Lens (geometry)

In 2-dimensional geometry, a lens is a convex set bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex). This shape can be formed as the intersection of two circular disks. It can also be formed as the union of two circular segments (regions between the chord of a circle and the circle itself), joined along a common chord. In 2-dimensional geometry, a lens is a convex set bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex). This shape can be formed as the intersection of two circular disks. It can also be formed as the union of two circular segments (regions between the chord of a circle and the circle itself), joined along a common chord. If the two arcs of a lens have equal radii, it is called a symmetric lens, otherwise is an asymmetric lens. The vesica piscis is one form of a symmetrical lens, formed by arcs of two circles whose centers each lie on the opposite arc. The arcs meet at angles of 120° at their endpoints. The area inside a symmetric lens can be expressed in terms of the radii R and arc lengths θ in radians: The area of an asymetric lens formed from circles of radii R and r with distance d between their centers is