A black circle circumscribed by a red square

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. In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ... A square as a geometric shape is described and illustrated at square (geometry). ... Table of Geometry, from the 1728 Cyclopaedia. ... Something is called planar if it is made up of flat planes, or pertaining to planes. ... In geometry, two sets have the same shape if one can be transformed to another by a combination of translations, rotations and uniform scalings. ... In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. ... Several equivalence relations in mathematics are called similarity. ...

Familiar examples include circles circumscribed around polygons, and triangles or regular polygons circumscribed around circles. In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ... Look up Polygon in Wiktionary, the free dictionary. ... A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ... A polygon (from the Greek poly, for many, and gonos, for angle) is a closed planar path composed of a finite number of sequential straight line segments. ...

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. 2-dimensional renderings (ie. ... In mathematics, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...

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