Delaunay triangulation

•  Penrose tiling

  A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. Because all tilings obtained with the Penrose tiles are non-periodic, Penrose tiles are considered aperiodic tiles. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right.

  

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•  Squaring the square

  A square with sides equal to a unit length multiplied by an integer is called an integral square. Squaring the square is the problem of tiling one integral square using only other integral squares. The name was coined in humorous analogy with squaring the circle. Squaring the square is a trivial task unless additional conditions are set. The most studied restriction is the "perfect" squared square, where all contained squares are of different size (see below).

  

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•  Voronoi diagram

  In mathematics, a Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g. , by a discrete set of points. It is named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation, In the simplest case, we are given a set of points S in the plane, which are the Voronoi sites.

  

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•  Packing problem

  Packing problems are one area where mathematics meets puzzles. Many of these problems stem from real-life problems with packing items.

  

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•  Tarski's circle-squaring problem

  Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. This was proven to be possible by Miklós Laczkovich in 1990; the decomposition makes heavy use of the axiom of choice and is therefore non-constructive. Laczkovich's decomposition uses about 10 different pieces.

  

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•  Bolyai–Gerwien theorem

  In geometry, the Bolyai–Gerwien theorem states that if two simple polygons of equal area are given, one can cut the first into finitely many polygonal pieces and rearrange the pieces to obtain the second polygon. "Rearrangement" means that one may apply a translation and a rotation to every polygonal piece.

  

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•  Kepler conjecture

  The Kepler conjecture, named after Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing and hexagonal close packing arrangements. The density of these arrangements is slightly greater than 74%.

  

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•  Sphere packing

  In mathematics sphere packing problems concern arrangements of non-overlapping identical spheres which fill a space. Usually the space involved is three-dimensional Euclidean space. However, sphere packing problems can be generalised to two dimensional space (where the "spheres" are circles), to n-dimensional space (where the "spheres" are hyperspheres) and to non-Euclidean spaces such as hyperbolic space.

  

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•  Digital geometry

  Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space. Simply put, digitizing is replacing an object by a discrete set of its points. The images we see on the TV screen, the raster display of a computer, or in newspapers are in fact digital images. Its main application areas are computer graphics and image analysis.

  

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•  Discrete geometry

  Discrete geometry or combinatorial geometry may be loosely defined as study of geometrical objects and properties that are discrete or combinatorial, either by their nature or by their representation; the study that does not essentially rely on the notion of continuity. Parts of its domain of research is often attributed to other kinds of geometry: digital geometry, computational geometry, finite geometry, and toric geometry. It also overlaps with convex geometry, and combinatorial topology.

  

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• Discrete geometry by likeorhate
• Geometric algorithms by likeorhate
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•  Duplicate bridge

  Duplicate bridge is the most widely used variation of contract bridge in club and tournament settings. It is called duplicate because the same bridge hand (i.e. arrangement of cards) is duplicated at other tables, in order to allow a fair comparison of playing skill and reduce "luck of the cards". In this way, every hand, whether good or bad, is played in competition with others playing the identical cards, and the element of skill is heightened whilst that of chance is reduced.

  

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•  Egregore

  Egregore (also "egregor") is an occult concept representing a "thoughtform" or "collective group mind", an autonomous psychic entity made up of, and influencing, the thoughts of a group of people. The symbiotic relationship between an egregore and its group has been compared to the more recent, non-occult concepts of the corporation and the meme.

  

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•  Gwenno Saunders

  Gwenno Saunders (born Gwenno Mererid Saunders on 23 May 1981) is a Welsh dancer and solo artist. She is best known as a singer and keyboardist with The Pipettes, and is also known by the name Gwenno Pipette.

  

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• Garowe by likeorhate
•  Touchstone (assaying tool)

  

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