Circles inscribed in different polygons

In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position The shape ( OE sceap Eng created thing) of an object located in some space refers to the part of space occupied by the object as determined In Mathematics, solid geometry was the traditional name for the Geometry of three-dimensional Euclidean space &mdash for practical purposes the kind of Specifically, there must be no object similar to the inscribed object but larger and also enclosed by the outer figure. Geometry Two geometrical objects are called similar if one is congruent to the result of a uniform scaling (enlarging or shrinking of the other

Familiar examples include circles inscribed in polygons, and triangles or regular polygons inscribed in circles. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the In Geometry a polygon (ˈpɒlɨɡɒn ˈpɒliɡɒn is traditionally a plane figure that is bounded by a closed path or circuit A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line General properties These properties apply to both convex and star regular polygons

More precisely, in the phrase "an inscribed F of X", the outer 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, an inscribed one is a figure of maximal size among those of the same shape enclosed by 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. In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it In Mathematics, a metric space is a set where a notion of Distance (called a metric) between elements of the set is defined