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An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space.Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points.
The second circle is centered at any point on the first circle. All following circles are centered on the intersection of two other circles. The design is sometimes expanded into a regular overlapping circles grid. Bartfeld (2005) describes the construction: "This design consists of circles having a 1-[inch] radius, with each point of ...
The vesica piscis is the intersection of two congruent disks, each centered on the perimeter of the other. The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. [1]
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. [6] For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii.
The circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle. [16] For example, the decoration of the 15th-century mosque in Yazd , Persia is based on a circle, divided into six by six circles drawn around it, all touching at its centre and each touching its two neighbours' centres to form a ...
A quatrefoil (anciently caterfoil) [1] is a decorative element consisting of a symmetrical shape which forms the overall outline of four partially overlapping circles of the same diameter. It is found in art, architecture, heraldry and traditional Christian symbolism . [ 2 ]
'quarter of the party') is an Ancient Arab symbol in the shape of an octagram, represented as two overlapping squares ۞. While its main utility today is to mark a division inside some copies of the Quran to facilitate recitation , it has originally featured on a number of emblems and flags in the past and continues to do so today.
Another argument for the impossibility of circular realizations, by Helge Tverberg, uses inversive geometry to transform any three circles so that one of them becomes a line, making it easier to argue that the other two circles do not link with it to form the Borromean rings. [27] However, the Borromean rings can be realized using ellipses. [2]