Talk:Radian/Archive 1

Archive 1

Untitled

Some talk has been archived in Talk:Radian/Dimensional analysis. — Preceding unsigned comment added by Brianjd (talk • contribs) 08:56, 16 November 2004 (UTC)

Mathematics and Physics?

What about other fields of science? Brianjd 09:57, 16 November 2004 (UTC)

Such as? --Doradus 14:31, 16 November 2004 (UTC)

Who invented the radian?

Who invented the radian? And when? — Preceding unsigned comment added by The Conquerer (talk • contribs) 19:07, 6 November 2005 (UTC)

image size reduction

I managed to reduce the image size by a half, by using only 32 colors (I know there are only 5, but for some reason when using only 5 colors the computer chooses the wrong colors) http://xs100.xs.to/xs100/06185/Radian_cropped_color.png deal with this as you'd like. — Preceding unsigned comment added by 87.69.22.188 (talk) 19:32, 3 May 2006 (UTC)

pick the palet Wolfmankurd 18:01, 27 May 2006 (UTC)

Dimensional analysis

Some of the symbols in the 'dimensional analysis' section are not displaying properly in my browser. (I'm using Internet Explorer.) What is the problem? Thanks. Axl 18:01, 13 January 2005 (UTC)

Hmm, I'm only having this problem when I use a thin client; the display is fine with a desktop PC. Axl 21:22, 13 January 2005 (UTC)

go to preferances>rendering math and mess around with the setting untill something works. One of them WILL work. — Preceding unsigned comment added by Haggis (talk • contribs) 11:53, 3 March 2005 (UTC)

I have moved jobs now and I no longer use a thin client. Thanks anyway. :-) Axl 20:13, 4 March 2005 (UTC)

Radians have units [L]/[L]. This matters when doing real dimensional analysis.Doolin 15:51, 2 May 2006 (UTC)

So add it. I would, but I have no idea what you mean by that, so I probably shouldn't. fel64 14:14, 3 June 2006 (UTC)

Angular velocity, angular frequency

It might be worth mentioning that angular velocities are often given in units of radians per second (rad/s or rad s^-1). This is common in mechanical and electrical engineering. And a conversion factor to revolutions per minute would be useful.

In electrical engineering, physics etc, angular frequencies (symbol omega) are also measured in rad/s. The conversion factor to hertz (cycles per second) is 2 pi.

Someone else do this. All my edits seem to get deleted these days. I suppose that's something to do with having a dynamic IP address and not being bothered to log in.

84.9.82.184 08:45, 1 May 2007 (UTC)

SI Multiples

This seems out of place here. Is there any practicle use for them at all? — Preceding unsigned comment added by 130.37.20.20 (talk) 10:34, 16 December 2005 (UTC)

I have never seen or heard anyone mention milliradians or microradians, let alone stuff like megaradians. I would indeed propose to remove the table of SI multiples. MHD 12:18, 3 February 2006 (UTC)

I believe that milliradians are used in gunnery in some countries, since 1 mrad corresponds conveniently to 1 m at a range of 1000 m. I doubt that prefixes larger than milli- have ever been used. Indefatigable 17:17, 3 February 2006 (UTC)

Not so familiar with gunnery myself, glad someone else is. Can I assume from your message that you acknowledge the uselessness of the complete table of multiples? We could place a reference to milliradians as used in gunnery somewhere in the article, the rest of the table is not needed. I am quite curious if someone could provide an example of the use of kiloradians, megaradians or even gigaradians. That is how many times a complete circle? :-) MHD 20:03, 3 February 2006 (UTC)

A gigaradian is $5\times 10^{8} \over \pi$ complete circles. Or was that a rhetorical question? I think it's OK to delete or truncate the table. Several months ago, some folks merged all articles with prefixes into the base unit articles (kilometre merged into metre, gram merged into kilogram, and so on), and it was at this time that prefix tables were added into the articles on all SI base and derived units. For radians it does not make much sense. Indefatigable 21:51, 9 February 2006 (UTC)

They are used when considering a bead on a string which is being spun for example, rather than the distance it rotates( circumfrences) being measured the radius( string length) and the number of revolutions is. The number of revolutions is sometimes in radians (4π being 1 revolution) leading to measurements of something which rotates at say 3 million rad/s would be 3 Megarad/s. I dont really see an application of this out side of examination questions. Further, Radians is no longer considered SI is it? seing as it has no units it is now a derived unit as Indefatigable said.Wolfmankurd 18:17, 27 May 2006 (UTC)

I am involved in precision shooting in which milliradians feature heavily. I would like to query the accuracy of the statement a milliradian is equal to a metre at a range of 1000 metres. I believe that this is quite incorect. At 1000 metres a milliradian (according to my calculations) is equal to 90 centimetres which is more like one yard not one metre. Might seem like a small thing bt it is a maths topic so the maths should be right. —Preceding unsigned comment added by 203.171.86.27 (talk) 04:27, 24 October 2007 (UTC)

A radian is a length only if measured along a circle. If you want the length of one milliradian at 1000 meters, the only way it is meaningful mathematically is to measure off 1/1000th of the range along the circle centered at the shooter. That gives a height of 1000 sin .001, which is indistinguishable from 1 meter (it's off by a fraction of a micrometer). Zaslav 05:47, 29 October 2007 (UTC)

Broken link

It looks like http://wolf.galekus.com/viewpage.php?page_id=10 doesn't work any more. Is it okay to remove it? - turbov21 —Preceding undated comment was added at 21:45, 14 September 2008 (UTC).

FAC?

Surely it would not be too diffcult to polish this article to featured standard? Apart from some reference, what else is missing? -- ALoan (Talk) 16:25, 14 February 2007 (UTC)

It's a good article I agree, but doesn't have much content, although trying to include it all would make the article pages and pages long. Wolfmankurd 19:24, 23 February 2007 (UTC)

One small thing I'd suggest is to switch the graphics so that the first graphic is the http://en.wikipedia.org/wiki/Image:Radian_cropped_color.svg and the second is the graphic of the angles. I think the picture is the best possible way to describe a radian, and should be the first thing you see. Lastly, in the description, I'd italicize 'angle' so it would say "An angle of 1 radian subtends an arc equal in length to the radius of the circle."

Or better yet, "An angle of 1 radian results in an arc with an equal length to the radius of the circle." —Preceding unsigned comment added by Nlspiegel (talk • contribs) 21:04, 31 October 2008 (UTC)

Thanks very much

I appreciate what you have done here. I haven't I have gone beyond Trigonometry and your explanation about Radian measure and your depiction of conversions from radian to degree and degree to radian is great!

Ti-30X (talk) 04:11, 31 March 2009 (UTC)

Made change to clarify

I changed 'can be mistaken for degrees' to 'is often mistaken for degrees'. Saying it 'can be mistaken for degrees' sounds like you're allowed to think of it as degrees. Daemonax (talk) 02:29, 19 July 2009 (UTC)

Radians rule

Someone has written in the article that the radian is the 'standard' unit of angular measurement, "in all areas of mathematics beyond the elementary level." I think that statement is meant to convey the dominance of the radian and the poor show of those who still play around with degrees.

The truth is that the vast majority of people only get as far as the elementary level referred to, and as a consequence, it is the degree which most people are familiar with and it is the degree which is used in most areas of life. That isn't to say that radians don't have their advantages, or that they are vastly superior for many purposes, but it is misleading to give the impression that the degree has little significance just because you happen to be a scientist or mathematician. Just my view. — Preceding unsigned comment added by 81.187.233.172 (talk) 20:22, 20 December 2009 (UTC)

The article has already explained why the radian is the natural unit for many desired calculations. The quotation does not seem to be unreasonable. --Rifleman 82 (talk) 01:24, 21 December 2009 (UTC)

Not talking about the fact that radians are naturally "bound" to the length of an arc, so that ang(radians)×radius gives this length (and we know the ratio of the circumference to its diameter (2radius) is pi, an important constant) --Ittakezou0 (talk) 08:39, 14 June 2010 (UTC)

Are you making a criticism? If I follow correctly, I think the article does make that point about the relation of radian measure and radius to length of the arc in the Definition section. Tystnaden (talk) 11:31, 16 June 2010 (UTC)

Proposal to edit the article

This is a good article but needs improvement. One of that is a simpler definition of radian and a derivation needs to be added for the conversion of radian to degree. Below are the changes I intend to make. Apple Grew (talk) 06:00, 15 May 2011 (UTC)

Changes committed. Apple Grew (talk) 15:47, 15 May 2011 (UTC)

Simpler definition of radian (this will be inserted in header and Definition sections)

Radian can also be defined as a ratio between the length of an arc and its radius.

After a friend's suggestion, it seems that it would be better to simplify the header summary and move the technically precise definition to Definition section. (I have italicized the new text.)

After this the heading section should read:-

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. It describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. The unit was fo...

and the Definition section should read:-

Radian describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an...

Apple Grew (talk) 06:28, 15 May 2011 (UTC)

Radian to degree conversion derivation (this will be added as a new section after Conversions section)

We know that the length of circumference of a circle is given by $2\Pi r$, where r is the radius of the circle.

So, we can very well say that the following equivalent relation is true:-

$360^{\circ }\iff 2\Pi r$ [Since a $360^{\circ }$ sweep is need to draw a full circle]

By definition of radian, we can formulate that a full circle represents:-

${\frac {2\Pi r}{r}}radian$

$=2\Pi radian\,\!$

Combining both the above relations we can say:-

$2\Pi radian=360^{\circ }$

$\Rrightarrow 1radian={\frac {360^{\circ }}{2\Pi }}$

$\Rrightarrow 1radian={\frac {180^{\circ }}{\Pi }}$

Proposal end

Please do let me know if you see any issues. Apple Grew (talk) 06:00, 15 May 2011 (UTC)

Clayton's "circ" notation

I've moved the following text from the article to here:

An article has appeared which claims to make the radian unit unnecessary.

As written, this text has some stylistic issues (for example, the citation should be formatted according to Wikipedia:Citing sources), and doesn't really explain anything about what this proposal would do. I'm also a bit skeptical about whether we want to be including things like this. People propose new notations with some frequency, and even the ones which get a lot of attention seem to be controversial on wikipedia, much less ones which have gotten little or no reaction. Kingdon (talk) 02:57, 6 July 2011 (UTC)

Typo in Criticisms Section

The third sentence in the Criticisms section reads: "..have been critical to the costume of expressing radians..."

Should be: "...critical to the custom of expressing..." Slibville (talk) 02:37, 19 July 2011 (UTC)

I've made that edit but feel free to Be bold in such situations in the future. Kingdon (talk) 00:15, 20 July 2011 (UTC)

Another typo

"a SI" should be "an SI." — Preceding unsigned comment added by 173.170.24.219 (talk) 00:12, 14 February 2012 (UTC)

Edit request on 15 February 2012

In the Criticism section, where it says "A constant representing 2π has been proposed...", I think the "constant representing 2π" could be a link to the Tau (2π) article.

193.84.186.81 (talk) 10:05, 15 February 2012 (UTC)

Done — Bility (talk) 16:45, 15 February 2012 (UTC)

Radian unit symbol and other points

The radian is represented by the symbol "rad" or, more rarely, by the superscript c (for "circular measure")

I've never seen an occurrence of such c-superscript symbol to denote radians. If it is too rare that the above statement could as well be replaced by "I once saw a superscript c to denote radians..." could it be simply ommited? Please note that I'm not trying to make a big deal of it. It's just that I found this odd.

Sorry if I am talking nonsense, I'm not used to more traditional geometry literature. I'm only saying this for the sake of the 'encyclopedicity' (an odd word) of the article. In this way, I would say that if there weren't a standard unit for the measure, than a section mentioning this and pointing the most commonly used units would be necessary. If some unit was often used in the past but fell after some standarization than both the standard unit and the old one should be mentioned - after the introduction - as, for example, in

Nowadays, according to the SI, the radian is represented by the symbol "rad", but it was most commonly represented by the superscript c in the past, as in the classic "Treatise on Geometry" of John Doe [references here].

(Wouldn't Florian Cajori's History of Mathematical Notations be enlightening here? I haven't read it.)

I think that not all aspects of the subject need to be mentioned in the introductory paragraph. In particular highly off-mainstream aspects worth to be mentioned in specific sections together with the appropriate references.

I would also remove the whole second paragraph from the introduction and place it in a more appropriate subsection (together with the first occurrence of the c-superscript thing in the article, perhaps...).

Doing like this, I think we end having a straight-and-clarifying introduction and enriching subsections spanning the whole subject.

Cheers! — Preceding unsigned comment added by Seneika (talk • contribs) 21:25, 21 January 2011 (UTC)

the superscript c symbol is used in the UK and is mentioned in the high school maths syllabus--Mongreilf (talk) 23:58, 4 April 2012 (UTC)

I haven't seen it in any of the syllabuses that I've read. Could you cite an example? Dbfirs 06:52, 6 April 2012 (UTC)

Edit request from 75.172.105.35, 27 January 2011

{{edit semi-protected}} a radian is not 180 / PI degrees, a degree is 180/PI radians.

75.172.105.35 (talk) 00:54, 27 January 2011 (UTC)

Not done: No, that's just wrong. Read the article and the math more carefully. Qwyrxian (talk) 04:34, 27 January 2011 (UTC)

I've altered the article slightly to try to avoid this misunderstanding of the statement. Dbfirs 17:38, 17 April 2012 (UTC)

Current conversions from radians to degrees and degrees to radians are wrong

360 degrees = 2pi radians. Therefore 1 degree = pi/180 radians. But the current section says degrees = radians * 180/pi, the inverse of what is correct. Earlier versions of this article had the correct conversion. Flenk (talk) 15:24, 8 December 2010 (UTC)

In this particular section, I added line breaks between the equations because to an inexperienced user it would look like you are raising 180 to pi in certain places. Tahabi (talk) 21:27, 6 April 2011 (UTC)

Eh? Degrees = radians * 180/pi is correct. One degree = pi/180 radians, and therefore number of degrees needed to make up an angle = number of radians * 180/pi. For instance, if the angle is 2pi radians, the formula gives degrees = 2pi * 180/pi = 360 which we know is correct. 2.25.140.75 (talk) 21:37, 3 September 2011 (UTC)

I'm looking at Michael Sullivan's text: 1 degree = (pi/180)*radian, and 1 radian = (180/pi)*degrees. The conversions on this page are switched. Why the ongoing confusion? Leebeck33 (talk) 14:04, 17 April 2012 (UTC)

There is a misunderstanding of the statement. I've tried to clarify. Does it help? Dbfirs 17:40, 17 April 2012 (UTC)

Criticism

What happened to the crticism section of the most useless unit of angle measurement ever? — Preceding unsigned comment added by 108.217.226.133 (talk) 03:51, 30 June 2012 (UTC)

I don't know, but we prefer facts over opinions. Dbfirs 06:52, 30 June 2012 (UTC)

Opening sentence

The opening sentence, "Radian is the ratio between the length of an arc and its radius", is not correct English. Could someone fix this? — Preceding unsigned comment added by 86.160.216.252 (talk) 19:57, 24 October 2012 (UTC)

How's this? —Tamfang (talk) 21:22, 24 October 2012 (UTC)

I've added "numerically equal to" to avoid the problem of the radian having units of length. Dbfirs 22:06, 24 October 2012 (UTC)

Thanks guys. If I might make another suggestion, perhaps the second sentence should be reworded so as to use the word "ratio"? The thing is, at the moment the text reads "An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle", then later "As the ratio of two lengths, the radian...", but at the time of the latter there has been no mention of any "ratio of two lengths". I just think it's a bit confusing. 86.160.216.252 (talk) 00:37, 25 October 2012 (UTC)

FYI, the lead used to look like this. This edit later turned it into something ungrammatical, which suprisingly seems not to have been spotted for a year and a half. 86.160.216.252 (talk) 00:59, 25 October 2012 (UTC)

I've moved the mention of ratio to the definition section, leaving the lead section as a very simple introduction. If anyone would prefer to go back to the earlier version, I'm also happy with that. What does anyone else think? Dbfirs 07:04, 25 October 2012 (UTC)

In my opinion, if the lead section is supposed to be a deliberately simple and non-technical explanation then it fails in that endeavour. In particular, people with no prior knowledge of the subject are unlikely to understand "unit circle" or "corresponding arc" . I know "unit circle" is linked, and there is also a diagram, but even so.... 86.160.209.181 (talk) 13:47, 25 October 2012 (UTC)

Edit request on 29 August 2013

Typo in section "Radian to degree conversion derivation": [Since a 360° sweep is need to draw a full circle] should be [Since a 360° sweep is needed to draw a full circle] 80.123.117.50 (talk) 14:07, 29 August 2013 (UTC)

Done. John W. Nicholson (talk) 00:13, 30 August 2013 (UTC)

I'm not convinced that this section should be retained, but at least we now have a grammatical sentence. I'll remove the conversational "we", pending acceptance or deletion of the section. Does anyone think it adds to the article? Dbfirs 10:11, 30 August 2013 (UTC)

Well, if you mean that all of the conversion sections need to be removed, then something needs to replace it as to explain the conversion factors. The part that I would change (but know am not the greatest with grammar) is the "As stated" at the beginning of "Conversion between radians and degrees" which relies on a prior weaker section and does not stand alone. John W. Nicholson (talk) 14:00, 30 August 2013 (UTC)

Sorry, no, I just meant the rather laboured explanation of where the conversion factor comes from. The facts have already been given in the definition section. I agree with you that "as stated" would be better omitted. Dbfirs 07:32, 31 August 2013 (UTC)

If no one objects, I'll remove the rather convoluted derivation in favor of something more like the radian to gradian explanation. There is no need to involve the circumference or radius in explaining the conversion between one angular measure and another. Regards, Celestra (talk) 18:18, 7 September 2013 (UTC)

I'll support that. Dbfirs 05:45, 8 September 2013 (UTC)

Failed to parse (unknown error): \tfrac{4}{5}\pi

I can't Edit this. Please fix it.--Dgbrt (talk) 07:58, 30 September 2013 (UTC)

Gobbledygook

"An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle..." To an unsophisticated visitor hoping to learn, this will read as impenetrable gobbledygook. Wikipedia academics just love to show how clever they are, and seem incapable of writing anything in simple, unadorned English.119.18.11.19 (talk) 13:11, 25 April 2014 (UTC)

I've moved your comment to the end where new comments should go. The statement does sound a bit technical, but it is accurate. Can you suggest a way to state the fact more clearly and concisely? Dbfirs 18:26, 25 April 2014 (UTC)

File:Circle radians.gif to appear as POTD

Hello! This is a note to let the editors of this article know that File:Circle radians.gif will be appearing as picture of the day on September 23, 2014. You can view and edit the POTD blurb at Template:POTD/2014-09-23. If this article needs any attention or maintenance, it would be preferable if that could be done before its appearance on the Main Page. Thanks! — Crisco 1492 (talk) 00:41, 5 September 2014 (UTC)

Picture of the day

The radian is the standard unit of angular measure, used in many areas of mathematics. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle, so one radian is just under 57.3 degrees (when the arc length is equal to the radius); a full circle corresponds to an angle of 2π radians. In the SI, the radian has the symbol "rad"; it was a supplementary unit until that category was abolished in 1995, and is now considered a derived unit.Diagram: Lucas V. Barbosa

"this category was abolished in 1995 "

Abolished by whom? Is there a supreme authority for mathematical terminology? If so, what authority abolished the term? Terry Thorgaard (talk) 17:05, 23 September 2014 (UTC)

Apparently there is a supreme authority for SI units, and Rifleman 82 has added a reference so that you can look it up. Dbfirs 20:04, 23 September 2014 (UTC)

Edit request on 30 August 2013

The conversion formula is wrong: it is not according to the explanation: it should be: 1 degree = PI/180 radians 94.126.240.2 (talk) 09:34, 30 August 2013 (UTC)

No, the formula is correct. You are also correct in your claim about one degree, but you are misunderstanding the purpose of a conversion formula. Dbfirs 10:08, 30 August 2013 (UTC)

What follows is a proposal separate from the above.....

RADIANS

the conversion to turns needs multiplying not dividing.....in CONVERSIONS after 2nd EXAMPLE

Proposal by Manas, Jaipur, India — Preceding unsigned comment added by 2620:117:C080:520:1A03:73FF:FE0A:7831 (talk) 09:42, 27 September 2014 (UTC)

The conversion given in the article is accurate, so please don't change it. Could you give us an example of how you think it fails, then we can explain. Dbfirs 11:26, 27 September 2014 (UTC)

Semi-protected edit request on 18 February 2015

I believe that in the small box on the right it should say that 1 radian ≈ 57.296, not 57.295 118.209.12.196 (talk) 10:50, 18 February 2015 (UTC)

 Done Correct, the 3 decimal place rounding should be 57.296, thank you for noticing. Joseph2302 (talk) 16:03, 18 February 2015 (UTC)

radians = m/m ?

This may be a rather abstruse point, as it makes no practical difference, but I can't recall seeing it discussed. If it has been discussed in a suitable source, it would be nice to mention it briefly in the article: Take the case of e.g. alternating current, described by a sinusoidal function of time. In this case, would it not be more accurate to describe the units of the argument: omega t to be radians = A/A, the 'angle' occuring in a complex plane with axes in amperes? The units cancel, but which units cancel surely depends on the physical quantity expressed.Dayfield (talk) 16:56, 25 November 2015 (UTC)

That's why the radian is described as a dimensionless quantity in the article. Dbfirs 20:30, 25 November 2015 (UTC)

unitless and dimensionless are not the same. AManWithNoPlan (talk) 03:46, 26 November 2015 (UTC)

Yes, radians are units, and also dimensionless, I don't think I suggested otherwise (I've been teaching this to my students for many years!). My query is as to why they are described, specifically, as metres per metre (e.g. in wikipedia article 'SI derived units' and the 'NIST Guide to the SI') rather than e.g. 'amps per amp' or 'volts per volt' etc. I can see why metres per metre would be true for an actual physical angle between two lines, but not for many other types of quantity which are described using radians. In all such cases the result is still dimensionless, as required.Dayfield (talk) 18:32, 26 November 2015 (UTC)

Apologies if I misunderstood your question. I can't find anywhere in this article where any unit is divided by itself, but if length is mentioned elsewhere it's just because the radian is defined in terms of length. Dbfirs 18:50, 26 November 2015 (UTC)

Sorry, my fault, I originally mixed this article up with the more general one on SI derived units. There, and in e.g. the 'NIST Guide to the SI', radians are described, specifically, as metres per metre.Dayfield (talk) 19:26, 26 November 2015 (UTC)

Angular velocity and acceleration

In the section "Use in physics", the order of the sentences "For the purpose of dimensional analysis, the units of angular velocity are s−1 and s−2 respectively." and "Similarly, angular acceleration is often measured in radians per second per second (rad/s2)." should be exchanged and the first sentence should be modified as "For the purpose of dimensional analysis, the units of angular velocity and acceleration are s−1 and s−2 respectively." Jmspar (talk) 09:07, 15 January 2016 (UTC)

Thank you for pointing that out. I've made the edit. Dbfirs 12:41, 15 January 2016 (UTC)

Trigonometric identities

According to the article, the use of radians makes the Limit of (sin x)/x as x approaces 0 equal to 1. However, this identity is true for any angle measurement unit. So why are radians used? --BrainInAVat 17:51, 1 October 2005 (UTC)

you are wrong, it's simply 1 only using radians... --Arirossa 09:46, 23 February 2007 (UTC)

really? 0 grads are 0 gradiants so i do not see clear why should be like that... is there any reference to probe that it is only valid for radians? - 02/2016 — Preceding unsigned comment added by 217.14.40.189 (talk) 17:13, 15 February 2016 (UTC)

I think you are misunderstanding the meaning of the limit. Try dividing sin 10 by 10 on your calculator, then sin 5 divided by 5, then sin 3 divided by 3 then sin 2 divided by 2, then sin 1 divided by 1, then sin 0.5 divided by 0.5 ... and so in degrees and in gradians. Your limit will not be 1. Dbfirs 18:23, 15 February 2016 (UTC)

Source?

I am trying to find a source for why this would work (with 𝜏 = 2π):

Start at any point on a unit circle, and rotate by any value which is not an integer multiple of 𝜏, which includes π, the starting value is not returned. However, rotating by 𝜏 or a integer multiple of 𝜏 returns to the starting value.

I am a little surprised that I did not a statement of this sort in a Wikipedia page. John W. Nicholson (talk) 05:29, 2 February 2013 (UTC)

What do you mean by "starting value"? —Tamfang (talk) 05:43, 15 July 2016 (UTC)

Presumably "starting configuration" was meant. Tau is the unique value with this property. But does it belong in this article? —Quondum 06:01, 15 July 2016 (UTC)

Edit requist

Please remove "tau" this is not relevant or needed on this page. — Preceding unsigned comment added by 83.104.248.190 (talk) 23:31, 29 February 2012 (UTC)

Of course it is, we’re talking about radians, angles, and pi; all of which make tau relevant. — Preceding unsigned comment added by Braŭljo (talk • contribs) 06:31, 4 September 2016 (UTC)

π radians ≠ 180°

This is a common misconception. Both are real numbers and dimensionless, both are a measure of the same angle. The measures are equivalent, the equivalence relation is given by the bijection $f(x)=x*{\frac {180}{\pi }}$, but not equal. — Preceding unsigned comment added by 109.88.96.245 (talk) 14:13, 20 May 2017 (UTC)

I think you are splitting microscopic hairs in that argument. For all practical purposes they are equal, and I think the article is correct in making that claim. Are you basing your argument on some obscure Hilbertian definition of angle? Dbfirs 15:35, 20 May 2017 (UTC)

I haven't edited the article for a similar reason. Yes, for all pratical purpose they are equal, but they are not technically equal. An angle is the equivalence class of 2 half-lines sharing the same starting point, with the equivalence relation :

[2 couples are equivalent if there exist a positive isomotry sending one to the other].

You can extend this definition, but let's stick in the euclidean plane. A measure is a function from the sets of all angles to the real numbers. So with have 2 functions, one for the degrees $m_{degrees}$ and one for the radians $m_{radians}$. The unit is here to notice which measure is used.

When you write "180° = π radians" what you mean is "an angle of a measure of 180° is equal to an angle of measur of π radians". Or more rigorously $m_{degrees}(x)$ = 180 and $m_{radians}(x)=\pi$ then x=y". Again, I don't want to edit the article, this error is just technical and mostly a shorcut. I just wanted to notice it, for the sake of keeping mathematics right. — Preceding unsigned comment added by 109.88.99.197 (talk) 16:48, 20 May 2017 (UTC)

Not all mathematicians take a Hilbertian approach, and if you define angle as simply an amount of turn then equality follows without a problem. Dbfirs 18:23, 20 May 2017 (UTC)

That's exactly the problem, in 2017 the angles are defined in the way I did. The "amount of turn" is hard to define in a rigorous way. Without rigor, we end up with paradoxes. — Preceding unsigned comment added by 109.88.99.197 (talk) 19:20, 20 May 2017 (UTC)

Here in the UK, we still teach Euclidean geometry, but I'm aware of the Hilbertian approach. I'm curious to know what paradoxes result from defining angle as an amount of turn. In the article, a radian is defined in terms of an arc length. Is there also a problem with defining equality of lengths? Dbfirs 19:35, 20 May 2017 (UTC)

The measure of an angle has to be dimentionless, or the dimensions break in physics. So the measure of an angle has to be a real number. You can change change the meaning of "degree" : "°" means "*${\frac {180}{\pi }}$" and radian means "*1". Then of course 180°=$\pi$. With the axiom "the measure of an angle has to be additive", every measure can be defined in terms of lengths. A radian is the measure of an angle intercepting an arc of length equal to the $r$, a degree is the measure of an angle intercepting an arc equal to ${\frac {\pi }{180}}*r$. I don't know what the definition of "amount of turn" is. I can sense the logic behind it but it has to be rigorous to be accepted. And sorry for my english, I wanted to say "without a rigorous definition, a paradox may arise", I was thinking about Russel's paradox. — Preceding unsigned comment added by 109.88.99.197 (talk) 20:09, 20 May 2017 (UTC)

Radian

Value of one angle in hexagonal(benzene) Kaptan hansawat (talk) 03:37, 17 January 2018 (UTC)

S.I. unit or derived unit?

The first paragraph makes two contradictory statements: first it says "radian . . . is the SI unit for measuring angles", but then it says "radian is . . . an SI derived unit".

Which is correct? A unit can't be both; it is either an official S.I. unit (like the kilogram) or an S.I.-derived unit (like the metric ton).

If it is a derived unit (as the Wikipedia article on derived units suggests), then this article should not only represent it as such, but ideally should also state what actual S.I. unit it is derived from. — Preceding unsigned comment added by 2601:601:E03:EBC0:E8DE:238A:F28F:65EE (talk) 06:46, 25 August 2018 (UTC)

The radian is a derived unit, being metres divided by metres. It is still an SI unit, along with other derived units such as newton, volt and ohm, but not a base unit. Dbfirs 06:55, 25 August 2018 (UTC)

simple english article?

English is my second language and I have no understanding of either radiation or the terms apparently needed to really describe the concept. (we just used degree's in the basic math I learned). This seems like the kind of article that deserves a simple-english version. I know the be bold principle, but it seems somewhat that knows somethign about this would be better equipped to start such an article. 2001:1C06:1E06:2200:8009:CEB2:3F5E:D2BE (talk) 21:52, 22 December 2018 (UTC)

You could read the Simple English version. Let us know if it is clearer than this version which is designed for mathematical readers. Dbfirs 22:31, 22 December 2018 (UTC)

Standard notation

@Deacon Vorbis: it's a bit WP:POINTy to remove information from the lead because it is not also covered in the body of the article. In my opinion, it is quite legitimate (essential even) for this article to state the international standards on unit notation. And as it happens, WP:LEAD does not have a hard proscription on the lead containing information not in the article body. In a few respects, like definition of article scope, it actually requires it. SpinningSpark 21:37, 22 September 2019 (UTC)

@Spinningspark: That wasn't really my intent, but I see your point (no pun intended). In fact, the notation is mentioned briefly elsewhere, so I guess keeping a brief mention might be in order. Maybe just something along the lines of: "Quantities in radians are sometimes given the symbol rad for emphasis, but this is usually omitted."? (This is kind of awkward, but you get the idea). But there really were a couple problems – the amount of detail about obsolete notation and about standards bodies was excessive, especially for information not in the article body. (I think it would have been excessive even if this was mentioned in the body too). If it has to be kept, I think the History section would probably make most sense. The wording that I changed before removing was problematic too. I'm not sure if you're objecting to that as well, or just the overall removal, so I'll stop here for now. –Deacon Vorbis (carbon • videos) 22:29, 22 September 2019 (UTC)

@Deacon Vorbis: The references to BIPM and ISO were not excessive. Both are required appropriate and I suggest you reinstate them. Without an RS to back it up your statement that the unit symbol is usually omitted is an opinion (that I do not share) and does not belong in the article. Dondervogel 2 (talk) 07:26, 23 September 2019 (UTC)

What do you mean that that "both are required"? Required how? By whom? Are you also objecting to moving this to the History section that I suggested above? Stating that the symbol is usually omitted gets into WP:SKYISBLUE territory; if we add the symbol to the lead, we should also note that it's rarely used in practice, as is mentioned under the Definition section. –Deacon Vorbis (carbon • videos) 12:43, 23 September 2019 (UTC)

Although what you say is mathematically correct, the tag is often attached to assist the challenged. Is it "usually omitted" in Engineering, for example? --John Maynard Friedman (talk) 13:07, 23 September 2019 (UTC)

I support reinstatement. WP:PRESERVE is more important here than WP:COPYEDIT as far as building an encyclopaedia goes. There is nothing stopping anyone doing the latter once the material is back in the article. SpinningSpark 12:52, 23 September 2019 (UTC)

I also support reinstatement, but not in the lead. History makes sense, since the source book for the strange suffixes is over 100 years old. --John Maynard Friedman (talk) 13:07, 23 September 2019 (UTC)

Agreed on not in the lead, especially the stuff about unicode characters—that really is getting down in the weeds. SpinningSpark 13:10, 23 September 2019 (UTC)

So per the above, I've added it back to the history section, removed the unicode stuff (wouldn't care if someone put it back in properly), and added a note along the lines of that in the Definition section. As far as sentence about steradians, that really has absolutely no business being in there. To elaborate on my later edit summary, the scope of the article is already clear from the lead. Introducing a higher-dimensional analog in such a way is totally out-of-scope for the subject and level of this article and does nothing but potentially confuse a reader. There's a mention of it in the See also section, which is the right way to point to it. –Deacon Vorbis (carbon • videos) 13:25, 23 September 2019 (UTC)

If you won't follow BRD and instead just delete it again, then it's wasting my time discussing with you at all. SpinningSpark 19:08, 23 September 2019 (UTC)

The symbol rad can be used to represent the radian

Maybe I'm being picky here, but is it really correct to refer to three letters as a symbol? How about The suffix "rad" can be used to denote a quantity in radians? I realise I'm walking into a mathematical nomenclature minefield here, per discussion above on dimensionless quantities. Is there a better way to express this? --John Maynard Friedman (talk) 18:59, 23 September 2019 (UTC)

It's not a suffix in either the grammatical or mathematical sense. SpinningSpark 19:06, 23 September 2019 (UTC)

There are plenty of examples of 3-letter unit symbols, and this is one of them. A few others that spring to mind are min (minute), bit (bit), kPa (kilopascal), lbf (pound-force) and Gal (gal). Dondervogel 2 (talk) 19:22, 23 September 2019 (UTC)

Isn't it just an abbreviation? Dbfirs 19:33, 23 September 2019 (UTC)

I like abbreviation, yes, I should have thought of that and it is certainly better than my original suffix idea. Min, kPa, kcal, mcg, etc are all abbreviations, not symbols. This ♀ is a symbol. So here is the (partially) revised proposal: The abbreviation "rad" can be used to denote a quantity in radians. The more significant issue is whether it is numerate to say "a quantity in radians"? --John Maynard Friedman (talk) 20:20, 23 September 2019 (UTC)

Or then again, maybe not? From Symbol (chemistry): In chemistry, a symbol is an abbreviation for a chemical element. Like I said, maybe I'm just being too picky? --John Maynard Friedman (talk) 20:25, 23 September 2019 (UTC)

According to NIST, the term to use is symbol and the symbol in this case is "rad". [1] SpinningSpark 21:18, 23 September 2019 (UTC)

And on whether the symbol should be used or treated as a number they say,

...certain quantities of dimension one have units with special names and symbols which can be used or not depending on the circumstances. Plane angle and solid angle, for which the SI units are the radian (rad) and steradian (sr), respectively, are examples of such quantities

— NIST Guide to the SI, ch. 7

At the risk of repeating myself, bit, kPa, lbf, and Gal are all symbols, not abbreviations. After all, "bit" and "Gal" would be pretty daft abbreviations of the units those symbols represent (bit and gal). But they are not daft because they are not abbreviations. One could argue that "min" is an abbreviation of "minute", in the same way as "sec" is an abbreviation of second, but their respective symbols are min and s. Dondervogel 2 (talk) 21:44, 23 September 2019 (UTC)

I'll get my coat. --John Maynard Friedman (talk) 22:57, 24 September 2019 (UTC)

Sorry, I did not mean to be dismissive. Let me explain the difference, at least how I see it: An abbreviation is something used in prose to replace a word in an English sentence, the purpose being to shorten the sentence. In the sentence "I covered 10 naut. miles in 5 mins.", naut and min are abbreviations. A symbol is a representation of a quantity or unit in an equation, the purpose being to provide an unambiguous representation of a physical or mathematical relationship between the different quantities or units or both. In the equations x = 10 nmi and T = 5 min, x and T are quantity symbols, and nmi and min are unit symbols. Dondervogel 2 (talk) 00:06, 25 September 2019 (UTC)

No offence taken. My abbreviated (!) reply meant that the arguments had already persuaded me that my picky question doesn't stand up to scrutiny. --John Maynard Friedman (talk) 09:43, 25 September 2019 (UTC)

Insert tau

Can we insert tau somehow? I don't know where I would put it, but it's sort of important. --XndrK (talk) 15:23, 17 April 2013 (UTC)

Others don't seem to consider tau to be important. It isn't even mentioned on the disambiguation page, and the article is just a redirect to pi. Why do you consider it important? Does anyone actually use it? Dbfirs 16:09, 17 April 2013 (UTC)

Well it is quite clearly a superior form of notation, if not we’re better off just using degrees for angular measure. — Preceding unsigned comment added by Braŭljo (talk • contribs) 06:28, 4 September 2016 (UTC)

We can put it in every formula and visual that has 2π, just like we display dual units in parentheses, just that we’d be using 𝛕. — Preceding unsigned comment added by Braŭljo (talk • contribs) 06:34, 4 September 2016 (UTC)

Agreed, this article is a mess because of its pure use of pi. Tau captures the fundamental essence of radians in a way that pi doesn't. The chart converting proportions of the circle into pi radians becomes trivial when using tau. 1/4 circle is tau/4 radians, 1/16 circle is tau/16 radians, etc. Radians, fundamentally, ARE in terms of tau. The use of pi complicates everything. — Preceding unsigned comment added by 63.155.56.179 (talk) 23:24, 21 October 2016 (UTC)

Please! Can someone include everything in tau (as well as pi)? The elegance of the measure will be self-apparent! 185.125.226.42 (talk) 12:48, 29 January 2020 (UTC)

I don't think so. Not for a system that is not already in widespread use. It can be mentioned somewhere, but littering the article with an unfamiliar symbol to most readers is just going to spread confusion. It's not our job to promote a new system (it was only proposed in 2010) even if it is better. SpinningSpark 18:42, 29 January 2020 (UTC)

I have come from the future to add my name to the list of people who consider tau important enough to be added to a wikipedia article supplementary to pi wherever the latter is present. More people are familiar with tau since the near-decade-ago your comment was written. Brosefzai (talk) 09:08, 1 September 2022 (UTC)

"Planck angle" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Planck angle. Please participate in the redirect discussion if you wish to do so. Andy Dingley (talk) 21:13, 26 February 2020 (UTC)

Lead uses too much specialised vocabulary

• What does "it subtends" mean?
• Whether or not it's an SI unit is secondary to the mathematical concept
• What is a "dimensionless value"? --Cornellier (talk) 14:48, 7 October 2020 (UTC)

"The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends;" This must be an embarrassing typo. It does not seem to relate to the descriptions in the references, and it does not seem to make any sense. I would change it except the topic seems to be locked. Without having thought about it before, I would suggest "A radian is the angle (in a circle) subtended by an arc equal in length to the diameter (of the circle)." JohnjPerth (talk) 08:22, 31 October 2020 (UTC)JohnjPerth

Apology -- not an 'embarrassing typo', just a bit convoluted for my 70yo brain. And also I meant to be starting a new topic. Maybe there should be an age limit on 'talk'. JohnjPerth (talk) 23:30, 31 October 2020 (UTC)JohnjPerth

Yeah

"The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends;"

This looks like a back-to-front definition, defining the length of an arc, rather than the radian. Also, I wanted to clarify it as "The length of an arc of a circle, measured in circle radii, is numerically equal to the measurement in radians of the angle that it subtends;"

On reflection, I must admit it is 'obvious' that 'unit circle' implies unit radius, in the units that the arc would be measured in - so the original is correct and very succinct like mathematicians like, but for me too subtle. Maybe too subtle for the general reader.

I suggest "A radian is the angle (in a circle) that is subtended by an arc equal in length to the radius (of that circle)."

(Now corrected for my earlier ignorance of the actual facts.)

I would make the change but there is a 'lock' symbol on the article.

JohnjPerth (talk) 03:09, 1 November 2020 (UTC)JohnjPerth

Why does the heading part of the article have to define a radian in double-dutch when the definition section has the perfect definition "One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle." Surely Wikipedia prefers plain language. Please someone unlock and fix. JohnjPerth (talk) 09:34, 23 January 2021 (UTC)JohnjPerth

Not only was the definition in the lead backward, it had other problems as well. A definition belongs more properly in the Definition section. Also, the units were incorrect, as arcs are measured in units of length and angles in radian measure are unitless. So, I removed it. I also replaced the definition in the Definitions section with a better definition and cited a reliable source. Thank you for pointing this out. Cheers!—Anita5192 (talk) 17:51, 23 January 2021 (UTC)

Mohr's and Phillips' dispute is flawed

From Mohr's and Phillips' paper (https://arxiv.org/abs/1409.2794) which is referenced in the article:

"For example, in the current SI, it is stated that angles are dimensionless based on the definition that an angle in radians is arc length divided by radius, so the unit is surmised to be a derived unit of one, or a dimensionless unit. However, this reasoning is not valid, as indicated by the following example. An angle can also be defined as “twice the area of the sector which the angle cuts off from a unit circle whose centre is at the vertex of the angle.” This gives the same result for the numerical value of the angle as the definition quoted in the SI Brochure, however by following similar reasoning, it suggests that angles have the dimension of length squared rather than being dimensionless. This illustrates that conclusions about the dimensions of quantities based on such reasoning are clearly nonsense."

Mohr and Phillips use the formula for the area $A$ of a circular sector, equivalently $\theta ={\frac {2A}{r^{2}}}$, substitute a dimensionless (!) quantity for $r$ and then say that it suggests that angles have the dimension of length squared. I suggest that "Mohr and Phillips dispute this assertion" be deleted from the "Definition" section, as their argument is fundamentally flawed and therefore irrelevant. A1E6 (talk) 13:37, 16 March 2021 (UTC)

Undue weight

Regarding https://www.nature.com/news/si-units-need-reform-to-avoid-confusion-1.22417 (a cited reference in the "Definition" section), it hardly implies that "There is controversy as to whether it is satisfactory in the SI to consider angles to be dimensionless." This is actually very unpopular and insignificant.

All we can say is that some unknown group of metrologists was proposing updates to the International System of Units. The reason they mention is that it confuses physicists when they have to deal with different quantities with the same dimension. It has been almost 4 years since the article came out, and nothing has happened.

The views of tiny minorities should not be included at all, except perhaps in a "See also" section (as stated in Wikipedia policy), yet they are present in the "Definition" section. A1E6 (talk) 20:36, 16 March 2021 (UTC)

Semi-protected edit request on 3 April 2021

TYPO: please change "In a similarly spirit," to "In a similar spirit," (last sentence of section 'Advantages of measuring in radians'). Thanks :) Skarisphathsai (talk) 10:13, 3 April 2021 (UTC)

To editor Skarisphathsai:  done, and thank you very much! Good catch! P.I. Ellsworth  ed. ^put'r there 11:37, 3 April 2021 (UTC)

😎👍 Skarisphathsai (talk) 21:25, 3 April 2021 (UTC)

Link to radian becoming a supplementary unit

Reference 2 has an out-of-date original link; the resolution that changed radian from a supplementary to a derived unit is now at https://www.bipm.org/en/committees/cg/cgpm/20-1995/resolution-8 — Preceding unsigned comment added by Mhvk (talk • contribs) 01:33, 27 April 2021 (UTC)

Semi-protected edit request on 21 October 2021

1) Change "The relation 2π rad = 360° can be derived using the formula for arc length. Taking the formula for arc length, or {\displaystyle \ell _{\text{arc))=2\pi r\left({\tfrac {\theta }{360^{\circ ))}\right)}." To "The relation 2π rad = 360° can be derived using the formula for arc length {\displaystyle \ell _{\text{arc))=2\pi r\left({\tfrac {\theta }{360^{\circ ))}\right)}" Reason, repetition, non-grammatical sentence and break in flow of reading. 2) Change "Assuming a unit circle; the radius is therefore 1." To " and by using a circle of radius 1." Reason, the statement made that a "unit circle" has to have a radius of 1 is not clear, without reference to an accepted definition of what a unit circle should be and possibly irrelevant at this point. 3) The rest of the paragraph, 3 sentences, is verging on circular in logic and weak as regards explanation unless the formula that circumference = 2 Pi r is emphasised as being the core assumption of validity for the definition being proposed. Some small token explanation regarding Pi such as "if we accept that C = 2 Pi r", is required to preface at this point in the definition which is important and otherwise good. Anzonix (talk) 16:34, 21 October 2021 (UTC)

 Done.

1° = ? Equation radian .

Sir 1°= equation radian. 2409:4042:D1C:B6DB:7AC5:B34E:EA2D:B210 (talk) 11:42, 28 November 2021 (UTC)

1° = ? Equation radian.

1 2409:4042:D1C:B6DB:7AC5:B34E:EA2D:B210 (talk) 11:44, 28 November 2021 (UTC)

Problem with the Dimensionless Analysis Section

Looks to have been quite a few edits recently, with the dimensionless analysis section saying again that it's "confusing" to treat radian as dimensionless. While true, there is crucial context that this version lacks. It is only "confusing" for lay people, who have a difficult time conceptualizing something physical that does not actually have any physical dimensions. Angular measure, like mechanical strain, radiation emissivity, and many other physical entities, is (conclusively) dimensionless. (This is easy to prove using the tack-and-string thought experiment of sweeping out an arc and taking the ratio of the arc length and the string radius.) The current version of the text dithers in several places on this important point. In fact, this edit added the Nature op-ed SI units need reform to avoid confusion to support the claim that "treating angular measure as a dimensionless quantity can lead to confusion". What it omitted was the refutation (M Wendl: Don't tamper with SI-unit consistency) that explains several mathematical contradictions that result from mistakenly assigning physical units to angular measure. One aspect is dimensionless groupings in physics, like the Womersley number mentioned below, which would no longer be unitless and would then require "patching" with various conversion factors. The other, more compelling factor which that article illustrates has to do with introducing contradictions in actual vector operations. Torque and energy have the same physical units: Newton * meters in SI. But torque, ${\vec {r}}\times {\vec {F}}$, is a vector (cross) product. Work has not been done (energy expended) until such torque is displaced through some unitless rotation, whereby energy $={\vec {r}}\times {\vec {F}}\cdot {\vec {\theta }}$, which is a scalar (dot) product. The reader would be served best if this section got the technical details correct and then simply added a parenthetic comment, something to the effect that lay people often find this issue to be confusing. The text should not give the false impression that there is any technical question or disagreement as to whether angular measurement has physical unitss, because there isn't. 128.252.11.235 (talk) 22:13, 18 April 2022 (UTC)

Just had a quick look. This section should make sure it is consistent with Torque#Relationship_between_torque,_power,_and_energy, which does explain the above issue correctly. 128.252.11.235 (talk) 22:21, 18 April 2022 (UTC)

"It is only "confusing" for lay people" – not only for lay people, but also for "scientists" like Philip Bunker who try to promote fringe theories via Wikipedia by references to their work or the work of their associates, preferably from the Metrologia journal.

"What it omitted was the refutation (M Wendl: Don't tamper with SI-unit consistency) that explains several mathematical contradictions" – I'll add this to the article. A1E6 (talk) 22:54, 18 April 2022 (UTC)

You may very well be right. I'm not familiar with this individual. The context for the comment I made is that undergrads in physical science courses are often not even aware of this issue and, if they aren't, the average person on the street likely isn't. Thanks. 128.252.11.235 (talk) 23:40, 18 April 2022 (UTC)

No problem. A1E6 (talk) 23:41, 18 April 2022 (UTC)

Dimensionless Analysis

Wandered by this article and was surprised to see protection status. I assume this is because the usual confusion/disagreement about angle dimensionality has led to problematic editing. As written, the dimensionless analysis section is a little confusing, since it mostly focuses on one of the many ad-hoc "patching" proposals (eta). The text refers to a few older ones, but there are still surprisingly many proposals even today. A 2017 editorial in Nature, SI units need reform to avoid confusion wanted to promote the radian to a physical unit, but this was refuted (M Wendl: Don't tamper with SI-unit consistency) because it would create contradictions for dimensionless groups like the Womersley number and for different physical entities having identical physical units, like torque (a vector product) versus energy (a scalar product). One sentence in this section is false, or at best very misleading: a majority of papers on the subject acknowledge that angles should be regarded as having an independent dimension and associated units, which cites a single preprint. Modern textbooks in physics and engineering refute this: they are crystal clear about the non-dimensional nature of angles, e.g. with respect to the entities of torque and energy just mentioned. To help readers with the non-intuitive fact that some physical things simply do not have dimensions, this section could perhaps refer to some other examples of inherently dimensionless entities, like mechanical strain or radiation emissivity. 2600:1700:8650:2C60:68D4:FED2:7981:B6EE (talk) 19:30, 13 April 2022 (UTC)

And all the citations involving Torrens' proposal are from Metrologia only (there are arXiv versions as well, but they're not peer-reviewed), I might as well label more stuff as WP:FRINGE and remove it. A1E6 (talk) 00:59, 14 April 2022 (UTC)

So Metrologia, "The leading international journal in pure and applied metrology", impact factor 3.157, is a fringe publication? As I understand WP:FRINGE that term is reserved for pseudoscience, not for peer-reviewed literature. For comparison the Nature letters in there now are not even peer reviewed, if anything they are what's fringe. Wendl's arguments are basically (1) I don't like it (2) the existing formulas are dimensionless (3) the units would change. None of these arguments are new and they are discussed in much more depth in the Metrologia articles. It is a poor refutation, and the IP's summary of it is wrong. There is no "contradiction"; Wendl's letter does not even use this term. As for torque vs energy, the discussion in [2] shows that torque can either be defined to the same units as energy or to N m / rad. The difference is a matter of convention, as with the overall definition of radians as a unit.

As far as "a majority of papers on the subject acknowledge that angles should be regarded as having an independent dimension and associated units", the preprint makes this claim based on a survey of the literature (c.f. the 67 citations). Dimensional analysis is somewhat unusual to begin with, and only those concerned with correctness publish their results in peer-reviewed journals. Hence since angle as dimension is the "correct" choice the scientific literature is overwhelmingly in favor of it. I searched for peer-reviewed papers arguing against angles as dimensions, but concluded there are none. The only source that doesn't define angle to be a dimension is SI, and as said in [3], the decision was purely to avoid upheaval of current practice. The scientific consensus (as opposed to political consensus) is that angle should be a dimension, and this sentence is included to reflect that. The sentence is verifiable now and I assume it will become reliable once the preprint is published.

As far as textbooks, this and this say peer-reviewed journals trump textbooks, particularly when the textbooks are unsourced and don't really have any reasoning besides the circular "this formula assumes radians are unitless so radians must be unitless".

As far as presenting Torrens' proposal, I think the section is not complete without at least one proposal, as all the proposals are quite similar, differing mainly in notation. [4] is a peer-reviewed literature review and says Torrens' is the best. An alternative could be the CCU 80-6 proposal, but that is not easily accessible.

Anyways, I will restore my version, so that at least the section does not contain misinformation. --Mathnerd314159 (talk) 03:00, 20 April 2022 (UTC)

If the Nature letters are problematic, I'll remove them.

The Metrologia journal is insignificant compared to the majority of modern physics textbooks and to the stance of the SI itself. From WP:SCHOLARSHIP, regarding the peer-review process in Metrologia:

Care should be taken with journals that exist mainly to promote a particular point of view. A claim of peer review is not an indication that the journal is respected, or that any meaningful peer review occurs. Journals that are not peer reviewed by the wider academic community should not be considered reliable, except to show the views of the groups represented by those journals.

WP:FRINGE is any view differing from the mainstream, which, for example, Mohr's and Phillips' view

"This gives the same result for the numerical value of the angle as the definition quoted in the SI Brochure, however by following similar reasoning, it suggests that angles have the dimension of length squared rather than being dimensionless. This illustrates that conclusions about the dimensions of quantities based on such reasoning are clearly nonsense."

ostensibly is. So I removed it.

I don't think you understand how WP:FRINGE theories work. If a group of people from one journal publishes several papers on a fringe theory, there is no need whatsoever for that fringe theory to be addressed by the same number of opposing papers.

Out of the "62 citations" in the preprint, 26 of them are from Metrologia, 2 are from P. R. Bunker (who regularly tries to edit the Radian article in a manner of egregious WP:COI under the name Bunkerpr, desperately wanting to promote the Metrologia articles – Metrologia's impact factor is totally irrelevant here). The rest of the citations supporting dimensional angles involve Brinsmade, Romain, Brownstein and Lévy-Leblond papers, but they're insignificant compared to the majority of all physics textbooks and to the SI, and mentioning them would be giving them WP:UNDUE weight, the same goes for Torrens' proposal from Metrologia. Again, if a fringe theory is proposed, there is no need whatsoever for it to be explicitly addressed and refuted by reliable sources.

"peer-reviewed journals trump textbook" – this is a false statement made by the user Reissgo, it is nowhere in Wikipedia policies regarding reliable sources, especially see WP:SCHOLARSHIP again. A1E6 (talk) 12:34, 20 April 2022 (UTC)

r.e. quote From WP:SCHOLARSHIP: Metrologia does not exist to promote a particular point of view. Per [5] it has a single blind peer review system managed by a professional editor based at the BIPM. It is not a fringe journal. The reason all the articles cited are from Metrologia is because Metrologia is one of the most respected journals in this area.

r.e. "modern physics textbooks", they are tertiary sources. There are several policies recommending avoiding tertiary sources, such as WP:TSF and WP:DONTUSETERTIARY. Textbooks do not seem particularly reliable for this subject. There are textbooks that discuss giving radians a dimension and introducing a physical constant, e.g. [6], actually very similar to Torrens' proposal. There are textbooks that discuss the CCU decision, [7], and that discuss the proposals to change it, [8]. But for the most part textbooks simply paraphrase the SI in one or two sentences and are not worth citing. What does not exist are any textbooks providing a real argument that radians are dimensionless, because no such argument exists. But I'll concede that textbooks show that the dimensionless radian is popular.

Per WP:MAINSTREAM, "mainstream" relies on the highest-quality sources and may sometimes be a minority view in society. The highest-quality sources are the Metrologia articles, particularly Quincey's review article that compares the existing proposals (including the SI definition). The SI decision was based purely on practical considerations and does not have much scientific basis.

I don't think you understand how WP:FRINGE works either. Even supposing that trivial discussions such as the SI brochure and modern textbooks count as the mainstream "scholarship in the field", angle as dimension would be an alternative theoretical formulation. As such the article should explain the "context with respect to the mainstream perspective." WP:FRINGE doesn't explain how to do this, as it mainly discusses pseudoscience, so we fall back on WP:NPOV: the article should "fairly represent all significant viewpoints that have been published by reliable sources, in proportion to the prominence of each viewpoint in the published, reliable sources." It was a divided decision by the CCU to make radians dimensionless, so the article should also be divided. The lead and the definition section quote the SI brochure and describe the radian as dimensionless; I think this is sufficient weight to that viewpoint. But what about Quincey's comparison of options? Why do you keep removing it? The article needs to represent the viewpoint that angles can be dimensions, and with your deletions it does not. It does not put the dimension decision into any sort of context, or explain "how the minority view differs from [the majority view]". My version does both of these things, via the discussions from Quincey and the presentation of Torrens' approach to show the difference in formulas. It is due weight to describe the minority view. The current state of "section with two sentences" is simply laughable.

As far as Mohr and Phillips (2015), there is indeed a hole in their argument, as you said in #Mohr's and Phillips' dispute is flawed. They forgot to divide by the unit area so in fact they should conclude that the angle is dimensionless rather than having units of length squared. But as far as removing the citation from the definition section, that I don't understand, because you simply changed attributed material into unsourced material, which does not improve the article in any way. --Mathnerd314159 (talk) 16:26, 20 April 2022 (UTC)

"What does not exist are any textbooks providing a real argument that radians are dimensionless, because no such argument exists." – I strongly disagree. Whatever...

Alright, I'll partially restore your version, but it must not contain statements like

1) "However, a majority of papers on the subject acknowledge that angles should be regarded as having an independent dimension and associated units"

(I addressed this "majority" thing in my previous comment),

2) "This definition of angle as dimension is mathematically consistent and can be extended to all mathematical and physical equations, allowing for defining formulas independent of the units used for angles."

3) "but for correct measurements and numerical calculations the information about angular dimension must still be preserved"

4) "The inability to use degrees in place of radians shows that angles are inherently dimensional"

5) "Treating angles as dimensionless can be confusing and problems can arise"

6) "Despite the benefits of applying dimensional analysis to angles"

I just think that something fishy is going on here, given Bunkerpr's connection with Metrologia and his history of illegitimate WP:COI and WP:REFSPAM edits.

"you simply changed attributed material into unsourced material" – the circular sector area formula is well-known and there doesn't need to be a reference promoting a fringe paper. A1E6 (talk) 17:00, 20 April 2022 (UTC)

(2) about consistency was mainly to ward off FUD like the Wendl paper that say you run into contradictions. But it doesn't seem to have helped in that respect so I guess leaving it out is reasonable. I'm fine with how the section is now. The only thing I think would improve it is making "Many scientists" more specific, something like the following:

At least a dozen scientists have made proposals to treat the radian as a base unit of measure defining its own dimension of "angle", as early as 1936 and as recently as 2022

The dozen scientists are Brinsmade (1936), Romain (1962), Eder (1982), Torrens (1986), Brownstein (1997), Lévy-Leblond (1998), Foster (2010), Mills (2016), Quincey (2021), Leonard (2021), and Mohr, Shirley, Phillips, Trott (2022) (with the last counting as 2). A dozen is close to the true amount and sounds a lot smaller than "many". --Mathnerd314159 (talk) 18:25, 20 April 2022 (UTC)

@Mathnerd314159: By the way, I can straightaway tell that Torrens' proposal is mathematically inconsistent: $\sin$ is an entire function and there exists one and only one sequence $(a_{n})_{n\geq 0}$ such that ${\textstyle \sin z=\sum _{n\geq 0}a_{n}z^{n}}$, by Cauchy's integral formula. So, any choice of $\eta$ other than $\eta =1$ is wrong. A1E6 (talk) 23:45, 20 April 2022 (UTC)

So actually there are two functions, the mathematical function $\sin(x)$ which is unchanged and a new unit-aware function ${\text{Sin}}(\theta )=\sin(\eta \theta )$. Then as an matter of notation $\sin(\theta )$ is written in place of ${\text{Sin}}(\theta )$, because the angular dimension of $\theta$ makes it clear that the unit-aware function is implied. With radians indeed the only reasonable choice is $\eta =1$, but using degrees one ends up substituting a value $\eta =\pi /180$ into the equations, as illustrated in the Radian#Advantages of measuring in radians section. That's the main advantage I see for the dimensional approach: one can measure angles in a mixture of degrees and radians and use them in formulas with the dimensional analysis and $\eta$ producing the conversion factors, and it all works out nicely. --Mathnerd314159 (talk) 02:24, 21 April 2022 (UTC)

It should have been made clear in the article that it's not "the" sine function, but something else. So I propose using \overline, or something like that. A1E6 (talk) 03:09, 21 April 2022 (UTC)

@Mathnerd314159: And speaking of mathematical inconsistency, Torrens' "version" of $\sin$ (and $\cos$, for that matter) is mathematically unusable. For example, consider the fact that

$\theta ^{2}={\frac {\pi ^{2}}{3}}+4\sum _{n\geq 1}{\frac {(-1)^{n}}{n^{2}}}\cos n\theta ,\qquad \theta \in (-\pi ,\pi ).$

The dimensions don't "work out" nicely. A1E6 (talk) 13:51, 22 April 2022 (UTC)

The dimensions can always be made to match by inserting $\eta$ in appropriate places. Here I think it would simply be

$$(\eta \theta )^{2}={\frac {\pi ^{2}}{3}}+4\sum _{n\geq 1}{\frac {(-1)^{n}}{n^{2}}}\cos(n\eta \theta ),\qquad \theta \in (-\pi {\text{ rad}},\pi {\text{ rad}}).$$ I've updated the article to distinguish Sin from sin. --Mathnerd314159 (talk) 16:21, 22 April 2022 (UTC)

This arbitrary inserting of $\eta$ is completely ad hoc, done only for the purpose of "saving" Torrens' theory from being falsified, and is devoid of any rationale, other than getting rid of nonsensical angular dimensions. A1E6 (talk) 16:34, 22 April 2022 (UTC)

The factors arise naturally when you work out the equations using variables which are ratios of angles to a standard angle. They're no more ad-hoc than factors of c in the Lorentz transformation. And just like the factors of c disappear when you use Planck units, the factors of $\eta$ disappear when you use the radian convention. Mathnerd314159 (talk) 03:33, 25 April 2022 (UTC)

The above arguments (I don't like it, The scientific consensus...is that angle should be a dimension, peer-reviewed journals trump textbooks, etc.) are absurdly and patently false. It is remarkable that an important technical concept is allowed to be jerked around in the manner that this article (and its gatekeepers) continue to do. There is no dispute within scientific, engineering, and mathematical circles regarding the dimensionless nature of angle, but the "dimensionless analysis" section misrepresents technical consensus with "Torren's proposal". This is not mainstream, nor is this idea used by scientists, engineers, or mathematicians because it is superfluous over-complication. In this sense, it is indeed FRINGE. One can look at this issue from numerous different perspectives, for instance:

• The argument I already made above: Torque and energy have the same physical units: Newton * meters in SI. But torque, ${\vec {r}}\times {\vec {F}}$, is a vector (cross) product. Work has not been done (energy expended) until such torque is displaced through some unitless rotation, whereby energy $={\vec {r}}\times {\vec {F}}\cdot {\vec {\theta }}$, which is a scalar (dot) product.
• The simple tack-and-string experiment showing angle as the dimensionless ratio of arc length and radius
• Frequency (in units of 1/s) mathematically integrated over a given time interval yields a dimensionless angular displacement (and vice-versa w.r.t. time derivative of angle)
• The Buckingham-Pi Thm used in dimensionless analysis of physical problems leads to dimensionless groups in which various angular measures (angle, angular rate, rotational acceleration) have no physical dimension associated with angular displacement
• differential equations for real-world phenomena, e.g. the simple spring-mass mechanical response equation $x''+C\cdot x=0$ have solutions indicating that angular displacement must be unitless

Again, in technical environments, there is no confusion about this simple fact. I don't know what the motivation and/or agenda are here, but this section seems to be a vehicle by which to promote a number of articles in a particular journal. The vastly larger technical literature (papers, textbooks, etc.) are clear on this. If one wants an authoritative source, you might include Percy Bridgman's book Dimensional Analysis (1931), in which he treats this issue in the first 3 pages. I am not a regular Wikipedia editor, so I do not have a horse in this race. I am only offering the opinion as someone who claims expertise in this area that your "dimensional analysis" section, as it now stands, is misleading, at best, is FRINGE, and is the sort of thing that hurts Wikipedia credibility. 128.252.79.225 (talk) 18:40, 29 April 2022 (UTC)

I don't think I have ever, in my life, seen angles treated as dimensionful. I mean, just to pluck an example off the top of my head, take Newton's second law for a pendulum not restricted to small angles: ${\ddot {\theta }}=-(g/L)\sin \theta$. The time derivatives on the left gives you units of T^-2, which match the units of $g/L$, the length dimension canceling. So if $\theta$ had units, then they must be the same as the units of $\sin \theta$, which are the units of $\theta$ and $\theta ^{3}$ and $\theta ^{5}$ and... It's just nonsensical. Literally nothing is gained from trying to make that work out. Life is too short, and the number of actually interesting physics problems is too big. Trigonometric, exponential, and logarithmic functions take dimensionless arguments.

Neither WP:TSF nor WP:DONTUSETERTIARY are policies. They are essays, which do not necessarily have any community consensus behind them. However, WP:UNDUE is policy, and it's very hard to see how the current "Dimensional analysis" section is compliant with it. XOR'easter (talk) 23:08, 29 April 2022 (UTC)

On April 20, I stripped Mathnerd314159's original version [9] off of statements which were blatantly going against Wikipedia policies. The current version is more neutral, but there are still some concerns regarding WP:UNDUE. Mathnerd314159's arguments "The reason all the articles cited are from Metrologia is because Metrologia is one of the most respected journals in this area." and "The highest-quality sources are the Metrologia articles" are dubious and need attention – in particular, to what extent should the Metrologia papers be covered in this article. A1E6 (talk) 00:14, 30 April 2022 (UTC)

This sort of argument from Mathnerd314159 should be recognized for what it is: a false dilemma. It frames our little debate here of whether angular measure has physical dimensions as an active research question. It is not. Angular measure was fully understood and resolved hundreds of years ago. Even Percy Bridgman's book Dimensional Analysis, which one could regard as the "Bible" on this topic, was already published by 1922. One perspective that this article could reflect is that this issue is confusing, especially for the lay person, which is true and which is why the issue only appears to be unsettled. It explains why there are still "research" papers that come out every few years that attempt to "patch" what is not even a problem in the first place. Before I close my parting comment here, I will again observe that Wikipedia's own rules seem to permit this sort of nonsense. The concept of technical correctness, the bedrock foundation of any encyclopedia, seems to be pushed ever further into the background by activists, editors who are topically ignorant, and agenda-based editing. I am again reminded why I am not a regular Wikipedia editor, which is that most of one's time is wasted trying to defend correctness against activism, ignorance, and agenda. Hope you all get this properly settled at some point. Over and out. 128.252.79.225 (talk) 12:58, 30 April 2022 (UTC)

Uh-oh. This is not the kind of argument that belongs on WP talk pages. It is unambiguously an "I'm right because I'm right" perspective that denies the possibility of a historical conceptual oversight. As a side note, A1E6 is sounding a little over the top too: just because Metrologia has the status of being the dominant and foremost forum for serious discussion of unit systems and thus that little is published elsewhere does not make it fringe. This is a deeper discussion than most people (scientist included) seem to allow for. WP should not go too deeply into presenting more than that this is controversial and that there are proposals to formalize angle as a dimensional quantity. Even the "Sin" proposal is more than is needed in the article. 172.82.47.18 (talk) 13:37, 30 April 2022 (UTC)

Pardon, but I can't help one more comment to respond to such a bureaucratic viewpoint. Your policy-based relativism is another one of the root problems that will prevent Wikipedia from ever becoming a reliable, citable source. Instead of "I'm right because I'm right", what you should have said is "I'm right because it's right". I will reiterate, in the strongest terms, that there is no ambiguity about whether angular measure has physical units. You might as well debate whether gravity points down or whether the earth is flat. And I will also reiterate that this is the sort of thing that hurts Wikipedia's credibility, especially when someone with expertise reads this. (This is exactly how I came to comment here. I tried to offer some expert opinion, despite not being a regular editor.) The bureaucratic echo chamber here is remarkable. Good luck. 128.252.79.225 (talk) 14:05, 30 April 2022 (UTC)

This discussion [10] is relevant. A1E6 (talk) 13:44, 1 May 2022 (UTC)

Can we not have a simple definition in the Lead for laymen?

Surely, we could just say "A radian is a unit of angular measurement of a circle that is equal to ~57.295779513082320876°". That way, I could read the header, and then know how to apply it in an example. Gehyra Australis (talk) 10:07, 20 January 2022 (UTC)

Simple English Wikipedia jumps to that punchline much more quickly, and is a great resource if you're looking for that kind of stuff, particularly when it comes to articles concerning subjects often steeped in rigour or technical detail, like mathematics and science. — JivanP (talk) 19:50, 11 May 2022 (UTC)