concentricring

Concentric rings are a geometric arrangement in which multiple circles share a common center. A single concentric ring is the region between two circles with the same center or the boundary of one circle when considered as an edge.

Mathematically, concentric circles have the same center (h, k) but different radii r. Their equations are (x − h)^2 + (y − k)^2 = r^2 for each radius r. Because they share a center, concentric circles do not intersect each other, and they form a family of nested curves radiating outward from the center.

A key related shape is the annulus, the ring-shaped region between two concentric circles of radii R and r with R > r. The area of an annulus is π(R^2 − r^2). In a set of multiple concentric rings with radii r1 < r2 < ... < rn, the total area is the sum of the individual annular areas.

Concentric rings appear in many contexts. They occur in art and design as bullseye motifs, in optics and wave physics as interference patterns such as Newton’s rings, and in astronomy and planetary science as the layered, roughly circular ring systems around planets. They also describe natural patterns such as tree rings, which reflect periodic growth around a central axis.

In summary, concentric rings are defined by a shared center and varying radii, yielding a symmetrical, nested structure with widespread mathematical and practical applications. See also annulus and circle for related concepts.