# User Contributed Dictionary

### Verb

circumscribing- present participle of circumscribe

# Extensive Definition

distinguish circumscription

In geometry, a circumscribed
planar shape or solid is
one that encloses and "fits snugly" around another geometric shape
or solid. Specifically, there must be no object similar
to the circumscribed object but smaller and also enclosing the
inner figure.

Familiar examples include circles circumscribed around
polygons, and triangles or regular
polygons circumscribed around circles. See in particular
circumscribed
circle.

More precisely, in the phrase "a circumscribed F
of X", the inner figure X is supposed to be a given, specific
figure (such as, for example, "the circle centered at A with radius
r"), whereas F stands for a class of figures (such as, for example,
"triangle"). Of these figures, a circumscribed one is a figure of
minimal size among those of the same shape enclosing X. Usually it
is unique in size, but not necessarily in position and
orientation.

The definition given above assumes that the
objects concerned are embedded in two- or three-dimensional Euclidean
space, but can easily be generalized to higher dimensions and
other metric
spaces.