Talk:Subtended angle/Archive 1

Archive 1

Subtend and insist

As far as I know, an angle is subtended by an arc, and not vice versa. Also, an object is subtended by a solid angle, and not vice versa. English is not my mother tongue. However, in my language there exists a second verb, which is used to express the opposite concept. I am not sure, but the most likely English translation of this verb is "to insist" (an angle insists on an arc = an angle defines the endpoints of an arc).

Thus, "subtended arc" is improper. The article should be called "subtended angle", and its text modified. Paolo.dL (talk) 17:20, 18 December 2007 (UTC)

Yes, this is very confusing. In the article listed as Solid Angle (http://en.wikipedia.org/wiki/Solid_angle), the following quote is made: "The solid angle, Ω, is the angle in three-dimensional space that an object subtends at a point." It appears there is confusion as to what subtend actually means. What should be the object of the verb? I must admit I see the statement that an object subtends an angle more frequently than visa versa. Should this article be corrected?Firth m (talk) 23:25, 24 February 2008 (UTC)

From a quick look at a few online dictionaries, it would seem to me that, in English at least, "subtend" appears to be a symmetric relation: if A subtends B, then B subtends A. The usage of a line/figure/object subtending a (solid) angle does seem to be somewhat more common, and is the only one given by MathWorld and thesaurus.maths.org, but the examples given in the general-purpose dictionaries strongly suggest that the opposite is linguistically valid as well. Indeed, some of the examples given, such as an arc subtending a chord, don't (directly) involve angles at all.

Incidentally, it is somewhat notable that most of the Google results for "subtend" are indeed dictionaries of some sort. It's just not a very commonly used word. —Ilmari Karonen (talk) 03:06, 3 November 2008 (UTC)

That's a lot of dictionaries. Let me add one more, the OED. According to the OED, "subtend" comes from the Latin subtendere, which comes from "sub-" meaning under and "tendere" meaning "stretch". As a transitive verb, it means "To stretch or extend under, or be opposite to: said esp. of a line or side of a figure opposite an angle; also, of a chord or angle opposite an arc." The sense of an angle subtending an arc goes back to the word's earliest use in English in Billingsley's 1570 translation of Euclid's Elements: "That angle is said to subtend a side of a triangle, which is placed directly opposite, and against that side." (I.IV.14) In the opposite direction, that of an arc subtending an angle, the earliest use is Leonard Digges, A geometrical practise named Pantometria (1571), which says, "This done conioyne their endes togither and the angle subtended of the longest staffe is a right." (I.xviii) So it seems that both "subtended angle" and "subtended arc", or equivalent constructions, have been used in English for over 450 years now. Ozob (talk) 15:28, 3 November 2008 (UTC)

It seems like Ozob's research is a bit more complete then mine. I just went to amazon and searched inside serveral geometry texts, but it does seem it is fine to use both constructions. Thenub314 (talk) 19:04, 3 November 2008 (UTC)

Another proposal: the arc subtends the angle; the angle intercepts the arc. Michael Hardy (talk) 19:13, 3 November 2008 (UTC)

If it helps any, people should remember that "sub" (as a prefix) does not always mean "under" in Classical Latin. It frequently means "coming up from below" (as in the verbs supporto, sustollo, and suffero). 216.99.198.254 (talk) 04:43, 21 June 2009 (UTC)

I think it is misleading to use dictionaries in this way. Dictionaries reflect usage, whether that usage is strictly-speaking correct. Also, this is part of a mathematics project, not English, so definitions and meaning could well be more specific.

Etymology is a much better method: But a word is coined to represent a specific concept – Just because another concept could be represented by that same word does not mean that was the original intention.

Original usage, therefore, is a good indicator of original intent, but that was 440 years ago: What should the modern meaning be – informed by years of use and interpretation and (mis)understanding?

Most disciplines have their own jargon, which is usually more (and extremely rarely, if ever, less) specific than common usage. And mathematics is surely the most disciplined of disciplines.

The most edifying observation is that MathWorld and thesaurus.maths.org only give one definition – a line subtends an angle.

So what do we want? – I want a word to describe one concept and have one meaning. What is acceptable should, I feel, carry little weight. We need a word that describes the construction of an angle from a line or similar, at a position, and 'subtend' fulfils that role admirably.

The angle subtended by a chord at the major arc of a circle, is constant, and is π minus the angle subtended at the minor arc.

We also need a word that describes the construction of an arc or line segment from an angle, although this would be less common in the practical sciences. Insist (which I like, but I'd have to look-up) and intercept, have been proposed here, but I don't know if there is an established convention. If I were writing about a line, I would probably use delineated, or segmented (as in a line-segment; but might be confused with the segment of a circle). A line-segment could be defined by an angle (and a line). An arc could be constrained by an angle.

We don't need to resort to overloading subtend. I think we should actively avoid this, as the two links above have done. Ζετα ζ (talk) 00:44, 3 July 2013 (UTC)