Concentricité

In geometry, two or more objects are said to be concentric when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyhedra, parallelograms, cones, conic sections, and quadrics. Geometric objects are coaxial if they share the same axis (line of symmetry). Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, conic sections, and surfaces of revolution. Concentric objects are often part of the broad category of whorled patterns, which also includes spirals (a curve which emanates from a point, moving farther away as it revolves around the point). In the Euclidean plane, two circles that are concentric necessarily have different radii from each other. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere). More generally, every two great circles on a sphere are concentric with each other and with the sphere. By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral. The circumcircle and the incircle of a regular n-gon, and the regular n-gon itself, are concentric. For the circumradius-to-inradius ratio for various n, see Bicentric polygon#Regular polygons. The same can be said of a regular polyhedron's insphere, midsphere and circumsphere. The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles.