īy 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. More generally, every two great circles on a sphere are concentric with each other and with the sphere. 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). However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. In the Euclidean plane, two circles that are concentric necessarily have different radii from each other. Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, conic sections, and surfaces of revolution.Ĭoncentric 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). Geometric objects are coaxial if they share the same axis (line of symmetry). 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. In geometry, two or more objects are said to be concentric when they share the same center. Kepler's cosmological model formed by concentric spheres and regular polyhedra
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