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Tetrad (geometry Puzzle)
In geometry, a tetrad is a set of four simply connected disjoint planar regions in the plane, each pair sharing a finite portion of common boundary. It was named by Michael R. W. Buckley in 1975 in the Journal of Recreational Mathematics. A further question was proposed that became a puzzle, whether the 4 regions could be congruent, with or without ''holes'', other enclosed regions.Martin Gardner, ''Penrose Tiles to Trapdoor ciphers'', 1989, p.121-12/ref> Fewest sides and vertices The solutions with four congruent tiles include some with five sides.Further Questions about Tetrads by Walter Trump However, their placement surrounds an uncovered hole in the plane. Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrad Solution0
Tetrad ('group of 4') or tetrade may refer to: * Tetrad (area), an area 2 km x 2 km square * Tetrad (astronomy), four total lunar eclipses within two years * Tetrad (chromosomal formation) * Tetrad (general relativity), or frame field ** Tetrad formalism, an approach to general relativity * Tetrad (geometry puzzle), a set of four simply connected disjoint planar regions in the plane * Tetrad (meiosis), the four cells produced by meiotic cell division * Tetrad (music), a set of four notes ** Tetrad (chord), a series of four notes * Tetrad (symbol), or tetractys, a triangular figure of ten points arranged in four rows, and mystical symbol * Medical triad, Medical tetrad, a group of four signs or symptoms which characterise a specific medical condition * Nibble, or tetrade, a 4-bit group * a tuple of length 4 * Tetrad Islands, in the Antarctic See also * * 4 * Triad (other) ('group of 3') * Pentad (other) ('group of 5') * Dark tetrad, group of four un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simply Connected
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question. The fundamental group of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected if and only if its fundamental group is trivial. Definition and equivalent formulations A topological space X is called if it is path-connected and any loop in X defined by f : S^1 \to X can be contracted to a point: there exists a continuous map F : D^2 \to X such that F restricted to S^1 is f. Here, S^1 and D^2 denotes the unit circle and closed unit disk in the Euclidean plane respectively. An equivalent formulation is this: X is simply connected if and only if it is path-connected, and whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Recreational Mathematics
The ''Journal of Recreational Mathematics'' was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue (volume 38, number 2) published in 2014. The initial publisher (of volumes 1–5) was Greenwood Periodicals. Harry L. Nelson was primary editor for five years (volumes 9 through 13, excepting volume 13, number 4, when the initial editor returned as lead) and Joseph Madachy, the initial lead editor and editor of a predecessor called ''Recreational Mathematics Magazine'' which ran during the years 1961 to 1964, was the editor for many years. Charles Ashbacher and Colin Singleton took over as editors when Madachy retired (volume 30 number 1). The final editors were Ashbacher and Lamarr Widmer. The journal has from its inception also listed associate editors, one of whom was Leo Moser. The journal contains: # Original articles # Book ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Tetrad
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A ''regular hexagon'' has Schläfli symbol and can also be constructed as a truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries (''rotational symmetry of order six'') and six reflection symmetries (''six lines of symmetry''), making up the dihedral group D6. The longest diagonals of a regular he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyform
In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes. Construction rules The rules for joining the polygons together may vary, and must therefore be stated for each distinct type of polyform. Generally, however, the following rules apply: #Two basic polygons may be joined only along a common edge, and must share the entirety of that edge. #No two basic polygons may overlap. #A polyform must be connected (that is, all one piece; see connected graph, connected space). Configurations of disconnected basic polygons do not qualify as polyforms. #The mirror image of an asymmetric polyform is not consider ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces of 1 to 6 squares were first published in '' Fairy Chess Review'' between the years 1937 to 1957, under the name of "dissection problems." The name ''polyomino'' was invented by Solomon W. Golomb in 1953, and it was popularized by Martin Gardner in a November 1960 "Mathematical Games" column in ''Scientific American''. Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyiamond
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle. The word ''polyiamond'' is a back-formation from ''diamond'', because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial 'di-' looks like a Greek prefix meaning 'two-' (though ''diamond'' actually derives from Greek '' ἀδάμας'' - also the basis for the word "adamant"). The name was suggested by recreational mathematics writer Thomas H. O'Beirne in ''New Scientist'' 1961 number 1, page 164. Counting The basic combinatorial question is, How many different polyiamonds exist with a given number of cells? Like polyominoes, polyiamonds may be either free or one-sided. Free polyiamonds are invariant under reflection as well as translation and rotation. One-sided polyiamonds distinguish reflections. The number of free ''n''-iamonds for ''n'' = 1, 2, 3, ... is: :1, 1, 1, 3, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhex (mathematics)
In recreational mathematics, a polyhex is a polyform with a regular hexagon (or 'hex' for short) as the base form, constructed by joining together 1 or more hexagons. Specific forms are named by their number of hexagons: ''monohex'', ''dihex'', ''trihex'', ''tetrahex'', etc. They were named by David Klarner who investigated them. Each individual polyhex tile and tessellation polyhexes and can be drawn on a regular hexagonal tiling. Construction rules The rules for joining hexagons together may vary. Generally, however, the following rules apply: #Two hexagons may be joined only along a common edge, and must share the entirety of that edge. #No two hexagons may overlap. #A polyhex must be connected. Configurations of disconnected basic polygons do not qualify as polyhexes. #The mirror image of an asymmetric polyhex is not considered a distinct polyhex (polyhex are "double sided"). Tessellation properties All of the polyhexes with fewer than five hexagons can form at least one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tiling Puzzles
Tiling may refer to: *The physical act of laying tiles *Tessellations Computing *The compiler optimization of loop tiling *Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People *Heinrich Sylvester Theodor Tiling (1818–1871), physician and botanist *Reinhold Tiling (1893–1933), German rocket pioneer Other uses *Neuronal tiling *Tile drainage, an agriculture practice that removes excess water from soil *Tiling (crater), a small, undistinguished crater on the far side of the Moon See also *Brickwork *Packing (other) Packing may refer to: Law and politics * Jury packing, selecting biased jurors for a court case * Packing and cracking, a method of creating voting districts to give a political party an advantage Other uses * Packing (firestopping), the proces ... * Tiling puzzle {{disambiguation, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
