Is there an elegant name for a square but with convex, curvy sides?
October 29, 2013 1:40 PM Subscribe
Is there an elegant name for a shape that is a square but with convex, curvy sides?
I am looking for an elegant name for a superellipse with n between 1 and 2. Here is an example. Essentially, I have a four "sided" shape with recognizable vertices, but curved sides. If it were a triangle, it would resemble a Reuleaux triangle, but there seems no standard name for this shape as a square. A squircle is not the name I am looking for, since that has flat sides and rounded corners. I am dealing with rounded sides, but identifiable "corners." I need this in the context of art and architecture, so it does not have to be a strictly geometric or mathematical term.
I am looking for an elegant name for a superellipse with n between 1 and 2. Here is an example. Essentially, I have a four "sided" shape with recognizable vertices, but curved sides. If it were a triangle, it would resemble a Reuleaux triangle, but there seems no standard name for this shape as a square. A squircle is not the name I am looking for, since that has flat sides and rounded corners. I am dealing with rounded sides, but identifiable "corners." I need this in the context of art and architecture, so it does not have to be a strictly geometric or mathematical term.
Best answer: A 'curved square' may be the best you can do. Here's a curved square plate.
posted by pipeski at 1:54 PM on October 29, 2013
posted by pipeski at 1:54 PM on October 29, 2013
I think that's called a "lozenge".
posted by Chocolate Pickle at 2:32 PM on October 29, 2013 [1 favorite]
posted by Chocolate Pickle at 2:32 PM on October 29, 2013 [1 favorite]
Best answer: Why not a Reuleaux square? See pages 4 and 5 of the article "General Reuleaux Polygon in Mathematics" [pdf] for figures.
posted by jedicus at 2:40 PM on October 29, 2013 [4 favorites]
posted by jedicus at 2:40 PM on October 29, 2013 [4 favorites]
No one seems to use the -lateral construction for anything other than four-sided figures, so I don't think you would be incurring much ambiguity by using 'curvilateral' for a square with curved sides.
posted by jamjam at 7:52 PM on October 29, 2013
posted by jamjam at 7:52 PM on October 29, 2013
Chocolate Pickle: "I think that's called a "lozenge"."
No, a lozenge is a diamond taller than it is wide.
In optics we call the two curve-sided squares that result from distortion "pin-cushion" (if the walls bow inwards) and "barrel" (walls bow outwards). I doubt most people would get either, though, since a barrel normally only bows on two sides.
posted by IAmBroom at 9:53 AM on October 31, 2013
No, a lozenge is a diamond taller than it is wide.
In optics we call the two curve-sided squares that result from distortion "pin-cushion" (if the walls bow inwards) and "barrel" (walls bow outwards). I doubt most people would get either, though, since a barrel normally only bows on two sides.
posted by IAmBroom at 9:53 AM on October 31, 2013
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posted by 2bucksplus at 1:44 PM on October 29, 2013 [1 favorite]