Talk:Reuleaux triangle

message: "By the Blaschke-Lebesgue theorem, the Reuleaux triangle has the least area of any curve of given constant width." - Doesn't a circle have less area? Or is this assuming an unspoken "nontrivial"? Or am I not understanding something (quite possible - I have only a sketchy layman's understanding of the topic!) - DavidWBrooks 19:01, 6 Apr 2004 (UTC)
thread_title: old talk

message: "By the Blaschke-Lebesgue theorem, the Reuleaux triangle has the least area of any curve of given constant width. In particular, the area is given by pi*d, where d is the diameter."
The dimensions of "the area" and "pi*d" are not the same. Can this be possible?
--Tonyho 06:21, 30 June 2006 (UTC)
replies: text: That's bogus. By my calculations, the area is \left({\pi\over2} - {\sqrt3\over2}\right)d^2. Anyone disagree? —Keenan Pepper 07:09, 30 June 2006 (UTC)
replies: text: Well, MathWorld agrees with me, so it's going in. —Keenan Pepper 07:27, 30 June 2006 (UTC)

text: Here, here. --Tonyho 08:21, 30 June 2006 (UTC)
thread_title:  Area 

message: The first sentence, which defines the subject of the article, reads:
"A Reuleaux polygon is a curve of constant width - that is, a curve in which all diameters are the same length."
Exactly what does the word "diameter" mean here?  The diameter of a circle is a well-known concept, but this is not a circle.  (This usage may refer to a line segment or to its length.)  
Also, the diameter of a point-set is a well-known concept in geometry: It is the supremum of all distances between points of that set.  (This is usually a number, not a line having that number as its length.)
But what kind of diameter are we discussing here?  It can't be the circle defintion.  And it can't be the supremum definition, (or a line segment between two points in the set that are at a distance equal to that supremum) ... since then a straight line segment would fit the definition of a curve of constant width, as would an equilateral triangle.
So how about either 
a) defining this use of the word "diameter", 
or
b) rewriting the definition without using mystery concepts.
Choice b) is  strongly preferred.Daqu (talk) 02:20, 16 November 2008 (UTC)
thread_title: First sentence needs rewriting

message: Okay, idea: how about a new lead image one that compares two Reuleaux triangles, each with a pair of parallel tangent lines drawn on it, showing that each pair is the same distance apart? --superioridad (discusión) 14:45, 1 May 2009 (UTC)
replies: text: Looking at the page again, that rotating image has a lot of visual impact that conveys something - maybe we should just move it up - DavidWBrooks (talk) 16:22, 1 May 2009 (UTC)
thread_title:  Image to go with lead 

message: Why does the method of construction say "start with an equilateral triangle"?
Try this:
* Choose a constant radius.
* Draw a circle (or such arc as sense indicates sufficient), say the blue one in the diagram, 
* With centre on that circle draw an arc, say of the green circle, to intersect the first circle, 
* Draw an arc of a third circle, say the red one, centred on the point of intersection of the first two circles. to intersect them.
* Voilà, surely, the bulgy bit is a Reuleaux triangle with no equilateral triangle drawn.--SilasW (talk) 18:17, 23 September 2009 (UTC)
thread_title:  Construction 

message: Under "Other Uses", the article mentions the following:
* A Reuleaux triangle rolls smoothly and easily, but makes a poor wheel because (...)
* Several pencils are manufactured in this shape, (...) having the advantage of not rolling off tables.
So which is it? Do they roll smoothly and easily, or do they not roll off tables? McGravin (talk) 03:41, 2 February 2010 (UTC)
replies: text: HA! Good catch. I've watered down both statements; does that seem enough? - DavidWBrooks (talk) 14:12, 2 February 2010 (UTC)
replies: text: There's no contradiction -- when there are two or more "rollers" of constant width (including Reuleaux triangles) resting on a flat surface with a flat sheet of material on top of them (:File:Reuleaux_triangle_54.JPG), then if you pull the top material forward, it will move purely horizontally (without any up-and-down bumpiness).  On the other hand, a Reuleaux triangle under gravity has a preferred (i.e. minimum potential energy) orientation with one point up; to get a Reuleaux triangle pencil rotating, you have to apply additional force beyond that necessary to overcome static friction, in order to raise its center of gravity.  However, in the case of a circular pencil, once you overcome static friction, it will start merrily rolling away... AnonMoos (talk) 12:57, 13 December 2010 (UTC)
thread_title:  Contradiction? 

message: It would be nice if the two articles could be better coordinated. AnonMoos (talk) 12:59, 13 December 2010 (UTC)
replies: text: yes, especially because this article says that these things "can be rolled" as if square wheels can't also be rolled. I don't mind if there is a semantic meaning behind this idea that says that square wheels cannot roll, but it's not obvious to me what it is. 96.224.41.4 (talk) 19:01, 21 January 2012 (UTC)
replies: text: Squares are not useful as rollers -- that is, when you rotate them, something placed on the top of them is not kept a constant distance off the ground.  Curves of constant width are useful rollers.  Consult :File:Reuleaux_triangle_54.JPG, and imagine what the difference would be if the upper sheet of material were resting on pegs of square cross-section... AnonMoos (talk) 05:36, 24 April 2012 (UTC)
replies: text: A counterexample. —David Eppstein (talk) 06:40, 24 April 2012 (UTC)
thread_title: Curve of constant width article

message: The signs are said to represent a prospector's shovel.  They do coincidentally resemble a Reuleaux triangle, but I don't think they're equilateral. —Tamfang (talk) 01:13, 7 February 2011 (UTC)
thread_title:  California highway signs 

message: Could you provide a pronunciation key for Reuleaux? Thanks, Yoninah (talk) 00:20, 25 June 2015 (UTC)
replies: text: I don't know a good source for the pronounciation. It looks like it should be pronounced in the French way (roo-LOW) but Reuleaux was actually German so it wouldn't surprise me if he used a different pronounciation. —David Eppstein (talk) 05:52, 25 June 2015 (UTC)
thread_title: Fascinating article!

message: The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:
* 
Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 17:03, 16 April 2021 (UTC)
replies: text: Swapped out for a different coin. —David Eppstein (talk) 18:41, 16 April 2021 (UTC)
thread_title:  A Commons file used on this page or its Wikidata item has been nominated for deletion 

message: I'm in no way an expert but given that the defining factor in manhole cover shape is "bigger than the hole", and the only reason the conversation came up (at least that I can find) is that Microsoft used "Why are manhole covers circuluar?" as an interview question, should we really keep the line about it in the article? I'm not going to just remove it as irrelevant partially because I'm happy to hear it defended and partially because if I did so with my non-account it'd likely just get bot reverted as vandalism, but to me it seems out of place at best and confusing at worst.
: It's not that it's "bigger" it's that it has a constant diameter and therefore there's no way to maneuver it so it will fit through the hole - unlike, say, a square, which can be dropped through its own hole if you orient it properly. - DavidWBrooks (talk) 11:41, 29 April 2021 (UTC)
thread_title:  Manhole cover shapes