Talk:Curve of constant width

terminology

Is there any way this page can be expressed in more laymans terms? I'm not a mathematician, but I am an engineer and even I had some trouble figuring out what the article was saying. -lommer 21:41, 6 Apr 2004 (UTC)

I'll try. It really is too concise now. When I figure out how to put in some diagrams things should get better (help with the diagrams would be appreciated). Dan Gardner 23:18, 6 Apr 2004 (UTC)

Sorry for adding more math, i felt like the page is actually missing some. Sonicrs (talk) 16:14, 15 January 2017 (UTC)

bicycle

Can someone explain what happens to the saddle while the Reuleaux-wheeled bike is being ridden? The recent times article said that it didn't bob up and down Humphrey Dalzell (talk) 11:37, 28 May 2009 (UTC)

The bike frame rests (via rollers) upon the top of the wheel, and is not supported by the wheel axle as normal bikes are. So although the wheel axle will bob up and down, the bike itself won't. 82.13.19.74 (talk) 23:33, 28 May 2009 (UTC)

first sentence of lead

Could someone change the first line to what it really is supposed to say? I would change it myself, but I don't know what should be there.ΠΑΕ.ΠΑΟΚ ₯ (talk) 20:15, 22 November 2009 (UTC)

So what makes you think it's wrong now? —Tamfang (talk) 00:20, 24 November 2009 (UTC)

"....intersecting its boundary in at least one point but not touching the interior..." It is impossible to intersect boundary and not touch the interior. If something different than 'having intersecting neighbourhoods' is meant by 'touching', another term should be used. 192.76.7.201 (talk) 18:52, 29 April 2012 (UTC)

I can only guess that it was talking about set intersection, as opposed to geometric intersection. I've rewritten it to make more sense. — Smjg (talk) 19:46, 29 April 2012 (UTC)

I find the sentence "[...] width (defined as the perpendicular distance between two distinct parallel lines each having at least one point in common with the shape's boundary but none with the shape's interior)" too much involved. You can replace with "[...] width (defined as the distance between two distinct parallel lines tangent to the curve)" — Preceding unsigned comment added by 134.206.55.73 (talk) 14:20, 30 January 2019 (UTC)

roller

It's a little odd that this article doesn't contain any mention of "roller" or rolling at all, since that's one of the main properties which they have and name which they are known by... AnonMoos (talk) 07:31, 28 November 2010 (UTC)

most general

Curves of constant width can be generated by drawing circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).

I believe, but cannot prove, that a CCW can be built on any set of lines in the plane, so long as no two are parallel. —Tamfang (talk) 18:38, 30 November 2010 (UTC)

I'm just going by what's in my source (Cundy and Rollett). There are diagrams there explaining details of the general triangular and pentagonal constructions; I may try to re-create the basic structural relationships of those diagrams in SVG form in the future. It might also be nice to have a GIF animation showing a flat sheet of material sliding across the top of two rollers (maybe a Reuleaux triangle and an irregular pentagonal-based curve). AnonMoos (talk) 19:53, 30 November 2010 (UTC)

There's a roller photo at File:Reuleaux_triangle_54.JPG , but it doesn't show too much in that static form (an animation would be more informative). AnonMoos (talk) 07:06, 12 December 2010 (UTC)

Did the general triangular construction diagram and added it to the article; probably won't do the pentagonal... AnonMoos (talk) 12:28, 13 December 2010 (UTC)

Nice diagram. What is y?--Salix (talk): 13:58, 13 December 2010 (UTC)

It's explained in detail on the image description page if you click on the diagram (go to File:How to make mathematical roller curve based on triangle.svg and scroll down slightly...) AnonMoos (talk) 15:21, 13 December 2010 (UTC)

Swedish?

I can't tell from sv:Liktjocking what the English equivalent is, or whether it has any relevance. AnonMoos (talk) 12:03, 16 December 2010 (UTC)

Additional source

Martin Gardner's "Mathematical Games" column in the February 1963 issue of Scientific American ("Curves of Constant Width, One of which Makes it Possible to Drill Square Holes") has additional facts and generalizations, but I probably won't be using it to update this article any time soon... AnonMoos (talk) 14:20, 30 July 2017 (UTC)

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Definitions

Please check:

 A curve of constant width is the set of all points with a common maximum distance from each other.

If this definition can be described as necessary and sufficient, there can't be any other definition. Still this can be explained by

 A set of all points meeting these requirements is a curve of constant width if there is a given distance and for each point in this set there is at least one other point in this distance in this set and no point in this set is more distant.

--Vollbracht (talk) 06:44, 25 February 2021 (UTC)

Your writing is difficult to understand. It seems plausible that a set $S$ of points forms a curve of constant width if and only if $S$ is maximal with the property that $S$ has the same radius from each of its points. However, we would need a published source to add that to the article. And it is obviously false that this is the only possible definition. —David Eppstein (talk) 06:58, 25 February 2021 (UTC)

Accepted! Still your way of putting it seems wrong in terms of using the word "radius" instead of "diameter". In addition it's dependent on supporting lines while a circle is defined with means of points and distances only. So I suggest an additional optional definition:

"Radius" is the standard term for the maximum distance within a given set from a specified center point. "Diameter" always means choosing two points with maximum distance from each other. —David Eppstein (talk) 17:24, 25 February 2021 (UTC)

 A curve of constant width is the outer border of a shape consisting of all points in a plane with a given maximum distance from each other.

And please - I know mathematicians don't like to hear this: this shape is of high technical relevance and no useless mathematics. Please don't delete the only given example drawn from life. There are even more. Please add the example of the shape drilled with two edge drills into thin sheet metal. You could add British 20 or 50 Pence coins as well. --Vollbracht (talk) 12:53, 25 February 2021 (UTC)

It is not true that a body of constant width has constant radius, it is only the curve forming its boundary for which this might still be true. And we still need published sources for this connection before adding it to the article. As for your image of a drill bit, that specific kind of bit is only for drilling circular holes, and this article is not the place to go in more detail into the geometry of circles. —David Eppstein (talk) 17:24, 25 February 2021 (UTC)

Yes, it is intended to drill circular holes. And when studying mechanical engineering you have to learn when and where it will do so and when it will drill a curve of constant width instead and how to avoid this to happen. (See de:Gleichdick#Auftreten von Gleichdicken in der Produktion) --Vollbracht (talk) 18:08, 25 February 2021 (UTC)