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Is there a prefix meaning "at most" or "capped at"? I'd like to describe a spherical cap (Wikipedia, Wolfram) that is at most a hemisphere. The blue solid in the diagram below shows the type of cap I'm comfortable referring to as a subhemispherical cap (a term I just made up to differentiate from the red solid, which is also a spherical cap,) however 'sub-' is strictly less than, whereas I mean to say less than or equal to. I thought of subhemispherical cap or hemisphere, which depicts nicely that a hemispherical cap is in fact a hemisphere, but it does sound somewhat cleaner to call it a subhemi- or hemispherical cap (although the oddity of calling a hemisphere a hemispherical cap makes me prefer the former.) I list hemi- second both times as it is the edge case.

Still, what I really want is to combine the two into one term, i.e. [prefix]hemispherical cap. This would avoid the awkwardness of those phrasings and would be an easily repeatable phrase in a paper.

By the way I do find unfortunate that the word cap here does not fit with the common English usage, synonymous with lid, if it did I could just call it a spherical cap.

Also this has to be easy to understand, if the prefix is too niche I can't use it (although I'd still be curious to hear it.)

Spherical Cap

EDITED: For extra clarity on what I want, what I came up with, and added an image.

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  • The word maximally could suit your need -- a maximally hemispherical cap. – Yosef Baskin Jul 24 '17 at 16:43
  • Thanks @YosefBaskin, I kinda like it! +1 for being a mathematical adjective. Although it does seem very slightly awkward, as in it's not entirely clear from your usage that 'maximally' refers directly to 'hemi-'. (This is mostly why I was hoping for a prefix.) It's the best I've got for now though. – Haumed Rahmani Jul 24 '17 at 16:58
  • It's up to you. The adverb modifies hemispherical directly. It means an at-most-half-globe of a cap. – Yosef Baskin Jul 24 '17 at 17:01
  • This doesn't work. If something is "maximally X", that means it is as X as it could possibly be, not that it varies with a maximum of X. – eyeballfrog Jul 24 '17 at 18:21
  • True, that's something else I couldn't put my finger on. Especially mathematically that would be implying that it is as hemispherical as possible (a useless thing to say.) – Haumed Rahmani Jul 24 '17 at 19:05
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You could say that the cap is within or inside of the hemispherical cap: Endohemispherical cap

End- meaning inside of or within, as in
endorse, endocardial, endergonic, endoskeleton, endoscope, endogenous

Source: https://www.quia.com/files/quia/users/skrichard/ComSkills2/RootsPrefixesSuffixes

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  • Thanks, seems the best! Doesn't have the implications of sub- and is common enough to be understood. – Haumed Rahmani Jul 29 '17 at 14:03
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Perhaps the language of topology would give you more scope than the language of spherical geometry, e.g.

  • The surface of the sphere is a set of points S

  • A partial cover of S a collection of subsets that contains
    some but not all of the points in S.

  • A bounded partial cover is a collection that satisfies some
    bound, e.g. on the shape, size, number of subsets, or any other
    property one might care to define.

  • A hemispherically bounded partial cover would then have the
    properties you are looking for, provided that you define
    "hemispherically bounded" in an earlier step.

This is not a single-word answer, but with such a definition you could then introduce a term of your own, such as a cup cover, and use it within the scope of your document.

I have to confess that this is a somewhat frivolous use of topological language, but it might do the job.

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  • Thanks, a helpful view and rigorous! I think too much explanation is required though for my purposes :) – Haumed Rahmani Jul 25 '17 at 13:44
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EDIT

Mathematically, you want to say where theta is <= 90 degrees.

By definition, a subset can also contain the entire set. By analogy, a sub-hemispherical cap can include the entire hemisphere. I would state this as a definition before using it.

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  • Sorry, not sure if you understood what a spherical cap is, I added an image to clarify. Both the blue and red sections above are spherical caps; however, I want to include in my definition those that are like the blue, also include those that are half a sphere, and exclude those that are like the red. Including the half a sphere in the description is of mathematical importance. I did also already see that Q&A, while you could refer to the red section as a superhemispherical cap that is not what I was looking for. They do not seem to discuss an alternative to 'sub-' that includes the object. – Haumed Rahmani Jul 24 '17 at 20:11
  • I understood what a spherical cap was. But I did misunderstand that you were asking for a range of subsets. I edited my answer accordingly. – MikeJRamsey56 Jul 24 '17 at 23:35
  • @MikeJRamsey56 Good point about subsets, but regarding sub- as a prefix, I'm not sure I agree, sub- usually means below or under. As far as I can tell, "subset" is the only use of the prefix where it can include the complete entity as well. It seems to me that prefixing a word with sub- probably would imply anything under that level. That's my take at least. – RaceYouAnytime Jul 24 '17 at 23:52
  • Thanks @MikeJRamsey56 and RaceYouAnytime. It is a great point that that works at the least with 'subset', so given a definition before usage I could see that as being a proper term. I do agree though that generally it seems unintuitive and bears the connotation of a strict inequality. (Dictionary.com) Then again, 'cap' also used strangely, so it might be fair. :) In other words I'm not extremely enthused but I could see it working. Minus a prefix that means what I want, this could be the way to go. – Haumed Rahmani Jul 25 '17 at 0:04

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