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Chiral Differential Operator
Chirality () is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from its mirror image; that is, it cannot be superposed (not to be confused with superimposed) onto it. Conversely, a mirror image of an ''achiral'' object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called ''enantiomorphs'' (Greek, "opposite forms") or, when referring to molecules, ''enantiomers''. A non-chiral object is called ''achiral'' (sometimes also ''amphichiral'') and can be superposed on its mirror image. The term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894: Human hands are perhaps the most recognized example of chirality. The left hand is a non-superposable mirror im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirality With Hands
Chirality () is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek language, Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from its mirror image; that is, it cannot be wikt:superpose, superposed (not to be confused with wikt:superimpose, superimposed) onto it. Conversely, a mirror image of an ''achiral'' object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called ''enantiomorphs'' (Greek, "opposite forms") or, when referring to molecules, ''enantiomers''. A non-chiral object is called ''achiral'' (sometimes also ''amphichiral'') and can be superposed on its mirror image. The term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894: Human hands are perhaps the most recognized example of chirality ... [...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 geometry, distance in a given direction (geometry), direction. A translation can also be interpreted as the addition of a constant vector space, vector to every point, or as shifting the Origin (mathematics), 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 (mathematics), image of a subset A under the function (mathematics), function T is the translate of A by T . The translate of A by T_ is often written as A+\mathbf . Application in classical physics In classical physics, translational motion is movement that changes the Position (geometry), positio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot (mathematics)
In mathematics, a knot is an embedding of the circle () into three-dimensional Euclidean space, (also known as ). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term ''knot'' is also applied to embeddings of in , especially in the case . The branch of mathematics that studies knots is known as knot theory and has many relations to graph theory. Formal definition A knot is an embedding of the circle () into three-dimensional Euclidean space (), or the 3-sphere (), since the 3-sphere is compact. Two knots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figure-eight Knot (mathematics)
In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number (knot theory), crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot. Origin of name The name is given because tying a normal figure-eight knot in a rope and then joining the ends together, in the most natural way, gives a model of the mathematical knot. Description A simple parametric representation of the figure-eight knot is as the set of all points (''x'',''y'',''z'') where : \begin x & = \left(2 + \cos \right) \cos \\ y & = \left(2 + \cos \right) \sin \\ z & = \sin \end for ''t'' varying over the real numbers (see 2D visual realization at bottom right). The figure-eight knot is Prime knot, prime, alternating knot, alternating, rational knot, rational with an associated value of 5/3, and is Chiral kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Groups
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension ''d'' is then a subgroup of the orthogonal group O(''d''). Point groups are used to describe the symmetries of geometric figures and physical objects such as molecules. Each point group can be represented as sets of orthogonal matrices ''M'' that transform point ''x'' into point ''y'' according to . Each element of a point group is either a rotation (determinant of ), or it is a reflection or improper rotation (determinant of ). The geometric symmetries of crystals are described by space groups, which allow translations and contain point groups as subgroups. Discrete point groups in more than one dimension come in infinite families, but from the crystallographic restriction theorem and one of Bieberbach's theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Of Symmetry
Plane most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface * Plane (mathematics), generalizations of a geometrical plane Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes'' (genus), marsh crabs in Grapsidae * '' Bindahara phocides'', the plane butterfly of Asia Maritime transport * Planing (boat), where weight is predominantly supported by hydrodynamic lift * ''Plane'' (wherry), a Norfolk canal boat, in use 1931–1949 Music *"Planes", a 1976 song by Colin Blunstone *"Planes (Experimental Aircraft)", a 1989 song by Jefferson Airplane from ''Jefferson Airplane'' *" Planez", originally "Planes", a 2015 song by Jeremih *"The Plane", a 1987 song on the '' Empire of the Sun'' soundtrack *"The Plane", a 1997 song by Kinito Méndez Other entertainment * Plane (''Dungeons & Dragons''), any fictional realm of the D&D roleplaying game's multiverse * ''Pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axis Of Symmetry
An axis (: axes) may refer to: Mathematics *A specific line (often a directed line) that plays an important role in some contexts. In particular: ** Coordinate axis of a coordinate system *** ''x''-axis, ''y''-axis, ''z''-axis, common names for the coordinate axes of a Cartesian coordinate system ** Axis of rotation ** Axis of symmetry ** Axis of a conic section Politics *Axis powers of World War II, 1936–1945. * Axis of evil (first used in 2002), U.S. President George W. Bush's description of Iran, Iraq, and North Korea *Axis of Resistance (first used in 2002), the Shia alliance of Iran, Syria, and Hezbollah * Axis of Upheaval (first used in 2024), foreign policy neologism of the Anti-western collaboration between Russia, China, Iran, and North Korea * Jakarta-Pyongyang-Peking Axis, diplomatic alignment and alliance between Indonesia, China, and North Korea during Sukarno's Presidency *Political spectrum, sometimes called an axis Science *Axis (anatomy), the second cerv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object ''X'' is ''G'' = Sym(''X''). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. Introduction We consider the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a wallpaper pattern. For symmetry of physical objects, one may also take their physical composition as part of the pattern. (A pattern may be specified formally as a scalar field, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a Convention (norm), convention and a mnemonic, utilized to define the orientation (vector space), orientation of Cartesian coordinate system, axes in three-dimensional space and to determine the direction of the cross product of two Euclidean vector, vectors, as well as to establish the direction of the force on a Electric current, current-carrying conductor in a magnetic field. The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either right thumb or left thumb. History The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways. Therefore, a fundamental p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetris
''Tetris'' () is a puzzle video game created in 1985 by Alexey Pajitnov, a Soviet software engineer. In ''Tetris'', falling tetromino shapes must be neatly sorted into a pile; once a horizontal line of the game board is filled in, it disappears, granting points and preventing the pile from overflowing. Over 200 versions of ''Tetris'' have been published by numerous companies on more than 65 platforms, often with altered game mechanics, some of which have become standard over time. To date, these versions of ''Tetris'' collectively serve as the second-best-selling video game series with over 520 million sales, mostly on mobile devices. In the 1980s, Pajitnov worked for the Computing Center of the Academy of Sciences, where he programmed ''Tetris'' on the Elektronika 60 and adapted it to the IBM PC with the help of Dmitry Pavlovsky and Vadim Gerasimov. Floppy disk copies were distributed freely throughout Moscow, before spreading to Eastern Europe. Robert Stein of Andro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
