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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 square tiling can be used as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 4 other circles in the packing (kissing number). [2] The packing density is π/4=78.54% coverage. There are 4 uniform colorings of the circle packings.
The truncated square tiling is used in an optical illusion with truncated vertices divides and colored alternately, seeming to twist the grid.. The truncated square tiling is topologically related as a part of sequence of uniform polyhedra and tilings with vertex figures 4.2n.2n, extending into the hyperbolic plane:
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.
Overlapping circles grid – Kind of geometric pattern; Pappus chain – Ring of circles between two tangent circles; Polar circle (geometry) – Unique circle centered at a given triangle's orthocenter; Power center (geometry) – For 3 circles, the intersection of the radical axes of each pair; Salinon – Geometric shape
Non-Doyle spiral patterns obtained by placing unit circles at equal angular offsets on Fermat's spiral; the central image is the one with golden-ratio angular offsets. Tangent circles can form spiral patterns whose local structure resembles a square grid rather than a hexagonal grid, which can be continuously transformed into Doyle packings. [13]
In mathematics, physics, and art, moiré patterns (UK: / ˈ m w ɑː r eɪ / MWAH-ray, US: / m w ɑː ˈ r eɪ / mwah-RAY, [1] French: ⓘ) or moiré fringes [2] are large-scale interference patterns that can be produced when a partially opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré ...
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...