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Decadences (talk | contribs) m i fixed one of my own changes to read a little better than i had changed it to. lol. sorry when i reviewed my edits, it was quite confusing to witness the way the how it was before vs how it is now portrayed and seemed as if the changes i made were even worse. even tho before i clicked on review i was certain that everything improved (albeit missing this specific change of mine that i believed was still needing improvement) Tags: Visual edit Mobile edit Mobile web edit |
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{{short description|In geometry, set that intersects every line into a single line segment}}
[[File:Convex polygon illustration1.svg|right|thumb|Illustration of a convex set which looks somewhat like a deformed circle. The line segment, illustrated in black above, joining points x and y, lies completely within the set, illustrated in green. Since this is true for any potential locations of any two points within the above set, the set is convex.]]
[[File:Convex polygon illustration2.svg|right|thumb|Illustration of a non-convex set. Illustrated by the above line segment whereby it changes from the black color to the red color. Exemplifying why this above set, illustrated in green, is non-convex.]]
In [[geometry]], a subset of a [[Euclidean space]], or more generally an [[affine space]] over the [[Real number|reals]], is '''convex''' if, given any two points in the subset, the subset contains the whole [[line segment]] that joins them. Equivalently, a '''convex set''' or a '''convex region''' is a subset that intersects every [[line (geometry)|line]] into a single line segment (possibly empty).<ref>{{cite book|last1=Morris|first1=Carla C.|last2=Stark|first2=Robert M.|title=Finite Mathematics: Models and Applications|date=24 August 2015|publisher=John Wiley & Sons|isbn=9781119015383|page=121|url=https://books.google.com/books?id=ZgJyCgAAQBAJ&q=convex+region&pg=PA121|access-date=5 April 2017|language=en}}</ref><ref>{{cite journal|last1=Kjeldsen|first1=Tinne Hoff|title=History of Convexity and Mathematical Programming|journal=Proceedings of the International Congress of Mathematicians|issue=ICM 2010|pages=3233–3257|doi=10.1142/9789814324359_0187|url=http://www.mathunion.org/ICM/ICM2010.4/Main/icm2010.4.3233.3257.pdf|access-date=5 April 2017|url-status=dead|archive-url=https://web.archive.org/web/20170811100026/http://www.mathunion.org/ICM/ICM2010.4/Main/icm2010.4.3233.3257.pdf|archive-date=2017-08-11}}</ref>
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