convex

English

Top: a spoon with its convex side up.
Bottom: a spoon with its concave side up.

A convex set. For any points x and y within the set, the connecting line lies within the set.

A convex polygon.

Etymology

Borrowed from Middle French convexe, from Latin convexus (“arched”).

Pronunciation

• (Received Pronunciation) IPA^(key): /ˈkɒnvɛks/
• (General American) IPA^(key): /ˈkɑnvɛks/
• The noun was often stressed on the second syllable by early writers, such as Milton, and occasionally by later poets.

Adjective

convex (comparative more convex, superlative most convex)

1. curved or bowed outward like the outside of a bowl or sphere or circle
   • Whewell

     Drops of water naturally form themselves into figures with a convex surface.

2. (mathematics, not comparable, of a set in Euclidean space) arranged such that for any two points in the set, a straight line between the two points is contained within the set.
3. (geometry, not comparable, of a polygon) having no internal angles greater than 180 degrees.
4. (functional analysis, not comparable, of a real-valued function on the reals) having an epigraph which is a convex set.

Antonyms

• concave

Derived terms

Terms derived from convex

• biconvex
• concavo-convex
• convex combination
• convex function
• convex hull
• convex lens
• convex set
• convexedly
• convexification

• convexify
• convexity
• convexly
• convexness
• convexoconcave
• convexoconvex
• convexoplane
• double-convex
• equiconvex

• hyperconvex
• nonconvex
• planoconvex
• plano-convex
• polyconvex
• pseudoconvex
• quasiconvex
• semiconvex
• subconvex

Translations

curved or bowed outward like the outside of a bowl or sphere or circle

• Armenian: ուռուցիկ (hy) (uṙucʿik)
• Asturian: convexu
• Bulgarian: изпъкнал (bg) (izpǎknal)
• Catalan: convex (ca)
• Cornish: bothgrom
• Czech: konvexní (cs)
• Danish: konveks
• Dutch: bol (nl)
• Esperanto: malkava, konveksa
• Estonian: kumer
• Finnish: kupera (fi)
• French: convexe (fr)
• Galician: convexo, comba (gl)
• German: konvex (de)
• Greek: κυρτός (el) (kyrtós)
• Hawaiian: ʻeʻemu
• Hebrew: קעור‎‎ (qa'ur)
• Hungarian: domború (hu), konvex (hu)
• Icelandic: kúptur
• Italian: convesso (it)

• Japanese: 凸面 (とつめん, totsumen)
• Kannada: ನಿಮ್ನದರ್ಪಣ (nimnadarpaṇa)
• Lithuanian: išgaubtas
• Norwegian:

  Bokmål: konveks (no)

  Nynorsk: konveks

• Occitan: convèx
• Persian: کوژ‎‎ (fa)
• Polish: wypukły (pl)
• Portuguese: convexo (pt)
• Russian: вы́пуклый (ru) (výpuklyj)
• Sindhi: گھُٻيل‎‎ (sd)
• Slovak: konvexný
• Slovene: konveksen (sl)
• Spanish: convexo (es)
• Swedish: konvex (sv)
• Tagalog: malukob
• Thai: นูน (th) (nuun)
• Turkish: konveks (tr), dışbükey (tr)
• Welsh: amgrwm (cy) m, amgrom f

Noun

convex (plural convexes)

1. Any convex body or surface.
   • Tickell

     Half heaven's convex glitters with the flame.

References

• “convex” in John A. Simpson and Edward S. C. Weiner, editors, The Oxford English Dictionary, 2nd edition, Oxford: Clarendon Press, 1989, →ISBN.

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Catalan

Etymology

Borrowed from Latin convexus.

Pronunciation

• (Balearic, Valencian) IPA^(key): /komˈvɛks/
• (Central) IPA^(key): /kumˈbɛks/

Adjective

convex (feminine convexa, masculine plural convexos, feminine plural convexes)

1. convex

Antonyms

• còncau

Related terms

• convexitat

Further reading

• “convex” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.