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Polyabolo
In recreational mathematics, a polyabolo (also known as a polytan) is a shape formed by gluing isosceles right triangles edge-to-edge, making a polyform with the isosceles right triangle as the base form. Polyaboloes were introduced by Martin Gardner in his June 1967 "Mathematical Games column" in ''Scientific American''. Nomenclature The name ''polyabolo'' is a back formation from the juggling object 'diabolo', although the shape formed by joining two triangles at just one vertex is not a proper polyabolo. By false analogy, treating the di- in diabolo as meaning "two", polyaboloes with from 1 to 10 cells are called respectively monaboloes, diaboloes, triaboloes, tetraboloes, pentaboloes, hexaboloes, heptaboloes, octaboloes, enneaboloes, and decaboloes. The name ''polytan'' is derived from Henri Picciotto's name ''tetratan'' and alludes to the ancient Chinese amusement of tangrams. Combinatorial enumeration There are two ways in which a square in a polyabolo can consist of two i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyabolo
In recreational mathematics, a polyabolo (also known as a polytan) is a shape formed by gluing isosceles right triangles edge-to-edge, making a polyform with the isosceles right triangle as the base form. Polyaboloes were introduced by Martin Gardner in his June 1967 "Mathematical Games column" in ''Scientific American''. Nomenclature The name ''polyabolo'' is a back formation from the juggling object 'diabolo', although the shape formed by joining two triangles at just one vertex is not a proper polyabolo. By false analogy, treating the di- in diabolo as meaning "two", polyaboloes with from 1 to 10 cells are called respectively monaboloes, diaboloes, triaboloes, tetraboloes, pentaboloes, hexaboloes, heptaboloes, octaboloes, enneaboloes, and decaboloes. The name ''polytan'' is derived from Henri Picciotto's name ''tetratan'' and alludes to the ancient Chinese amusement of tangrams. Combinatorial enumeration There are two ways in which a square in a polyabolo can consist of two i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyform
In recreational mathematics, a polyform is a plane (mathematics), plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex polygon, convex plane-filling polygon, such as a Square (geometry), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Games Column
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for ''Scientific American'' magazine. During the next years, through June 1986, Gardner wrote 9 more columns, bringing his total to 297, as other authors wrote most of the "Mathematical Games" columns. The table below lists Gardner's columns. Twelve of Gardner's columns provided the cover art for that month's magazine, indicated by "over in the table with a hyperlink to the cover. Other articles by Gardner Gardner wrote 5 other articles for ''Scientific American''. His flexagon article in December 1956 was in all but name the first article in the series of ''Mathematical Games'' columns and led directly to the series which began the following month. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a ''square''. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertices ''ABCD'' would be denoted as . The word rectangle comes from the Latin ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (angle). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperboli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order20Polyabolo
Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of different ways * Hierarchy, an arrangement of items that are represented as being "above", "below", or "at the same level as" one another * an action or inaction that must be obeyed, mandated by someone in authority People * Orders (surname) Arts, entertainment, and media * ''Order'' (album), a 2009 album by Maroon * "Order", a 2016 song from ''Brand New Maid'' by Band-Maid * ''Orders'' (1974 film), a 1974 film by Michel Brault * ''Orders'', a 2010 film by Brian Christopher * ''Orders'', a 2017 film by Eric Marsh and Andrew Stasiulis * ''Jed & Order'', a 2022 film by Jedman Business * Blanket order, purchase order to allow multiple delivery dates over a period of time * Money order or postal order, a financial instrument usually int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrakis Square Tiling
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane. It is a square tiling with each square divided into four isosceles right triangles from 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, with the diagonals alternating in direction, or by overlaying two square grids, one rotated by 45 degrees from the other and scaled by a factor of √2. Conway, Burgiel, and Goodman-Strauss call it a kisquadrille, represented by a kis operation that adds a center point and triangles to replace the faces of a square tiling (quadrille). It is also called the Union Jack lattice because of the resemblance to the UK flag of the triangles surrounding its degree-8 vertices. It is labeled V4.8.8 because each isosceles triangle face has two types of vertices: one with 4 triangles, and two with 8 triangles. As a dual uniform tiling It is the dual tessellation of the truncated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Plane
In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions of parallel lines, and also metrical notions of distance, circles, and angle measurement. The set \mathbb^2 of pairs of real numbers (the real coordinate plane) augmented by appropriate structure often serves as the canonical example. History Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other topics. Later, the plane was described in a so-called '' Cartesian coordinate system'', a coordinate system that specifies each point uniquely in a plane by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solomon W
Solomon (; , ),, ; ar, سُلَيْمَان, ', , ; el, Σολομών, ; la, Salomon also called Jedidiah ( Hebrew: , Modern: , Tiberian: ''Yăḏīḏăyāh'', "beloved of Yah"), was a monarch of ancient Israel and the son and successor of David, according to the Hebrew Bible and the Old Testament. He is described as having been the penultimate ruler of an amalgamated Israel and Judah. The hypothesized dates of Solomon's reign are 970–931 BCE. After his death, his son and successor Rehoboam would adopt harsh policy towards the northern tribes, eventually leading to the splitting of the Israelites between the Kingdom of Israel in the north and the Kingdom of Judah in the south. Following the split, his patrilineal descendants ruled over Judah alone. The Bible says Solomon built the First Temple in Jerusalem, dedicating the temple to Yahweh, or God in Judaism. Solomon is portrayed as wealthy, wise and powerful, and as one of the 48 Jewish prophets. He is also the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David A
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...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 study ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
