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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 ...
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The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
One possible pattern used in a game of Patterns II.. One player, the Designer, designs a pattern and then places a symbol within each cell of a 6x6 grid using an agreed upon set of symbols (e.g., plus, circle, triangle, square, star).
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Crop circle – Pattern in a crop field; Dip circle – Instrument used for surveying, prospecting and demonstrating geomagnetism; List of gear nomenclature; Peaucellier–Lipkin linkage – Mechanical linkage transforming rotary motion into linear; Pitch circle; Repeating circle – Type of angular measurement instrument
Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.