A set in Euclidean space is convex
set if it contains all the line segments
connecting any pair of its points. If the set does not contain
all the line segments, it is called concave.
A convex set is always star convex, implying pathwise-connected, which
in turn implies connected.
A region can be tested for convexity in the Wolfram
Language using the function Region`ConvexRegionQ[reg].
See alsoConnected Set
, Convex Domain
, Convex Function
, Convex Optimization Theory
, Convex Set
, Minkowski Convex Body
, Simply Connected
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ReferencesBenson, R. V. Euclidean Geometry and Convexity. New York: McGraw-Hill, 1966.Busemann,
Surfaces. New York: Interscience, 1958.Croft, H. T.; Falconer,
K. J.; and Guy, R. K. "Convexity." Ch. A in Unsolved
Problems in Geometry. New York: Springer-Verlag, pp. 6-47, 1994.Eggleston,
H. G. Problems
in Euclidean Space: Applications of Convexity. New York: Pergamon Press,
1957.Gruber, P. M. "Seven Small Pearls from Convexity."
Math. Intell. 5, 16-19, 1983.Gruber, P. M. "Aspects
of Convexity and Its Applications." Expos. Math. 2, 47-83, 1984.Guggenheimer,
H. Applicable Geometry--Global and Local Convexity. New York: Krieger, 1977.Kelly,
P. J. and Weiss, M. L. Geometry
and Convexity: A Study of Mathematical Methods. New York: Wiley, 1979.Webster,
Oxford, England: Oxford University Press, 1995.
Referenced on Wolfram|AlphaConvex
Cite this as:
Weisstein, Eric W. "Convex." From MathWorld--A
Wolfram Web Resource. https://mathworld.wolfram.com/Convex.html