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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.
A rhombitrihexagonal tiling: tiled floor in the Archeological Museum of Seville, Spain, using square, triangle, and hexagon prototiles Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as tiles , can be arranged to fill a plane without any gaps, according to a given set of rules.
The word (then spelled mappe) is attested in English in 1496, but new refinements and variations of mop designs have been introduced, from time to time.For example, American inventor Jacob Howe received US patent #241 for a mop holder in 1837 [2] and Thomas W. Stewart (US patent #499,402) in 1893.
A stone pillar in the 6th-century Marundeeswarar Temple in India shows three equilateral triangles rotated from each other to form a regular enneagram; like the Borromean rings these three triangles are linked and not pairwise linked, [12] but this crossing pattern describes a different link than the Borromean rings. [13]
The boundary of a Reuleaux triangle is a constant width curve based on an equilateral triangle. All points on a side are equidistant from the opposite vertex. A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. [1]
a pattern using only part of the dot grid. If that is the case, the same pattern or a different pattern fills/uses up the remaining dot grids. Most of the times, these patterns together end up becoming a complex pattern. [citation needed] a pattern in which a stroke runs around each dot incompletely, but open.
Pascal triangle extended: Image title: Binomial coefficients C(n, k) extended for negative and fractional n, illustrated with expansion of a simple binomial by CMG Lee. It can be observed that Pascal's triangle is rotated and alternate terms are negated. The case n = −1 gives Grandi's series. Width: 100%: Height: 100%
Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}. English mathematician John Conway called it a deltille , named from the triangular shape of the Greek letter delta (Δ).