Diameter of a set

This usage of diameter also occurs in medical terminology concerning a lesion or in geology concerning a rock.

For any bounded set in the Euclidean plane or Euclidean space, the diameter of the object or set is the same as the diameter of its convex hull.

For any convex shape in the plane, the diameter is the largest distance that can be formed between two opposite parallel lines tangent to its boundary.

Jung's theorem provides more general inequalities relating the diameter to the radius.

[8] Just as the diameter of a two-dimensional convex set is the largest distance between two parallel lines tangent to and enclosing the set, the width is often defined to be the smallest such distance.

[9] The diameter or width of a two-dimensional point set or polygon can be calculated efficiently using rotating calipers.

In differential geometry, the diameter is an important global Riemannian invariant.

For instance, the unit sphere of any dimension, viewed as a Riemannian manifold, has diameter

According to Cheng's maximal diameter theorem, the unique manifold with the largest diameter for a given curvature lower bound is a sphere with that curvature.

Special cases of graph diameter include the diameter of a group, defined using a Cayley graph with the largest diameter possible for a given group, and the diameter of the flip graph of triangulations of a point set, the minimum number of local moves needed to transform one triangulation into another for two triangulations chosen to be as far apart as possible.