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Superformula
The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula, which expired effective 2020-05-10. In polar coordinates, with r the radius and \varphi the angle, the superformula is: :r\left(\varphi\right) = \left( \left, \frac \ ^ + \left, \frac \ ^ \right) ^. By choosing different values for the parameters a, b, m, n_1, n_2, and n_3, different shapes can be generated. The formula was obtained by generalizing the superellipse, named and popularized by Piet Hein, a Danish mathematician. 2D plots In the following examples the values shown above each figure should be ''m'', ''n''1, ''n''2 and ''n''3. A GNU Octave program for generating these figures f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superellipse
A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape. In the Cartesian coordinate system, the set of all points (x,y) on the curve satisfy the equation :\left, \frac\^n\!\! + \left, \frac\^n\! = 1, where n,a and b are positive numbers, and the vertical bars around a number indicate the absolute value of the number. Specific cases This formula defines a closed curve contained in the rectangle −''a'' ≤ ''x'' ≤ +''a'' and −''b'' ≤ ''y'' ≤ +''b''. The parameters ''a'' and ''b'' are called the ''semi-diameters'' of the curve. The overall shape of the curve is determined by the value of the exponent ''n'', as shown in the following table: If ''n'' 2, a hyperellipse. When ''n'' ≥ 1 and ''a'' = ''b'', the superellipse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Journal Of Botany
The ''American Journal of Botany'' is a monthly peer-reviewed scientific journal which covers all aspects of plant biology. It has been published by the Botanical Society of America since 1914. The journal has an impact factor of 3.038, as of 2019. As of 2018, access is available through the publisher John Wiley & Sons ( Wiley). From 1951 to 1953, Oswald Tippo served as its editor; the current editor is Pamela Diggle. History In the early 20th century, the field of botany was rapidly expanding, but the publications in which botanists could publish remained limited and heavily backlogged. By 1905, it was estimated that 250,000 contributions were generated in 8 or 9 languages. At the 1911 annual meeting of the society in Washington D.C., it was noted that at least 300 pages of American botanical contributions were sent abroad for publication, with a backlog resulting in a one-year delay in publication. On 31 December 1907, the Botanical Society of America met in Chicago and formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinates
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the ''pole'', and the ray from the pole in the reference direction is the ''polar axis''. The distance from the pole is called the ''radial coordinate'', ''radial distance'' or simply ''radius'', and the angle is called the ''angular coordinate'', ''polar angle'', or ''azimuth''. Angles in polar notation are generally expressed in either degrees or radians (2 rad being equal to 360°). Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th century. The initial motivation for the introduction of the polar system was the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piet Hein (scientist)
Piet Hein (16 December 1905 – 17 April 1996) was a Danish polymath (mathematician, inventor, designer, writer and poet), often writing under the Old Norse pseudonym Kumbel, meaning " tombstone". His short poems, known as '' gruks'' or grooks ( da, gruk), first started to appear in the daily newspaper ''Politiken'' shortly after the German occupation of Denmark in April 1940 under the pseudonym "Kumbel Kumbell". He also invented the Soma cube and the board game Hex. Biography Hein, a direct descendant of Piet Pieterszoon Hein, the 17th century Dutch naval hero, was born in Copenhagen, Denmark. He studied at the Institute for Theoretical Physics (later to become the Niels Bohr Institute) of the University of Copenhagen, and Technical University of Denmark. Yale awarded him an honorary doctorate in 1972. He died in his home on Funen, Denmark in 1996. Resistance Piet Hein, who, in his own words, "played mental ping-pong" with Niels Bohr in the inter-War period, found himself co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denmark
) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of Denmark , established_title = Consolidation , established_date = 8th century , established_title2 = Christianization , established_date2 = 965 , established_title3 = , established_date3 = 5 June 1849 , established_title4 = Faroese home rule , established_date4 = 24 March 1948 , established_title5 = EEC accession , established_date5 = 1 January 1973 , established_title6 = Greenlandic home rule , established_date6 = 1 May 1979 , official_languages = Danish , languages_type = Regional languages , languages_sub = yes , languages = GermanGerman is recognised as a protected minority language in the South Jutland area of Denmark. , demonym = , capital = Copenhagen , largest_city = capital , coordinates = , ethnic_groups = , ethnic_g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sf2d
SF may refer to: Locations * San Francisco, California, United States * Sidi Fredj, Algeria * South Florida, an urban region in the United States * Suomi Finland, former vehicular country code for Finland In arts and entertainment Genres * Speculative fiction (usually ''sf'') ** Science fiction or sci-fi (usually ''SF'') In film and television * , the Swedish film industry ** SF Film Finland, a Finnish film distributor * SF Channel (Australia) * , a German-language television network in Switzerland * , a Finnish film production company In music * Sforzando (musical direction) or sf, a musical accent * ''Subito forte'', a musical notation for dynamics (music) * Switchfoot, a band * Sasha Fierce, on-stage alter ego of American entertainer Beyoncé, and namesake of her album '' I Am... Sasha Fierce'' Other media * Saikoro Fiction, a Japanese role-playing game system * ''Street Fighter'', a series of fighting video games by Capcom Businesses and organizations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language. As part of the GNU Project, it is free software under the terms of the GNU General Public License. History The project was conceived around 1988. At first it was intended to be a companion to a chemical reactor design course. Full development was started by John W. Eaton in 1992. The first alpha release dates back to 4 January 1993 and on 17 February 1994 version 1.0 was released. Version 7.1.0 was released on Apr 6, 2022. The program is named after Octave Levenspiel, a former professor of the principal author. Levenspiel was known for his ability to perform quick back-of-the-envelope calculations. Development history Developments In additio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Product
In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids.Alan H. Barr (1992), ''Rigid Physically Based Superquadrics''. Chapter I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Surface
A parametric surface is a surface in the Euclidean space \R^3 which is defined by a parametric equation with two parameters Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence theorem, are frequently given in a parametric form. The curvature and arc length of curves on the surface, surface area, differential geometric invariants such as the first and second fundamental forms, Gaussian, mean, and principal curvatures can all be computed from a given parametrization. Examples * The simplest type of parametric surfaces is given by the graphs of functions of two variables: z = f(x,y), \quad \mathbf r(x,y) = (x, y, f(x,y)). * A rational surface is a surface that admits parameterizations by a rational function. A rational surface is an algebraic surface. Given an algebraic surface, it is commonly easier to decide if i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or ''parallels'', run east–west as circles parallel to the equator. Latitude and ''longitude'' are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, the term "latitude" normally refers to the ''geodetic latitude'' as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or ''normal'') to the ellipsoidal surface from the point, and the plane of the equator. Background Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over the ocea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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