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  • ...t of values to another set of values, assigning to each value in the first set exactly one value in the second. For instance, one function may map 1 to 1 Let <math>A</math>,<math>B</math> be [[set]]s and let <math>f</math> be a [[subset]] of <math>A\times B</math>, which
    10 KB (1,761 words) - 02:16, 12 May 2023
  • ...are two types of polygons: [[convex polygon|convex]] and [[concave polygon|concave]]. In their most general form, polygons are an ordered [[set]] of [[vertex|vertices]], <math>\{A_1, A_2, \ldots, A_n\}</math>, <math>n \
    2 KB (372 words) - 18:04, 30 May 2015
  • ...points <math>(x,y) </math> such that <math>y \ge f(x) </math> is [[convex set | convex]]. Equivalently, <math>f </math> is convex if for every <math> \l ...math>f </math> is (strictly) '''concave''' (or, occasionally, that it is ''concave down'') if <math>-f </math> is (strictly) convex.
    2 KB (417 words) - 23:10, 19 February 2016
  • A '''convex polygon''' is a [[polygon]] whose [[interior]] forms a [[convex set]]. That is, if any 2 points on the [[perimeter]] of the polygon are connec The [[convex hull]] of a [[finite]] set of points is a convex polygon with some or all of the points as its [[verte
    948 bytes (147 words) - 21:10, 27 February 2020
  • We note that the [[function]] <math>x \mapsto \ln x</math> is strictly [[concave]]. Then by [[Jensen's Inequality]], Now, set
    12 KB (2,171 words) - 13:45, 11 October 2024
  • ...the case <math>A</math>, <math>B</math>, <math>C</math> are collinear, we set <math>m(ABC) = 0</math>. Let <math>A</math>, <math>B</math>, <math>C</math> If <math>ABCX</math> is concave or a degenerate quadrilateral, assume without loss of generality that <math
    4 KB (854 words) - 10:30, 21 November 2023
  • ...the given inequality so that <math>1</math> is isolated on the right side. Set the left side to be <math>f(x, y, z)</math>. Now a routine computation show which shows that <math>f</math> is convex (concave up) in all three variables. Thus the maxima can only occur at the endpoints
    889 bytes (153 words) - 18:11, 3 July 2013
  • ...the same line. For example, the three red shaded circles count as one such set.) <math>ABCD</math> is a concave quadrilateral with <math>AB = 12</math>, <math>BC = 16</math>, <math>AD = C
    7 KB (1,100 words) - 17:40, 11 July 2021