Zirkumskriptiven

Zirkumskriptiven refers to the geometric concept of circumscription, where a polygon or polyhedron is drawn around a circle or sphere such that all its sides or faces are tangent to the inscribed circle or sphere. In essence, the circumscribed figure encloses the inscribed figure.

For polygons, a circumscribed polygon has its sides tangent to an inscribed circle. This means the circle is inside the polygon, and each side of the polygon touches the circle at exactly one point. A common example is a circumscribed triangle, where the triangle's sides are tangent to its incircle. Not all polygons can be circumscribed about a circle; only tangential polygons possess this property.

Similarly, a circumscribed polyhedron is a polyhedron whose faces are tangent to an inscribed sphere. The sphere lies within the polyhedron, and each face of the polyhedron touches the sphere at a single point. For instance, a circumscribed cube has its faces tangent to an inscribed sphere at their centers. Like polygons, not all polyhedra can be circumscribed about a sphere; only tangential polyhedra have this characteristic.

The term "zirkumskriptiven" is the German equivalent and is used in mathematical contexts to describe this relationship between enclosing and enclosed geometric shapes. It highlights the property of tangency between the boundaries of the two figures.