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January 27

Diameter of the circumscribed circle of a Canadian Loonie

The Loonie article contains a bit of a contradiction:

 The coin's outline is an 11-sided Reuleaux polygon. Its diameter of 26.5 mm...

A Reuleaux polygon does not have a diameter. Instead, it has a width. In the context of coins, the Circumscribed circle of a Reuleaux polygon does indeed have a diameter. This leads me to believe that the 26.5 mm measure may be referring to the diameter of the Circumscribed circle instead.

But I found this site which claims that the width of the Loonie is 26.5 mm[1]. If that's indeed the case, then the diameter of the Circumscribed circle would be slightly larger than 26.5 mm.

So which is true here?

A. The Loonie has a width of 26.5 mm (and a larger circumscribed circle diameter).

B. The Loonie has a circumscribed circle diameter of 26.5 mm (and a smaller width).

Helian James (talk) 04:47, 27 January 2023 (UTC)[reply]

Is the size difference smaller than 0.05 mm so that it doesn't matter? Anyone have a handy formula? Rmhermen (talk) 05:01, 27 January 2023 (UTC)[reply]

The size difference is very tiny. User:Jacobolus on the Math reference desk just solved the ratio to be approximately 1.0103[2]. So the difference is approximately 0.27 mm. Helian James (talk) 05:30, 27 January 2023 (UTC)[reply]

One common mathematical definition for the diameter of an arbitrary bounded shape is the maximal distance between any two points on its boundary. Equivalently (for planar shapes), it is the width of the least square in which the shape can rotate. There is no common mathematical definition for the width of an arbitrary shape, but a plausible definition is the width of a rectangle of least height in which the shape will fit. So the diameter of a 3×4 rectangle equals 5, while its width would be 4. These two notions coincide for circles. For Reuleaux polygons, these notions coincide too, which is in fact a defining feature. --Lambiam 08:09, 27 January 2023 (UTC)[reply]

First, mathematicians love to generalize the meanings of words. You say the figure doesn't have a diameter; I look at "Generalized Diameter" on Mathworld and say that for this curve of constant width, what you (Helian) call the width may also legitimately be termed the diameter. I certainly assumed that what the Mint calls the diameter here was the width. But I was assuming.

Second, I just took two loonies from my wallet and measured them using two different household rulers. In each case the width (from one vertex to the opposite curve) was clearly very close to 26 mm: I would estimate it at 26.1 mm. So I wonder if maybe the 26.5 mm figure does indeed relate to the circumscribed circle. --142.112.220.65 (talk) 08:13, 27 January 2023 (UTC)[reply]

--142.112.220.65 (talk) 08:13, 27 January 2023 (UTC)[reply]

Given the margin of error in the construction of household rulers and the tolerances for the size of a coin in circulation, which can get worn and dinged in various ways, anything within a half a millimeter in either direction is functionally the same; Which is to say that 26.1 and 26.5 are going to be essentially the same in this context. --Jayron 32 12:51, 27 January 2023 (UTC)[reply]

Is there a ~~doctor~~ Canadian in the room who has access to a metric vernier caliper? --Lambiam 16:02, 27 January 2023 (UTC)[reply]

Note that the 26.5 mm figure comes from the Royal Canadian Mint who actually make the thing. Alansplodge (talk) 17:32, 27 January 2023 (UTC)[reply]

Right. My point was mainly that 26.1mm (obtain by sticking a loonie next to a wooden ruler) and 26.5mm are not functionally different measurements, given the tolerances of the measuring method in question. --Jayron 32 19:42, 27 January 2023 (UTC)[reply]

I didn't say "wooden"; they were transparent plastic rulers, which are easier to use for this sort of measurement. And the difference between 26.1 and 26.5 mm is large enough that error in the ruler does not seem likely to account for it. See also Lambiam's item below. --142.112.220.65 (talk) 04:50, 28 January 2023 (UTC)[reply]

How bold of you to assume the tolerance in the construction of the ruler means that the markings are within 0.5mm/26 (about 2%). I would suspect the average household ruler, made of any material, is not likely to be more accurate than +/-2% --Jayron 32 13:04, 30 January 2023 (UTC)[reply]

The question is, though, whether the Mint used the term diameter in the sense defined in our article Metric space as the "diameter of a metric space" and at MathWorld as "generalized diameter", or did they perhaps use it in the sense of the diameter of the circumscribed circle? While the difference between 26.1 and 26.5 mm is small, it is not beyond the precision of generally available accurate measuring instruments to tell the difference. --Lambiam 00:44, 28 January 2023 (UTC)[reply]

A Canuck with a metric vernier caliper says: both my 1989 and my 2012 Loonies measure 26.45 to 26.50 mm from the flats to the various diametrically opposed points. Per the Canadian Mint site (thanks user:Alansplodge) both of these Loonies are listed as having a "diameter" of 26.5 mm. Let the analysis begin. I don't know that this is going to help, since without a reliable source as to what the Mint means by "diameter", all we can say is that the Mint specifies a "diameter" of 26.5 mm. Meters (talk) 06:03, 28 January 2023 (UTC)[reply]

Thanks, your measurement with a more reliable instrument is appreciated, albeit surprising. --142.112.220.65 (talk) 04:15, 30 January 2023 (UTC)[reply]

It means we can now all enjoy a restful sleep, no longer tossing and turning worried that the Royal Canadian Mint abused the mathematical term diameter in a non-mathematical way. Since the Susan B. Anthony dollar has the same diameter but is circular and thus smaller than a Loonie circularified by circumscription, it follows that a Loonie in a stack of Susans has points sticking out by approximately 0.27 mm, which one should be able to notice by the fine sense of touch in one's fingertips. --Lambiam 11:12, 28 January 2023 (UTC)[reply]

I'd have to go digging to find my vernier, but I can tell you as a Canadian that has handled many loonies that the sidings for a loony are very susceptible to deforming. Hot off the press, the edges are clean and clear but they very quickly become rounded. The only loony I've got at hand is one from 2012 and it's only just possible to discern that it ever had edges at all: at even less than arm's length it appears circular. Matt Deres (talk) 19:45, 31 January 2023 (UTC)[reply]

Book I can't remember the name of

There's a book I remember reading a while ago but I can't remember the name of. It is about a man who worked in the PR industry and his boss didn't like him, and the man ends up getting fired. He has two daughters and swears at them as they watch a special on Comedy Central. The book goes into detail on his job search as he looks for a new job. It talks about how he was in Africa somewhere and had guns pulled on him at a border crossing, but his group got out of it because one of them spoke French and offered the border guards a carton of cigarettes. If I remember correctly it had a forward or review by Mika Brzezinski. In the end the guy doesn't get a job but starts his own PR firm. Any help? Therapyisgood (talk) 05:08, 27 January 2023 (UTC)[reply]

Found it, it was Reset: How to Beat the Job-Loss Blues and Get Ready for Your Next Act. Therapyisgood (talk) 05:18, 27 January 2023 (UTC)[reply]

Resolved

African American names ending with -us

I've noticed a significant number of African Americans with given names ending with -us as if in an ancient Roman fashion: Cassius Clay, Marcus Allen, Titus Bramble, Demetrius Jackson, Tadarrius Bean, etc. Could this be explained somehow? 212.180.235.46 (talk) 18:52, 27 January 2023 (UTC)[reply]

See African-American names. It's a complex set of etymologies without a singular source, as can be seen under the "influences and conventions" section. For example, the "European and Biblical names" notes that "it is also still common for African Americans to use biblical, historic, or European names. Daniel, Christopher, Michael, David, James, Joseph, and Matthew were among the most common names for African-American boys in 2013" (bold mine). Cassius and Titus being common historical names, and Marcus also common enough among males of European descent (of which I have known several Marcuses). For the others such as Demetrius of Teadarrius, see the section of that article titled "Afrocentric and inventive names". In his dictionary of black names, Cenoura asserts that in the early 21st century, black names are "unique names that come from combinations of two or more names, names constructed with common prefixes and suffixes...'conjugated' with a formula..." So a name like "Tadarrius" could have been constructed by starting with "Darius" (an historical and Biblical name, see Darius the Great), with the prefix "Ta-". It looks from doing some google research that the book Black Names Matter by Bobby Cenoura may have some good, well-researched information on the topic as well. There are a number of other sources for further exploration in the Wikipedia article as well. --Jayron 32 19:39, 27 January 2023 (UTC)[reply]

Thank you. 212.180.235.46 (talk) 11:32, 29 January 2023 (UTC)[reply]

Note that Cassius Marcellus Clay (Muhammad Ali) was named after Cassius Marcellus Clay (his father), who was named after Cassius Marcellus Clay (unrelated), who was a notable abolitionist (but not African-American) who came from a family that was fond of using Roman names (and who named two of his own sons Cassius Marcellus Clay as well). Iapetus (talk) 13:58, 3 February 2023 (UTC)[reply]

Women working at lunch counters

Something is confusing me. In regards to any Woolworth lunch counter, was a woman working at one regarded as a lunch lady?2603:7000:8100:9390:A8F4:C049:6AB3:6D9A (talk) 20:28, 27 January 2023 (UTC)[reply]

The term ”Lunch lady” is usually associated with those serving at school cafeterias, not commercial establishments. Blueboar (talk) 21:02, 27 January 2023 (UTC)[reply]

[3]Dinner lady?
Sleigh (talk) 01:47, 28 January 2023 (UTC)[reply]

"Tuck shop arms", or "tuck shop lady arms" has some currency Down Here. -- Jack of Oz ^{[pleasantries]} 20:23, 28 January 2023 (UTC)[reply]