Talk:Sexagesimal

message: What symbols were used historically for digits 11-59 in sexagesimal?  If those used today (obviously in very narrow practice) are different, what are those, as well?
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Today the symbol ':' is used for times (HH:MM:SS) in ISO 8601 and so is a de facto delimiter for sexagesimal digits. So we could have for example
  Sexagesimal  Decimal
        15         15
     01:03         63
     05:00        300
     16:41       1001
  02:05:00       7500
I also put the fractions in the article into this notation, keeping the '.' as the sexagesimal point.
Karl 24 March 2004, 21 July 2004
I think some sort of example like this should go into the article, unless it contravenes some style guideline. What are the rules concerning examples in articles? ais523 11:26, 16 June 2006 (UTC)
thread_title:  Symbols used 

message: The Ancient Indians had a sexagesimal system as well; as clearly explained in the Surya Siddhanta.  I think there needs to be a paragraph on that. In fact, the two cultures, Sumeria & India, developed the sexagesimal system independently.  —Preceding unsigned comment added by 67.180.39.64 (talk) 16:50, 22 April 2008 (UTC)
replies: text: Supply appropriate sources (both for their use in the Surya Siddhanta and, if you wish it stated in the article, for the independence of their development from the Sumerians) and we can add it easily enough. —David Eppstein (talk) 16:55, 22 April 2008 (UTC)
replies: text: The Surya Siddhanta is usually dated to the 3rd century CE based on the position of its vernal equinox, which is 'frozen' sidereally, now near April 14. This is many centuries after the Babylonians, and even after the Hellenistic astronomers, Hipparchus and Ptolemy, had used a sexagesimal system using Greek numerals. The supposed version dating to the 3rd century BCE is probably the Vedanga Jyotisha of Lagadha. Even that is still about 2500 years after the Sumerians are known to have used a fully formed sexagesimal system (except for zero) during the 3rd millennium BCE, based on surviving cuneiform tablets. I can't remember whether the Surya Siddhanta itself used sexagesimal notation. — Joe Kress (talk) 20:47, 22 April 2008 (UTC)
replies: text: Regardless of the (lack of) merit of any priority claims, or the pointlessness of claiming priority for sexagesimal when they have a much stronger and more important claim for decimal, if some ancient Indians actually used sexagesimal then we should mention it in the article. —David Eppstein (talk) 22:36, 22 April 2008 (UTC)
replies: text: Sixty was indeed used as a fraction system in india, especially since we have the day divided into 60 ghurries, each of 60 pali, of 60 vipali.  India acquired the zero by way of the arabs, who got it from the greeks.  --Wendy.krieger (talk) 11:02, 2 September 2009 (UTC)
thread_title: Sexagesimals in Ancient India

message: One should note that for the greater time, sixty-wise numbers are intended to be a division system, where the unit column is at the left, and more right-places are more precision.  For example, 15 hours, 15:00 hours and 15:00:00 hours are all the same thing, going to minutes and seconds respectively.
Zeros in the sumerian system reflect the division system, so they have leading zeros and medial zeros, but not trailing ones: we see eg 0:0:1 for 1 second, and 1:0:1 for 1 hour 1 second, but not 1:0 for 1 hour 0 minutes.  One could shift the lead column by changing the unit, eg 1:4 shock is 1.03333 shocks (of 60 in number), giving 64.
The ancient sumerian use of this system is a division-system (means of writing fractions), designed to avoid the arithmetic division.  We note that one of the common tables that come down to us is the table of ordered recriprocals, eg  3 -- 20   3.20 -- 18  etc,  one doing general division by way of interpolating this table.  
Neugebauer gives a reference to Sachs having 'recently' found a tablet dealing with the evaluation of 1/7, 1/11, etc, in the sense that :08:34:16:59 < 1/7 < :08:34:18, when a division give the correct value of :08:34:17:08...  
Neugebauer also gives the number of the sumerians for the multiplication scale.  It's a mixture of units, such as using i (one), x (10), I (60 = big 1) and X (big 10 = 100), along with U (120 = 2*60).  A date consistently refered to in the table as 3:12, would elsewhere be written as XIxxii (ie hundred+sixty+thirty+two).  
I have yet to see a practical application of sixty as a multiple-system, in the sense of other bases.  
Ref: O Neugebauer "the exact sciences in antiquity"
--Wendy.krieger (talk) 12:07, 27 August 2009 (UTC)
thread_title:  Sixty as a division-system 

message: I removed a dew sentences in the opening paragraph because I feel they are self references.  They are almost verbatim of the first item from Wikipedia:Manual of Style (self-references to avoid).  Rather then just revert I wanted to discuss the issue.  The exact quote is as follows: In this article, all sexagesimal digits are represented as decimal numbers...How is that line not a self-references?  meshach (talk) 23:36, 10 November 2010 (UTC)
replies: text: Did you read the section "Neutral self-references are acceptable" in the style guide you linked to? Because this example seems almost exactly like the ones in that section to me. —David Eppstein (talk) 06:31, 11 November 2010 (UTC)
replies: text: Yes I read that section but I did not think it applied here.  But I guess I see how it is possible.  Cheers, meshach (talk) 18:44, 12 November 2010 (UTC)
thread_title:  Self-reference in introduction 

message: The external link to Base 60 on Kubaz's mathematical corner was removed as spam (although it contains a description of digits of base 60 that should manifest mathematical logic). Is there any reason to keep the other link to Community Standard Sexagesimal, since, as far as I can see, it is just a description of digits used in a fictional universe created by the author of the website? The “Community“ in the name of the website is just a fictional community established in 2057… 90.176.211.48 (talk) 12:56, 30 December 2010 (UTC)
thread_title:  External links 

message: The paragraph about modern French is not really correct:
> A vestige of the sexagesimal system exists in the European and Canadian dialects of the French language, 
> where the numbers from 70 to 79 are rendered by adding a number to 60: 70, for example, renders as 
> soixante-dix (sixty-ten), and 75 is called soixante-quinze (sixty-fifteen).
This is a residue of a vigesimal (base 20 system), in which there are words for 60 and 80, but 70-79 and 90-99, are made by adding the numbers 10 to 19 to 60 or 80. 80 is also 'quatre-vingt' or 4-20, showing more evidence of a vigesimal system. 
In short, this is nothing to do with sexagesimal and I suggest that this paragraph be removed.  — Preceding unsigned comment added by Komaba (talk • contribs) 12:17, 14 February 2011 (UTC)
replies: text: Done. I'm not sure you can see from the modern words whether there is a historical connection to sexagesimal system, but it would require a source - and I'm pretty sure there IS no such connection, where as the vigesimal roots of French (and Danish) number words is undisputable.--Nø (talk) 15:07, 14 February 2011 (UTC)
replies: text: I agree with removing this. —David Eppstein (talk) 17:04, 14 February 2011 (UTC)

text: One should check out Old English where the numbers from 60 to 120 are of the form hundsixty, hundseventy, ... hundelefty.  Even though there is a base 20 substrate in french, the change at sixty should be noted.  --Wendy.krieger (talk) 07:33, 15 February 2011 (UTC)
replies: text: Linguistic remnants of sexagesimal in Old English or French should be noted if, and only if, they can can be properly sourced as being accepted by experts in the subject. —David Eppstein (talk) 07:44, 15 February 2011 (UTC)
replies: text: Who would ye like?  Sweet? Clark Hall? Onions? A list of numbers in OE does show the change at sixty.--Wendy.krieger (talk) 07:14, 16 February 2011 (UTC)
thread_title:  Sexagesimal in modern French 

message: Does the numbering system used by digital microwave ovens fit within the definition of sexagesimal as a modern usage? I ask because it appears to be a hybrid of sexagesimal and decimal, allowing values >59 in the seconds columns.  — Preceding unsigned comment added by TimWooley (talk • contribs) 15:08, 26 April 2011 (UTC)
replies: text:  It's actually mmss, but ye are permitted to enter 90 seconds as such, not as 130.  Nothing restricts you to using digits in the normal range in any number system: it's just that the normal name for the number is in the reduced range.--Wendy.krieger (talk) 07:39, 28 April 2011 (UTC)
replies: text: There is actually a hybrid system used by some ancient astronomers of recording the whole number part of a number in decimal notation and the fractional part in sexagesimal notation.  --SteveMcCluskey (talk) 22:47, 25 October 2012 (UTC)
thread_title:  Modern Usage 

message: I just revised the recent addition on "Facts on the Calculation of Degrees and Minutes" to make it accurately reflect the source, but after doing it, I'm uncertain whether it contributes much to the article.  If anyone else feels it's superfluous, go ahead and delete the section and I won't be the least offended.  SteveMcCluskey (talk) 17:46, 31 March 2013 (UTC)
thread_title:  External links 

message: When the article describes the factors of 60, it says it has 2 prime factors, but there is a third one: 2.71.204.170.66 (talk) 14:52, 11 October 2013 (UTC)
replies: text: It says that "two, three, and five" are the prime numbers. That does not mean "two prime factors, the numbers three and five" — for that meaning, the punctuation would be different (see oxford comma). It means "the prime factors are the numbers two, three, and five". —David Eppstein (talk) 16:15, 11 October 2013 (UTC)
thread_title: An error

message: I have this belief that somewhere along the line, sexagesimal fractions were written by some scholars using Roman numeral superscripts for the parts, with an invented "0", like this:
: 120 23I 34II 45III 56IV
Furthermore, this notation either influenced or was influenced by the familiar degree sign and single, double, triple prime notation, due to the obvious visual similarity.  Did I make this up, or did I read it somewhere? —Steve Summit (talk) 17:55, 18 December 2015 (UTC)
replies: text: Ah.  I didn't make this up, and it's mentioned at Degree (angle)#Subdivisions. —Steve Summit (talk) 21:09, 18 December 2015 (UTC)
replies: text: You may be right; I vaguely recall seeing it in some discussions of 17th c. astronomy (Newton?  Kepler?  Halley?) but it does need a citation.  There is a citation needed flag in the Degree article.  --SteveMcCluskey (talk) 23:31, 18 December 2015 (UTC)
replies: text:  It is definitely a known notational style, it is used throughout the English language translation of the Almagest.  I am viewing a version translated by R. Catesby Taliaferro.  The only question I have us whether this is the precedent for the ' and  notations for minutes and seconds.  I am sure it is, but I am searching for confirmation (which is how I stumbled on this discussion BTW). LaurentianShield (talk) 23:58, 24 June 2017 (UTC)
replies: text: I suspect it's a variant of the notation that Cajori attributes to Wallis's Mathesis universalis of 1657 (see the reference in the article).  It makes sense that someone using Wallis's notation might change it to describe minuta quarta with a superscripted iv instead of '.  That would place the introduction of that notation somewhere around the 17th century.  --SteveMcCluskey (talk) 01:39, 25 June 2017 (UTC)

text:  Found an excellent reference: Samuel Jeake A Compleat Body of Arithmetic. He explains the Roman Numeral superscript notation explicitly. I am still searching for better general explanations, but the term to search on is "Astronomicals". LaurentianShield (talk) 02:00, 25 June 2017 (UTC)
thread_title:  Roman numeral superscripts? 

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thread_title:  External links modified 

message: It's interesting to see the base 60 numerals:
0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWX FreddieBimble384 (talk) 07:32, 11 September 2021 (UTC)
thread_title:  Base 60 

message: On the iPhone app for the English Sexagesimal article, the main photo displayed doesn't relate to the topic. However when clicked on, a different photo, related to the article and displayed later on is displayed. This photo doesn't appear in the web version, and I'm not sure if this is an isolated issue to my device, but it was a jarring experience to open the article and see what appears to be a medical or surgical photo I wasn't prepared for. 68.186.87.217 (talk) 19:05, 13 September 2023 (UTC)
replies: text: There was some template vandalism a week ago that might have caused this, quickly removed (within two minutes of its occurrence). I have bumped the protection level of the template in hope of preventing repeat incidents. —David Eppstein (talk) 20:32, 13 September 2023 (UTC)

text: Yeah so this is still the case. It’s weird. If I on the first time upon viewing the article tap and hold on the bad image (it only works the first time), I could see which one it is: https://commons.m.wikimedia.org/wiki/File:Lipoma_04.jpg Please be advised the image may not be for the squiemish. It’s a surgical/medical image. I’m not sure if this is a case of data corruption somewhere because the image is not in this article. Northgrove (talk) 21:27, 27 September 2023 (UTC)
replies: text: It never was in the article itself. The vandalism was to a template used by the article. Anyway, if you're still seeing it, weeks later, it's probably in your browser cache. We can't do anything about that from this side. Maybe explicitly asking your browser to reload will help. —David Eppstein (talk) 21:30, 27 September 2023 (UTC)
replies: text: @Northgrove If you go to Special:Preferences and click to the "gadgets" tab, there is a checkbox for "Add a 'Purge' option to the top of the page, which purges the page's cache". Ticking this will add a "*" link at the top of pages which will clear cached images, which can sometimes help fix this kind of issue. (Sometimes you may need to clear your local browser cache instead.) –jacobolus (t) 02:07, 28 September 2023 (UTC)
thread_title:  iPhone incorrect photo (English)