The word "convex" comes from the Latin convexus, originally meaning "bulging, curved and rounded outward"; a convex curve is sometimes said to "curve upward," unlike a concave curve, which "curves downward."
Geometry has long studied convex polygons in the plane and convex polyhedra in space; a polygon is described as "convex" if the whole figure lies on the same side of the line containing any one of its sides. More generally, convex sets are studied; intuitively, they are characterized by having "no indentations."
A curve with both a convex and a concave section.
