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Arrangement of lines information


A simplicial line arrangement (left) and a simple line arrangement (right).

In geometry, an arrangement of lines is the subdivision of the plane formed by a collection of lines. Problems of counting the features of arrangements have been studied in discrete geometry, and computational geometers have found algorithms for the efficient construction of arrangements.

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Arrangement of lines

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geometry, an arrangement of lines is the subdivision of the plane formed by a collection of lines. Problems of counting the features of arrangements have been...

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Arrangement of hyperplanes

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hyperplanes are lines; such an arrangement is often called an arrangement of lines. Historically, real arrangements of lines were the first arrangements investigated...

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Curve of constant width

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crossings of an arrangement of lines, as the involutes of certain curves, or by intersecting circles centered on a partial curve. Every body of constant...

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Trihexagonal tiling

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edges form an infinite arrangement of lines. Its dual is the rhombille tiling. This pattern, and its place in the classification of uniform tilings, was...

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Zone theorem

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complexity of the zone of a line in an arrangement of lines. A line arrangement, denoted as A ( L ) {\displaystyle A(L)} , is a subdivision of the plane...

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Tetrakis square tiling

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the center point, forming an infinite arrangement of lines. It can also be formed by subdividing each square of a grid into two triangles by a diagonal...

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Rikka

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the arrangement consisted of seven main lines, and roughly starting in 1800, it consisted of nine main lines, each of which supports other minor lines. Important...

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Velodrome

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have lines laid out in a specified arrangement. Some other tracks also follow these protocols, but others have a different arrangement of lines to suit...

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Charles Howard Hinton

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cross-sections of a static four-dimensional arrangement of lines passing through a three-dimensional plane, an idea that anticipated the notion of world lines. Hinton's...

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Ikebana

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art of flower arrangement. It is also known as kadō (華道, 'way of flowers'). The origin of ikebana can be traced back to the ancient Japanese custom of erecting...

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Edge tessellation

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of the tiles form lines through the tiling, so each of these four tessellations can alternatively be viewed as an arrangement of lines. In the second four...

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Floral design

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flower arrangement is the art of using plant material and flowers to create an eye-catching and balanced composition or display. Evidence of refined...

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Traction current pylon

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current lines with two systems (4 conductor cables) typically have a single level arrangement of the conductor cables. For traction current lines with four...

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Power kite

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kite's angle of attack, which is set by the bridle; the arrangement of lines which terminate the main kite lines and attach to a number of points across...

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Blue Lines

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minimal arrangements" in the 1980s towards "deep, organic textures" in the 1990s. Concluding his review for AllMusic, John Bush deemed Blue Lines "one of the...

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By the Way

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writing most of the album's melodies, backing vocal arrangements, bass lines, and guitar progressions, therefore changing the direction of the recording...

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The Starry Night

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"an exaggeration from the point of view of arrangement" to further his argument that the painting is "an amalgam of images." However, it is by no means...

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History of flower arrangement

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The history of flower arrangement dates back to ancient Egyptian times. The earliest known flower arranging dates back to ancient Egypt. Egyptians were...

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Circle Limit III

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boundary". However, as Coxeter demonstrated, there is no hyperbolic arrangement of lines whose faces are alternately squares and equilateral triangles, as...

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