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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] [Amazon] |
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 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rhombus
In plane Euclidean geometry, a rhombus (: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the Diamonds (suit), diamonds suit in playing cards which resembles the projection of an Octahedron#Orthogonal projections, octahedral diamond, or a lozenge (shape), lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (which some authors call a calisson after calisson, the French sweet—also see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle. Every rhombus is simple polygon, simple (non-self-intersecting), and is a special case of a parallelogram and a Kite (geometry), kite. A rhombus with right angles is a square. Etymology The word "rhombus" comes from , meaning something that spins, which derives from the verb , roman ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Symmetry
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant under some Transformation (function), transformations, such as Translation (geometry), translation, Reflection (mathematics), reflection, Rotation (mathematics), rotation, or Scaling (geometry), scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a space, spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including scientific model, theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Diamond
Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Diamond is tasteless, odourless, strong, brittle solid, colourless in pure form, a poor conductor of electricity, and insoluble in water. Another solid form of carbon known as graphite is the Chemical stability, chemically stable form of carbon at Standard temperature and pressure, room temperature and pressure, but diamond is metastable and converts to it at a negligible rate under those conditions. Diamond has the highest Scratch hardness, hardness and thermal conductivity of any natural material, properties that are used in major industrial applications such as cutting and polishing tools. Because the arrangement of atoms in diamond is extremely rigid, few types of impurity can contaminate it (two exceptions are boron and nitrogen). Small numbers of lattice defect, defects or impurities (about one per million of lattice atoms) can color ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Calisson
Calissons are a traditional French candy consisting of a smooth, pale yellow, homogeneous paste of candied fruit (especially melons and oranges) and ground almonds topped with a thin layer of royal icing. They have a texture similar to that of marzipan, but with a fruitier, distinctly melon-like flavour. They are often almond-shaped and are typically about five centimeters (two inches) in length. Calissons are traditionally associated with the town of Aix-en-Provence, France, and most of the world's supply is still made in the Provence region. History The calisson is believed to have its origins in south of France. Its most probable etymology, established by the sociolinguist specializing in Provençal Philippe Blanchet in 1998, is that the Provençal word ''calissoun'' is formed from "''chalice''" and from the diminutive "''-oun''", meaning "''small chalice''". Small in size and small in sacred value. The word "''chalice''", in fact, in Provençal as in French (we have the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Back-formation
Back-formation is the process or result of creating a neologism, new word via Morphology (linguistics), morphology, typically by removing or substituting actual or supposed affixes from a lexical item, in a way that expands the number of lexemes associated with the corresponding root (linguistics), root word.Crystal, David. ''A Dictionary of Linguistics and Phonetics, Sixth Edition'', Blackwell Publishers, 2008. James Murray (lexicographer), James Murray coined the term ''back-formation'' in 1889. (''Oxford English Dictionary, Oxford English Dictionary Online'' preserves its first use of 'back-formation' from 1889 in the definition of ''to burgle''; from ''burglar''.) For example, the noun ''resurrection'' was borrowed from Latin, and the verb ''resurrect'' was then back-formed hundreds of years later from it by removing the ''-ion'' suffix. This segmentation of ''resurrection'' into ''resurrect'' + ''ion'' was possible because English language, English had examples of Latin words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
