continued fractions? I have the idea that it's not since they keep getting larger, and in the examples I've seen they get smaller. I will work out the continued fraction for 2.170391682 on my own and see what insight this gives me. Cheers. --TimL (talk) 13:16, 25 July 2011 (UTC)
The successive steps are:
2 = 2/1
1/5 + 2 = 11/5
1/1 + 5 = 6; 1/6 + 2 = 13/6
1/6 + 1 = 7/6 ; 6/7 + 5 = 41/7; 7/41 + 2 = 89/41 .
etc.
Tom Peters (talk)
I think the problem is I hate maths. It's my relative weak point and my brain has to work much harder to wrap my head around it, where as science and verbal reasoning just comes naturally, like breathing. I have yet to do the continued fraction myself, though, I want to do it so I understand, but part of me loathes the idea! I'm sure it's not so bad. --TimL (talk) 00:20, 26 July 2011 (UTC)
BTW, is there a trick to formatting tables like that? In the wiki editor it does not look like a table at all, do you just make it it a text editor with a fixed-width font and copy it over? --TimL (talk) 13:22, 25 July 2011 (UTC)
Use dfrac (see http://en.wikipedia.org/wiki/Help:Displaying_a_formula ). Victor Engel (talk) 16:28, 25 July 2011 (UTC)
If you start a line with a blank (space), Wiki will display text in fixed font - simplest way of aligning text. Tom Peters (talk)
Of course, a complication is lining up the rows with the corresponding fractions. I don't know the math coding well enough to suggest how to do that, but I'm sure it's possible. Since I've never used dfrac before, I'm going to use this comment as a test.

${\displaystyle 2+{\dfrac {1}{5+{\dfrac {1}{1+{\dfrac {1}{6+{\dfrac {1}{1+{\dfrac {1}{1+{\dfrac {1}{1+{\dfrac {1}{1+{\dfrac {1}{1+{\dfrac {1}{11+{\dfrac {1}{1+{\dfrac {1}{...}}}}}}}}}}}}}}}}}}}}}}}$ Victor Engel (talk) 19:09, 25 July 2011 (UTC)

I like the(slightly modified) output from this site http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html :
```2.170391682    half DM/SM      decimal       named cycle (if any)
Convergents:
2:               2/1     = 2
5:              11/5     = 2.2
1:              13/6     = 2.166666667   semester
6:              89/41    = 2.170731707
1:             102/47    = 2.170212766   octon
1:             191/88    = 2.170454545
1:             293/135   = 2.170370370   tritos
1:             484/223   = 2.170403587   saros
1:             777/358   = 2.170391061   inex
11:            9031/4161  = 2.170391732
1:            9808/4519  = 2.170391679
...
```
The reason I like it is because it doesn't show a continued fraction at all (I think complicated looking fractions, frankly, scare some people ;-) , tho notation is less confusing to me, and one can refer to continued fractions article to understand "convergence". JMO. --TimL (talk) 17:14, 25 July 2011 (UTC)
That works for me, however, I don't see that format in the wikipedia article for continued fractions or a straightforward explanation of convergents. If switching to that format, probably a reference using it would be a good idea.Victor Engel (talk) 19:09, 25 July 2011 (UTC)
It dos not work for me. What are convergents, how do you get them, and how do you use them to compute the fractions? For me how the numbers relate is immediately obvious if you write them in a chain of fractions with numerators and denominators over and under the division line(s), like Victor and myself have tried. Tom Peters (talk)
If you know know what a continued fraction is, why wouldn't you know these things? It works for me because I can't wrap my head around these nested fractions. How about leaving out the continued fraction part and just say in the text that the method of continued fractions was used to derive the ratios? I'm not sure I see the need for the computation (the lengthy fraction) to be shown. If someone knows how to do continued fractions, they can check it out for themselves. --TimL (talk) 00:38, 26 July 2011 (UTC)
It strikes me that TimL seems to be the only one to be confused by the nested fractions. Does it make sense to rework an article because one person (who admittedly is weak in math) is confused by elementary arithmetic? That comment is not meant as a sleight, please understand. However, this topic is in essence mathematical, and if you can't come to terms with the math, maybe you should leave the editing to someone else. The concept really is not very difficult.
I notice that the confusion tag is now gone, but I think the situation is now more confusing than before. Now we have text that shows two decimals being represented by the same series of continued fractions (except for the start). But they're shown in different formats, so they're not obviously the same. If a point is going to be made that they are the same, shouldn't they be displayed in the same format?
The comment "Less accurate cycles may be constructed by combinations of these" leads a reader to wonder why would someone want a less accurate cycle. Without an explanation, this seems like an odd thing to say.Victor Engel (talk) 14:19, 26 July 2011 (UTC)
I see Tom Peters changed the format while I was writing my previous comment.Victor Engel (talk) 14:21, 26 July 2011 (UTC)

## Beat period?

Beat period? What is a beat period? It's the interval between to successive beats according to the inter webs. What is the "beat period" of two different cycles? I can see why there has been so much frustration with how this article was written. I think only the author of it understood what he was talking about. No one can type in beat period on wikipedia or the internet to get clarification on this. --TimL (talk) 10:26, 23 July 2011 (UTC)

A beat period between two frequencies is simply the time between their phases lining up. In music, when you have two tones playing at the same time, they interfere with each other producing a third tone. This is called a beat. Eclipse cycles are no different. They just take longer.Victor Engel (talk) 03:43, 24 July 2011 (UTC)
I've used openoffice.org to create an illustration of the beat period in this case. See <URL:http://www.pbase.com/victorengel/image/136651391>. The blue represents the synodic period. The red represents the draconic period. The yellow represents the eclipse year. I didn't place units on the illustration, because the point is to show that one beat of the eclipse year happens each time the other two line up. That's what a beat period is. Victor Engel (talk) 04:23, 24 July 2011 (UTC)
One step ahead of you ;). I linked to beat (acoustics) in the article, which has a nice visual. Your picture is very nice, it took me a while to understand until I realized the the yellow part should cross the midline whenever the months line up or are 180 degrees out of phase. (half draconic month). What I see happening is when the month's are closely in phase or closely out of phase, the yellow area is near zero. It peaks when the two months are neither in, nor out of phase (dissonant I guess). My confusion was in trying to compare your graph to this graph --TimL (talk) 17:43, 24 July 2011 (UTC)
It's not where the peaks of the beat period are that matters but how far apart the peaks are. In my graphs, all three curves start at the left hand side at zero. This is because I used a sine function. Had I used cosine instead of sine, they all would have started at the top instead of the middle. The graph you linked to is probably more usual, since you can think of the beat period to be a scalar times the sum of the two other curves that way.Victor Engel (talk) 22:21, 24 July 2011 (UTC)
But the peaks are farthest apart at the middle of the graph. This is what I find confusing. If the yellow areas represents how far away the peaks are, why doesn't it peak in the middle of the graph? However if by closeness of peaks you mean regardless of sign (i.e. absolute value of the peaks) then it makes sense. The peaks do line up in the middle, they are simply π/2 out of phase. Is that correct?--TimL (talk) 22:45, 24 July 2011 (UTC)
I see you misunderstood. One the one hand, we need to look at how far apart the red and blue peaks are from each other. On the other hand, we need to look at how far yellow peaks are to other yellow peaks. In fact, it doesn't need to be peaks. That's just a convenience. We just need to see that the yellow curve will repeat when the red and blue curves diverge from each other by the same amount. On the left side of my graph, the red and blue curves coincide, and the yellow curve is ascending at zero. If we scan the graph until the next time the red and blue curves coincide, the yellow curve should have the same state (ascending at zero). The point is that the spacing between times that the red and blue curves relate to each other the same way matches the wavelength of the yellow curve. Victor Engel (talk) 16:22, 25 July 2011 (UTC)
What you say makes sense. It's a different representation than the graph at the Beat (acoustics) article. But the fact is in either representation the peaks (or midpoints) are the same distance apart. Your representation seems more appropriate for the subject matter (an eclipse cycle rather than a sound wave). Thanks! --TimL (talk) 19:41, 25 July 2011 (UTC)
I made two more graphs. The first one, http://www.pbase.com/victorengel/image/136706225 shows a horizontal scale in days and graphs of the synodic month, draconic month, anomalistic month, eclipse year, and fumocy. See the wikipedia article on fumocy for a description of that period. You can think of it as the period over which a full moon approaches and recedes from Earth. It is the beat period of the synodic and anomalistic months, whereas the eclipse year is the beat period of the synodic and draconic months.
Out of curiosity, I created another graph, http://www.pbase.com/victorengel/image/136706248 showing the beat period between the eclipse year and the fumocy. Victor Engel (talk) 21:51, 25 July 2011 (UTC)
Neat graphs, Victor. I noticed you deleted a sentence before I could reply, I guess the relationship in question would be between the synodic month and the eclipse year, as during a saros series they gradually fall out of sync, as fumocy would merely change the magnitude of the eclipse over time. --TimL (talk) 22:09, 25 July 2011 (UTC)

## Octon

I made a table of an octon series if anyone is interested. --TimL (talk) 00:47, 24 July 2011 (UTC)

Thanks. Just updated the eclipse cycle table by adding a coulmn showing each cycle in terms of the inex (i) and saros (s).
The octon is 2i – 3s. Also made a one-day correction in the tetradia duration. — Glenn L (talk) 05:25, 24 July 2011 (UTC)

## Repeating Decimals

I undid the repeating decimals change. First, indicating repeating decimals adds nothing to the article. Second, there's no indication which digits are repeated, making the ellipses worthless. Victor Engel (talk) 15:50, 26 July 2011 (UTC)

Understood. Was just extending what you have started, but it's better that they have been all reverted. — Glenn L (talk) 16:04, 26 July 2011 (UTC)

I added the Tzolkinex, although based on this chart it is a very poor eclipse cycle. I don't know yet how to derive the Inex/Saros formula for it, though I do know it is one saros minus one tritos. Perhaps I can figure it out from that. Is it worthy of an article (doubtful, too poor)? --TimL (talk) 03:05, 27 July 2011 (UTC)

## Question and comment

I notice the cycles hepton thru inex form a Fibonacci sequence. Can anyone explain the meaning of this? I think I found the answer to this by reading the article on the Fibbonacci series which, not coincidentally I'm sure, had a link to continuing fractions. Also, seems like there a quite a lot of cycles not listed, tirple tritos, triple tzolkinex, (both of which have close to an integer number of anomalistic months, even a triple octon comes close, though not very). I find the relationships between the inex, saros, tritos, and tzolkinex interesting. And the Fibbonacci sequence suggests that there are more cycles than you get from just representing the continued fraction.

Also I notice both the inex and the tritos both visit consecutive saros series with each member, or from the text "[the tritos] relates to the saros like the inex". Is there a cycle the tzolkinex relates to the saros like? --TimL (talk) 18:10, 27 July 2011 (UTC)

As the text says: "Less accurate cycles may be constructed by combinations of these". The continued fractions are the best approximations with the smallest denominators. Of course the number of combinations is infinite so it is pointless to start try list them all. Everything can be expressed as a combination of saroses and inexes. And then also tripling each cycle is trivial and they are not really new cycles. Historically the exeligmos (triple saros) has been noteworthy because it is close to an integer number of days and at a given site, solar eclipses are observable every 54 years, not 18 years. I object to inventing and introducing obscure and inaccurate cycles - there must be some historical justification, a reference to literature that discussed it. For instance, I would like to see a demonstration that the trriple tzolkinex was actually used in meso-america. Otherwise get rid of it!
As for the fibonacci relations: that is because in the continued fraction, 5 successive quotients are 1 .
Tom Peters (talk) 07:56, 28 July 2011 (UTC)
Took me a while (!), but I removed the phrase "triple tzolkinex" and simply replaced it with an explanation of the close anomalistic returns of every third tzolkinex. --TimL (talk) 18:13, 13 August 2011 (UTC)

## 'Eclipse series' which is 19 'eclipse years' (223 synodic months)

eclipse series which is 19 eclipse years (223 synodic months) - Ben Franklin 71.206.87.9 (talk) 16:08, 26 April 2013 (UTC)

How long an eclipse series lasts depends on the eclipse cycle being referred to. I removed the change. 20:53, 26 April 2013 (UTC)

## "Semetzi"

While working on my user page I noticed an interesting "coincidence". The total Solar eclipse of August 21, 2017 and the total Solar eclipse of April 8, 2024 cross paths over North America. That is one tzokinex minus one semester (I'll call it "semetzi" for short). The total Solar eclipse of August 12, 2045 and the total Solar eclipse of March 30, 2052 also cross paths over North America. Again one semetzi. There are others I've found as well. They are a half integer (2421.51) solar days apart (so the earth has rotated 180 degrees) so I don't understand how consecutive "semetzis" could fall on the same side of the earth. I think the half year offset ensures they cross paths, but I'm not sure why, in the examples I've found, eclipses near spring tend to track northwest and eclipses near fall tend to track southwest. This also seems to depend on the gamma of the eclipse as well as the time of year. This never seems to happen more than once in a row. For example the eclipse one semetzi after 2024 does occur on the other side of the earth like I would expect due to the half integer of days. Each eclipse is 6 saros apart so I can see why the pattern would break as the saros gets too old, but I can't explain why the 2024 eclipse seems to fall on the "wrong" side of the earth. Hmmmm.... 12:02, 19 November 2013 (UTC)

## Phi from continued fractions (fibonacci numbers in saros and inex)

I dont speak English very well, the reason that i wont edit the page, but if you want, you are free to do yourself. Since the beginning of past century astronomers noted a secuence of fibonacci starting in 6 moons (semester) then 41 moons, then 47 moons then 88 moons then 135 moons then 223 moons then 358 moons ... All this cycles have numbers of fibonacci in their components inex and saros, for examplo 5 inex - 8 saros in semester (6 moons), the continued fraction on Phi is 1;1,1,1,1,1,1,1,1,1,1.... and you will note that 2;5,1,6,1,1,1,1,1,11,... and 5;1,6,1,1,1,1,1,1,11... have five numbers one, in this numbers one we see from semester to inex, 5 cycles that belong to the secuence fibonacci, Finally we see the ratio sinodical month / half eclipse year of all eclipses that belong fibonacci serie, in continued fraction 5;1,6,1,1,1,1,1,1,1,1,1,1..... Today i have edited this talk too, because i noted that with continued fractions 2;5,1,6,1,1,1,1,1,11 and 5;1,6,1,1,1,1,1,11 the number of members of each eclipse cycles increase until the last cycle with 12 inex + 1 saros (9808 half draconitic months, 4519 synodic months and 770 half eclipses) that it is the knowed eclipse cycle with more life expectancy The fractions 5;1,6,1,1,1,1,1,1,1,1,.... and 2;5,1,6,1,1,1,1,1,1,1,1,.... (that contains the cycles with fibonacci numbers in inex and saros components) are only aproximations, but good aproximations, the difference continues after 1 saros and then 1 inex, that are the two cycles basis of all the eclipses cycles — Preceding unsigned comment added by Ignacio Colmenero Vargas (talkcontribs) 02:32, 18 March 2014 (UTC)

"the difference continues after 1 saros and then 1 inex, that are the two cycles basis of all the eclipses cycles", This fact is mentioned in the article on the Inex. I have added it to this article.  —  01:44, 19 March 2014 (UTC)

## The 12 inex + 1 saros the cycle with major number of members

All the values about eclipses change depending what epoch, i only talk about year 2000. In this year 12 inex + 1 saros has 14911 members, this cycle is the continued fractions 2;5,1,6,1,1,1,1,1,11,1 and 5;1,6,1,1,1,1,1,11,1, I think that it is the cycle with major number of members because the value of sidereal month / half draconitic month in continued fractions is 2;5,1,6,1,1,1,1,1,11,1,19,3,1,1,1,11 and the value of of half eclipse year / sidereal month is 5;1,6,1,1,1,1,1,11,1,20,1,2,1,130,1, so, just after the 12 inex + 1 saros, the calculated values are differents, for example after 12 inex + 1 saros the next cycle is or 239 inex + 20 saros or 251 inex + 21 saros (depending what value we use of both values)in a cycle we have the ratio sidereal month / half draconitic month is more accurate and in the other cycle the ratio half eclipse year / sidereal month is more accurate, but they isn't more accurate in both ratios, i am talking about calculated values i don't know if with real values it occurs the same, and i don't know if that the diference of both cycles is ¡¡¡12 inex + 1 saros!!! is only a concidence Ignacio Colmenero Vargas (talk) 14:58, 19 March 2014 (UTC)

## Aristarchus' Great Year

I think Aristarchus' Great Year of 45 Saroi should be included. This was found by Tannery correcting a digit in Censorinus and seems to be widely accepted. 9and50swans (talk) 12:00, 3 August 2015 (UTC)