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Axial Symmetry
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. glossary of meteorology. Retrieved 2010-04-08. For example, a without trademark or other design, or a plain white tea saucer, looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially symmetric. Axial symmetry can also be |
Surface Of Revolution Illustration
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth". The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called ''surface'', sometimes with some qualifier, such as algebraic surface, smooth surface or fractal surface. The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagonal Prism
In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices. As a semiregular (or uniform) polyhedron If faces are all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a '' truncated pentagonal hosohedron'', represented by Schläfli symbol t. Alternately it can be seen as the Cartesian product of a regular pentagon and a line segment, and represented by the product ×. The dual of a pentagonal prism is a pentagonal bipyramid. The symmetry group of a right pentagonal prism is ''D5h'' of order 20. The rotation group is ''D5'' of order 10. Volume The volume, as for all prisms, is the product of the area of the pentagonal base times the height or distance along any edge perpendicular to the base. For a uniform pentagonal pris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Meteorological Society
The American Meteorological Society (AMS) is the premier scientific and professional organization in the United States promoting and disseminating information about the Atmospheric sciences, atmospheric, Oceanography, oceanic, and Hydrology, hydrologic sciences. Its mission is to advance the atmospheric and related sciences, technologies, applications, and services for the benefit of society. Background Founded on December 29, 1919, by Charles Franklin Brooks at a meeting of the American Association for the Advancement of Science in St. Louis and incorporated on January 21, 1920, the American Meteorological Society has a membership of more than 13,000 weather, water, and climate scientists, professionals, researchers, educators, students, and enthusiasts. AMS offers numerous programs and services in the sphere of water, weather and climate sciences. It publishes eleven atmospheric and related oceanic and hydrologic journals (in print and online), sponsors as many as twelve conf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baseball Bat
A baseball bat is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher. By regulation it may be no more than in diameter at the thickest part and no more than in length. Although historically bats approaching were swung, today bats of are common, topping out at to . Terminology A baseball bat is divided into several regions. The "barrel" is the thick part of the bat, where it is meant to hit the ball. The part of the barrel best for hitting the ball, according to construction and swinging style, is often called the " sweet spot." The end of the barrel is called the "top," "end," or "cap" of the bat. Opposite the cap, the barrel narrows until it meets the "handle," which is comparatively thin, so that batters can comfortably grip the bat in their hands. Sometimes, especially on metal bats, the handle is wrapped with a rubber or tape "grip". Finally, below the handle is the "knob" of the bat, a wider piece that keeps t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saucer
A saucer is a type of small dishware. While in the Middle Ages a saucer was used for serving condiments and sauces, currently the term is used to denote a small plate or shallow bowl that supports a cup – usually one used to serve coffee or tea. Overview The center of the saucer often contains a depression or raised ring sized to fit a matching cup; this was only introduced in the mid 18th century. The saucer is useful for protecting surfaces from possible damage due to the heat of a cup, and to catch overflow, splashes, and drips from the cup, thus protecting both table linen and the user sitting in a free-standing chair who holds both cup and saucer. The saucer also provides a convenient place for a wet spoon, as might be used to stir the drink in the cup in order to mix sweeteners or creamers into tea or coffee. Some people pour the hot tea or coffee from the cup into the saucer; the increased surface area of the liquid exposed to the air increases the rate at which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Symmetry
In mathematics and geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called ''reflections'' or ''interchanges''. In mathematics and theoretical physics, a discrete symmetry is a symmetry under the transformations of a discrete group—e.g. a topological group with a discrete topology whose elements form a finite or a countable set. One of the most prominent discrete symmetries in physics is parity symmetry. It manifests itself in various elementary physical quantum systems, such as quantum harmonic oscillator, electron orbitals of Hydrogen-like atoms by forcing wavefunctions to be even or odd. This in turn gives rise to selection rules that determine which transition lines are visible in atomic ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiality (geometry)
In the geometry of the Euclidean plane, axiality is a measure of how much axial symmetry a shape has. It is defined as the ratio of areas of the largest axially symmetric subset of the shape to the whole shape. Equivalently it is the largest fraction of the area of the shape that can be covered by a mirror reflection of the shape (with any orientation). A shape that is itself axially symmetric, such as an isosceles triangle, will have an axiality of exactly one, whereas an asymmetric shape, such as a scalene triangle, will have axiality less than one. Upper and lower bounds showed that every convex set has axiality at least 2/3.. Erratum, . This result improved a previous lower bound of 5/8 by . The best upper bound known is given by a particular convex quadrilateral, found through a computer search, whose axiality is less than 0.816. For triangles and for centrally symmetric convex bodies, the axiality is always somewhat higher: every triangle, and every centrally symmetric conve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Symmetry
In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1). Reflective circular symmetry is isomorphic with the orthogonal group O(2). Two dimensions A 2-dimensional object with circular symmetry would consist of concentric circles and annular domains. Rotational circular symmetry has all cyclic symmetry, Z''n'' as subgroup symmetries. Reflective circular symmetry has all dihedral symmetry, Dih''n'' as subgroup symmetries. Three dimensions In 3-dimensions, a surface or solid of revolution has circular symmetry around an axis, also called cylindrical symmetry or axial symmetry. An example is a right circular cone. Circular symmetry in 3 dimensions has all pyramidal symmetry, C''n''v as subgroups. A double-cone, bicone, cylinder, toro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection Symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical. Symmetric function In formal terms, a mathematical object is symmetric with respect to a given operation such as reflection, rotation or translation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa). The symm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in ''m''-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of ''E''+(''m'') (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Symmetry
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion. It is negative (“left-handed”) if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: “left” is negative, “right” is positive. The chirality ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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