# What is an Isometric Surface? [closed]

The term Isometric Surface brings up surprisingly unrelated search results on google. So I thought I would ask here. What is an isometric surface? I do have an understanding of what it is, but I need to confirm it as it may be completely wrong. If in your answer, you could give a brief comparison between them and implicit surfaces as well as parametric surfaces (I have a guess that isometric and parametric surfaces are similar/same... but I may be completely wrong), that would be great.

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## closed as unclear what you're asking by Rahul, dfeuer, Vedran Šego, Nicholas R. Peterson, Cameron BuieSep 22 '13 at 3:16

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If Robert Israel is right (which is to say, if the sun comes up tomorrow), there's no such thing as an isometric surface, and the rest of the question is a fishing expedition, so I've voted to close, pending some effort on Samaursa's part to put this in better shape. –  Gerry Myerson May 20 '11 at 5:51
Are you sure rather you mean Isoperimetric surface? –  Arjang May 20 '11 at 5:57
@GerryMyerson Okay, but there does seem to be a lot of people who think that they exist: encyclopediaofmath.org/index.php/Isometric_surfaces, google.ca/…. Plenty of research papers talk about this as well. This is an old question but I will revisit it once I run across those papers again. –  Samaursa Apr 9 at 16:00
I think you are missing Robert Israel's point. There is no such thing as an isometric surface, much as there is no such thing as a similar triangle, or a parallel line. Just as parallel lines are two or more lines that are parallel to each other, with no one line in isolation being a parallel line, isometric surfaces are two or more surfaces that are isometric to each other, with no one surface in isolation being an isometric surface. –  Gerry Myerson Apr 10 at 0:38
@GerryMyerson I definitely missed the point and that makes perfect sense! The similar-triangle and parallel-line example you gave finally put it all together for me, thanks! –  Samaursa Apr 10 at 11:54