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Symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" 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 spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymmetry
Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. The absence of or violation of symmetry that are either expected or desired can have important consequences for a system. In organisms Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension. Louis Pasteur proposed that biological molecules are asymmetric because the cosmic .e. physicalforces that preside over their formation are themselves asymmetric. While at his time, and even now, the symmetry of physical processes are highlighted, it is known that there are fundamental physical asymmetries, starting with time. Asymmetry in biology Asymmetry is an important and widespread ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and "rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is an isometry. As a function If \mathbf is a fixed vector, known as the ''translation vector'', and \mathbf is the initial position of some object, then the translation function T_ will work as T_(\mathbf)=\mathbf+\mathbf. If T is a translation, then the image of a subset A under the function T is the translate of A by T . The translate of A by T_ is often written A+\mathbf . Horizontal and vertical translations In geometry, a vertical translation (also known as vertical shift) is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system. Often, vertical translations a ... [...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 geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation (mathematics)
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire -dimensional flat of fixed points in a -dimensional space. Mathematically, a rotation is a map. All rotations about a fixed point form a group under composition called the rotation group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation which if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection (mathematics)
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis would look like q. Its image by reflection in a horizontal axis would look like b. A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state. The term ''reflection'' is sometimes used for a larger class of mappings from a Euclidean space to itself, namely the non-identity isometries that are involutions. Such isometries have a set of fixed points (the "mirror") that is an affine subspace, but is possibly smaller than a hy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymmetric (PSF)
Asymmetric may refer to: * Asymmetry in geometry, chemistry, and physics Computing *Asymmetric cryptography, in public-key cryptography * Asymmetric digital subscriber line, Internet connectivity *Asymmetric multiprocessing, in computer architecture Other *Asymmetric relation, in set theory * Asymmetric synthesis, in organic synthesis *Asymmetric warfare, in modern war *Asymmetric Publications, a video game company * ''Asymmetry'' (Mallory Knox album), 2014 * ''Asymmetry'' (Karnivool album) *Asymmetry (population ethics) *Asymmetry (novel) ''Asymmetry'' is the first novel by American author Lisa Halliday, published in February 2018 by Simon & Schuster. The novel has received critical acclaim with ''The New Yorker'' calling it "a literary phenomenon" and ''The New York Times'' incl ..., a 2018 novel by Lisa Halliday See also * * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect of all human societies, a cultural universal. While scholars agree that music is defined by a few specific elements, there is no consensus on their precise definitions. The creation of music is commonly divided into musical composition, musical improvisation, and musical performance, though the topic itself extends into academic disciplines, criticism, philosophy, and psychology. Music may be performed or improvised using a vast range of instruments, including the human voice. In some musical contexts, a performance or composition may be to some extent improvised. For instance, in Hindustani classical music, the performer plays spontaneously while following a partially defined structure and using characteristic motifs. In modal jazz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quilt
A quilt is a multi-layered textile, traditionally composed of two or more layers of fabric or fiber. Commonly three layers are used with a filler material. These layers traditionally include a woven cloth top, a layer of batting or wadding, and a woven back combined using the techniques of quilting. This is the process of sewing on the face of the fabric, and not just the edges, to combine the three layers together to reinforce the material. Stitching patterns can be a decorative element. A single piece of fabric can be used for the top of a quilt (a "whole-cloth quilt"), but in many cases the top is created from smaller fabric pieces joined, or patchwork. The pattern and color of these pieces creates the design. Quilts may contain valuable historical information about their creators, "visualizing particular segments of history in tangible, textured ways." In the twenty-first century, quilts are frequently displayed as non-utilitarian works of art but historically quilts were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and ''molecule'' is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.g. water (two hydrogen atoms and one oxygen atom; H2O). In the kinetic theory of gases, the term ''molecule'' is often used for any gaseous particle regardless of its composition. This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are typically not consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pamment
Tiles are usually thin, square or rectangular coverings manufactured from hard-wearing material such as ceramic, stone, metal, baked clay, or even glass. They are generally fixed in place in an array to cover roofs, floors, walls, edges, or other objects such as tabletops. Alternatively, tile can sometimes refer to similar units made from lightweight materials such as perlite, wood, and mineral wool, typically used for wall and ceiling applications. In another sense, a tile is a construction tile or similar object, such as rectangular counters used in playing games (see tile-based game). The word is derived from the French word ''tuile'', which is, in turn, from the Latin word ''tegula'', meaning a roof tile composed of fired clay. Tiles are often used to form wall and floor coverings, and can range from simple square tiles to complex or mosaics. Tiles are most often made of ceramic, typically glazed for internal uses and unglazed for roofing, but other materials are also c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Model
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject. Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. The following was said by John von Neumann. There is also an increasing attention to scientific modelling in fields such as science education, philosophy of science, sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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