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Using only a single word in each case, I'm attempting to describe two different variations involving constancy of a certain attribute:

  1. Variation of an object without changing its weight.

  2. Variation of an object without changing its length.

(For those interested in the context, the object whose variation I'm considering is a weighted mathematical knot.)

Words like "isobaric" and "isothermic" immediately spring to mind, but obviously they won't do here. "Isometric" is close to describing case 2, but since it's already attached to a precise mathematical definition that slightly differs from case 2 I'd like to avoid using it. I've searched through lists like those found here and here, but these lists are not exactly short and seem to contain mostly technical language specifically related to biology and chemistry.

Does anybody know of words that could end this search for me? They certainly don't need to use the "iso" prefix; I simply thought that would be a good place to start. Any advice whatsoever is most appreciated.

I would use such a word as follows: "The next theorem presents a first-variation formula describing the isobaric variation of any weighted knot."

Essentially, I'm looking for a legitimate way to say "isolength" and "isoweight".

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  • Mathematicians have long since given up on trying to remember all the different names for every type of global constraint. So they decided to have a generic name for any and all such global constraints. The earliest global constraint for calculus of variations was the isoperimeter problem, so they went with that. If you have one global constraint that can be formulted to yield a constant, you have an isoperimetric problem. see page 5. So I would go with length-isoperimetric for 2.
    – Phil Sweet
    Commented Sep 11, 2018 at 23:52
  • As for 1, it depends. If the weight is hanging on the end of the knot, then it is a local constrain, not a global one. But if the weight is distributed along the knot, then it is global.
    – Phil Sweet
    Commented Sep 11, 2018 at 23:52

2 Answers 2

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You may perhaps use words (or neologism) based on Latin prefix, i.e. "equi":

  • same weight: Equiponderal (from equiponderate, equiponderation),
  • same length: Equilength.
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  • One final question I've encountered since the original post: is there a way to say "constant total"? (equitotal?)
    – AegisCruiser
    Commented Jan 19, 2016 at 23:37
  • For "constant total", I have no proposal. The best is perhaps to use the expressions "at constant total" or "at constant sum".
    – Graffito
    Commented Jan 20, 2016 at 10:42
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Would invariant work for you? Example: Variation of an object with invariant length

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  • "Invariant" was a possible choice if I couldn't find a more specialized word. Unfortunately, I'm considering variations of a curve and wanted to avoid unwieldy terms like "invariant length variation."
    – AegisCruiser
    Commented Apr 25, 2016 at 21:15
  • Perhaps "Variation of an object with fixed weight" would be better then.
    – Hank D
    Commented Apr 25, 2016 at 22:49

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