Talk:Vinculum (symbol)

Overline
Vinculum may be displayed using Template:Overline. E. g. $\overline{AB}$ or &radic;$\overline{2+x}$. — Monedula 1 July 2005 08:05 (UTC)

Fictional usage
In the Star Trek universe, a Vinculum is the computer core aboard a Borg ship which interlinks all the Borg aboard and passes tasks to appropriate drones. Each Vinculum functions as one node in the Borg collective network. It is likely the name is derived from the Latin word as well.

The term Vinculum was also used in the video game Killer7 to refer to a set of gates. These Vinculum Gates were used to link the present situation experienced by Garcian Smith/Emir Parkreiner to the memories of his past, which are represented as chapters thoughout the rest of the game.

I removed the preceding definitions, as they have nothing to do with the topic of this article. I don't think they're notable enough to deserve their own articles complete with disambiguation, so I'll let them die here. Melchoir 06:51, 25 February 2006 (UTC)


 * Of course theyre not important enough to have their own articles, thats why they are minor sidenotes. In the name of Harman.....


 * As Back Matter should suffice and is on the disambig page. 98.4.124.117 (talk) 15:25, 18 November 2017 (UTC)

Bracket precedence
From my high-school mathematics, I remember that the vinculum is used to 'bracket' parts of a mathematical expression. This is the order of precendence for evaluating a mathematical expression which had multiple types of 'brackets' (from memory):
 * 1) Vinculum
 * 2) Parentheses
 * 3) Brackets []
 * 4) Braces {}

That is, the vinculum binds more tightly than any of the other brackets, and braces are the least binding.

VedLuap 04:23, 28 August 2006 (UTC)


 * That makes no sense. &radic;$\overline{2&times;(3+5)}$ can mean only one thing, and your suggestion gets us nowhere. Nesting dictates the order of evaluation with brackets.
 * On the other hand, it's a useful observation that the vinculum is a tool to group symbols, similar to the way brackets are used. The article should probably mention this.
 * &mdash;Herbee 00:32, 4 October 2007 (UTC)

The current example is perhaps not the most ideal. The vinculum turns a + b - c into a + (b - c)... which happen to be exactly the same thing. It's demonstrating the use of a vinculum in a situation in which it doesn't actually do anything. 82.34.94.95 (talk) 15:33, 5 October 2009 (UTC)


 * Fair enough. — Emil J. 15:55, 5 October 2009 (UTC)


 * Brackets precedence? That makes no sense. The nesting already does this job unambiguously and definitively, regardless of the style of brackets used. I think you have been told that, when nesting from inner to outer groupings, you should use these styles; indeed the list you give is the canonical order for this typographical rule. But if I take an expression that is well-formed according to this rule and then change the bracket styles, nothing changes as regards the order of evaluation. 2A01:CB0C:CD:D800:881E:A6AF:CA0:836A (talk) 13:10, 1 April 2021 (UTC)

Vinculums more common than indicated in article
Wow. Vinculums are everywhere! More places than was previously indicated in this article, and so I changed it.
 * Vincula, not vinculums. :P It's a latin word, you see. (I'm just saying, because when I read that, I actually had to pause for a second or two to parse "vinculums" (I didn't immediately see that you intended it to be the plural of vinculum, but I'm strange like that) ) S. Morrow 23:30, 16 July 2007 (UTC)


 * Reality check: Merriam-Webster accepts both vinculums and vincula. &mdash;Herbee 00:32, 4 October 2007 (UTC)

Antiparticles

 * Similarly, in particle physics, antimatter particles get vinculated, for example, if we use &beta; to represent an electron then we can use $\overline{&beta;}$ to be a positron, the antiparticle of the electron.

Bad example. (Anti)leptons are usually identified by their electric charge, as in e&minus; and e+ for electron and positron. Antibaryons are indicated with a vinculum, however. I rewrote the example accordingly. &mdash;Herbee 23:44, 3 October 2007 (UTC)
 * Isn't that a macron? Macrons are not used as grouping symbols. Instead, they are an overline for a single character to indicate some sort of change to the character. See:

--107.191.1.213 (talk) 23:21, 6 April 2017 (UTC)
 * You are correct, but then any horizontal line used in maths might be regarded as a vinculum, even the one you use when writing down a fraction. But in the sense of a grouping symbol, you are correct, as a single glyph needs no grouping. 2A01:CB0C:CD:D800:881E:A6AF:CA0:836A (talk) 13:13, 1 April 2021 (UTC)

Is a fraction bar a vinculum?
The citation at the bottom of this page - Eric W. Weisstein, Vinculum at MathWorld. - has no reference to vinculum also denoting the line between the numerator & denominator of a fraction. In the Wikipedia article on fractions these lines are referred to as vinculum. Is Weisstein correct that this line, aka "fraction bar", is in fact NOT a vinculum? I sure don't know which use is correct (though I'd suspect Weisstein right, huh.) Depending on which is, for consistency either the Wikipedia article on fractions or the article on vinculum ought to be changed. [User:Chris Weller] May 7, 2008 —Preceding unsigned comment added by 24.128.48.92 (talk) 23:51, 7 May 2008 (UTC)

I agree that Wikipedia seems to be the only 'source' for the vinculum name for the fraction bar in 'traditional display fractions.' It would only add to the idea that certain bits of Wikipedia are made up as their authors feel like. — Preceding unsigned comment added by 94.197.120.149 (talk) 16:53, 24 September 2013 (UTC)

Clearly you guys don't know how to google. https://books.google.com.au/books?id=PiAAAAAAMAAJ&pg=PA28&dq=vinculum+fraction&hl=en&sa=X&redir_esc=y#v=onepage&q=vinculum%20fraction&f=false mike40033 (talk) 14:26, 11 October 2015 (UTC)


 * Perhaps you should hold your erstwhile contempt. In the source you have given, the term vinculum does not refer to the fraction bar. It is properly used to indicate the parts in the diagrams that are to be treated as a unit. The symbol used is more of a brace than a straight line, but this is of no consequence in terms of the meaning of vinculum. I corrected your edit accordingly. Bill Cherowitzo (talk) 17:57, 11 October 2015 (UTC)

The older literature almost universally refers to bar between the numerator and the denominator as a vinculum. For example, "The line between the terms of a fraction serves as a vinculum both to the numerator and the denominator..." An Elementary Course of Practical Mathematics, James Elliot 1860

"a horizontal Bar ( such as separates the Numerator of a Fraction from its Denominator, ) is sometimes employed as a Vinculum." The Constructive Arithmetic. A School Treatise, Developing a New Method of Teaching, Etc, James A. Christie 1865

"The horizontal line in a fraction acts as a vinculum for both numerator and denominator." Elementary Lessons in Algebra, Stewart B. Sabin, Charles D. Lowry 1894

"So the line that separates the numerator and denominator of an algebraic fraction acts as a vinculum in uniting the terms of the numerator into one quantity..." Elements of Algebra, John Herbert SANGSTER 1876

"The line which separate the numerator and denominator of a fraction may be regarded as a sort of vinculum..." An Elementary Treatise on Algebra, Bewick Bridge, Thomas Atkinson, J. M. Phillips 1848  — Preceding unsigned comment added by 2601:440:C500:E0:ECA8:4D3A:BBF0:77C0 (talk) 00:55, 16 October 2020 (UTC)


 * While this is an interesting collection of quotes and you should be thanked for collecting them, I don't think that they actually support your claim that this term was "almost universally used" in this way. Two things pop out at me from this listing. First of all, almost none of them actually define the fraction bar as a vinculum, they hedge their bets by saying things such as; "...may be regarded as a sort of ...", "...acts as ..." and "...is sometimes employed as...". Furthermore, these are all elementary texts, written by school masters and not by mathematicians. A kind of Shaum outline of its day. I would not infer very much about their accuracy. --Bill Cherowitzo (talk) 21:18, 16 October 2020 (UTC)


 * If a vinculum is any horizontal line used for grouping, then the bar used in writing repeating decimals (when the period is more than one digit), and the fractional line (when the denominator is a sum, difference or product) is a vinculum. But I acknowledge that this observation does not settle the question beyond doubt (e.g., what if the period is just "3", or the denominator is "2" or "x"?).--Nø (talk) 23:59, 16 October 2020 (UTC)

Yet another use of vincula
I used to use them in statistical notation to indicate the mean, so I tracked this down and added a brief note. — Preceding unsigned comment added by 86.21.159.9 (talk) 08:46, 24 March 2012 (UTC)

The mean is a macron, not a vinculum. See --107.191.1.213 (talk) 23:23, 6 April 2017 (UTC)

Pi calculation
The page says in signed-digit representation, in balanced ternary:
 * $$\pi \approx 10.011\overline{1}111\overline{1}000\overline{1}011\overline{1}1101\overline{1}11111100\overline{1}0000\overline{1}1\overline{1}\overline{1}\overline{1}\overline{1}0\overline{1}$$

Can someone confirm this? As I understand it, it doesn't seem to converge to anything like pi. I get 2 + 0.25 + 0.125 - 0.0625 + 0.03125 = 2.21875 for the first several terms. It seems to me that it would be much closer with:
 * $$\pi \approx 11.01\overline{1}01\overline{1}000100000\overline{1}10\overline{1}1\overline{1}1\overline{1}001\overline{1}001\overline{1}0001\overline{1}10\overline{1}1\overline{1}0$$

Calculating out the first few terms again (assuming I'm understanding the terminology correctly), I get 2 + 1 + 0.25 - 0.125 + 0.03125 = 3.15625, and by the 27th digit, it gives 3.141592652. It wouldn't hurt if someone could briefly indicate why this is a useful way to show pi as well, but that is probably beyond the scope of the article. In any event, figuring out how to work this out in Excel was an interesting exercise. --205.254.147.8 (talk) 13:56, 16 July 2013 (UTC)
 * It’s balanced ternary, not binary: $$10{.}011\overline{1}1=3+1/9+1/27-1/81+1/243\approx3{.}14$$.—Emil J. 14:53, 16 July 2013 (UTC)
 * Ah, I see. Thanks. --205.254.147.8 (talk) 16:27, 16 July 2013 (UTC)

All that lines is vinculum?
I should like to see primary or even secondary examples of the use of the term vinculum for anything other than grouping together. It is most likely that the most correct use of vinculum is in the binding of terms, that is, the European pre-print precedent of the mathematical parenthesis/brackets, especially since that agrees with the Latin root.

"Tanton’s Take On … The Vinculum" says 15th – and 16th century European mathematicians used a horizontal bar, called a vinculum, to indicate “grouping together.” in the same sense as parentheses. Tranton presents cogent arguments for calling other horizontal lines vinculum, yet he doesn't cite sources. Tranton does not call negation, tristate, conjugate, antiparticle, Boolean algebra, or roman numeration symbols vinculum.

Abu Bakr al-Hassar developed the modern symbol for fractions, which is the use of a horizontal line (―) where the numerator and denominator are separated, but did he actually call it a vinculum? It makes some sense to call al-Hassar's mark a vinculum, but was it called that? Did he call it that?

I don't see the sense of calling a negation overstrike a vinculum, isn't that symbol more of reflection sof the history of the minus sign? Vedic Math seems to be the source of the overscore meaning negation, but is it really proper to call Vedic numbers "Vinculum numbers", especially since Tranton and others call something completely different "Vinculum numbers"?

Can we at least get references to pre-1980 math text books that uses the term vinculum for anything? IveGoneAway (talk) 18:27, 21 January 2014 (UTC)


 * I have not found a single reliable dictionary source that uses the term vinculum for anything other than grouping together. The math historian D.E. Smith used vinculum in two senses; 1) to indicate multiples of 1000 (sometimes) in Roman numerals, especially in the works of Pliny (1st Century) and 2) the Romans and others later in the Middle Ages used it to distinguish numbers from words. In both of these usages he is using the term as a synonym for overline. More importantly, Smith does discuss the fraction bar and does not use the word vinculum in reference to it. He also talks about the solidus as the slanted fraction bar, so it is highly unlikely that vinculum had the fraction bar meaning for him. My other go to source on notational questions is Cajori, and he does not use vinculum in that way either. I propose that all uses of vinculum other than the grouping ones which are unsourced should be pulled out of the main article and treated in a special section where they can be clearly labelled as possible misuses of the term. Bill Cherowitzo (talk) 05:31, 12 June 2014 (UTC)


 * Pulling out the unsourced, non-grouping uses seems a good idea. I don't have any time right now to write much more, but I did get to the OED over lunch, the general citations were 1700s, generally concerning delimiting (binding) compound roots in the expression of derivatives in Calculus (e.g., if I understand correctly, expressing the square root a polynomial grouped under a vinculum). IveGoneAway (talk) 22:40, 16 June 2014 (UTC)


 * Well I have finally gotten around to the edits I suggested above. And I have fixed the overline article as well. Bill Cherowitzo (talk) 19:37, 25 March 2015 (UTC)

Since the vinculum is etymologically a tie-bar, we might surmise that its primary meaning was always that of a grouping device, as per Bill's insistence here. Moreover, I think the spreading of its meaning to any horizontal bar in maths came about naturally through type-setters' jargon, who would of course refer to the physical piece of typesetting sort as the vinculum. 2A01:CB0C:CD:D800:881E:A6AF:CA0:836A (talk) 13:20, 1 April 2021 (UTC)

Vinculum vs. Parentheses
There is currently some disagreement between editors of this article as to whether the vinculum is an old notation superseded by parentheses, or whether it is still commonly used.

To the best of my knowledge, the vinculum is the main notation used today to indicate repeating decimals in the U.S., Canada, France, and Switzerland. In those countries, parentheses are typically used when the vinculum is not available (e.g., typographical systems that do not support mathematical symbols); some people also use them as an alternative notation. The situation may be different in other countries.

Please indicate below, if possible with references, what the situation is in your country. This will help us improve the phrasing of the introduction. Thanks. J.P. Martin-Flatin (talk) 10:17, 6 February 2018 (UTC)


 * I fail to see why there is any issue here. The historical record is quite clear. The standard references on mathematical notation (Cajori and Smith) are in complete agreement; a vinculum was used to group things together. With the advent of printing this function was replaced by the use of parentheses since they did not require over- or under-line typsetting. The only major remnant of this function is in repeating decimals where the use of parentheses to indicate the grouping would, I imagine, give an unpleasant visual image to the number (having extraneous in-line symbols). Although different cultures may use other ways to indicate repeating decimals, the replacement of a vinculum by parentheses in mathematical writing is almost universal except for this use. --Bill Cherowitzo (talk) 20:41, 6 February 2018 (UTC)
 * In my initial revert, I complained about the edit distorting the source. From the above it is now clear to me that this distortion was in fact OR, so I have now removed it. I do believe that there has been some misunderstanding here, so I also rewrote the intro paragraph to clarify the statement. If the added citations say that "the bar above a repetend is called a vinculum", then that is fine. However, if they say that "a vinculum is the bar above a repetend" then that is incorrect and the citation should be removed. In other words, the bar above a repentend is a vinculum, but not all vinculi are bars above repetends. I do not have access to these sources to check this myself. --Bill Cherowitzo (talk) 23:04, 6 February 2018 (UTC)


 * The new wording is much clearer and addresses the issue, as far as I am concerned. The two references that I added show how to indicate the repetend of a repeating decimal using a vinculum. J.P. Martin-Flatin (talk) 22:51, 7 February 2018 (UTC)

Roman numerals
The old Romans (bless 'em) had a totally different use - a vinculum over a Roman numeral multiplied it by 1,000 ! thus = 4,000. Just might rate a quick mention? --Soundofmusicals (talk) 18:25, 8 November 2020 (UTC)


 * I made an addition here. &mdash; Umofomia (talk) 21:45, 28 April 2022 (UTC)

math
The Horizontal line above a number 58.69.112.65 (talk) 07:48, 18 November 2021 (UTC)

Magic Dash
On Thursday October 13, 2022 Pete created a math term called MAGIC DASH was created instead of using the term Vinculum. Now we are trying to make this name known world wide and a national holiday on October 13 every year. BlueGaming2012 (talk) 23:15, 16 October 2023 (UTC)