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Rankine Curve
A weighted catenary (also flattened catenary, was defined by William Rankine as transformed catenary and thus sometimes called Rankine curve) is a catenary curve, but of a special form: if a catenary is the curve formed by a chain under its own weight, a weighted catenary is the curve formed if the chain's weight is not consistent along its length. Formally, a "regular" catenary has the equation :y = a \, \cosh \left(\frac\right) = \frac for a given value of ''a''. A ''weighted catenary'' has the equation :y = b \, \cosh \left(\frac\right) = \frac and now ''two'' constants enter: ''a'' and ''b''. Significance A freestanding catenary arch has a uniform thickness. However, if # the arch is not of uniform thickness, # the arch supports more than its own weight,Re-review: Catenary and ParabolaRe-review: Catenary and Parabola accessdate: April 13, 2017 # or if gravity varies,MathOverflowclassical mechanics - Catenary curve under non-uniform gravitational field - MathOverflow a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Rankine
William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularly focusing on its First Law. He developed the Rankine scale, a Fahrenheit-based equivalent to the Celsius-based Kelvin scale of temperature. Rankine developed a complete theory of the steam engine and indeed of all heat engines. His manuals of engineering science and practice were used for many decades after their publication in the 1850s and 1860s. He published several hundred papers and notes on science and engineering topics, from 1840 onwards, and his interests were extremely varied, including, in his youth, botany, music theory and number theory, and, in his mature years, most major branches of science, mathematics and engineering. He was also a singer, pianist and cellist as well as a rifleman. Life Rankine was born in Edinburgh t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notices Of The American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine since January 1995 is available in its entirety on the journal web site. Articles are peer-reviewed by an editorial board of mathematical experts. Beginning with the January 2025 issue, the editor-in-chief is Mark C. Wilson, succeeding past editor Erica Flapan. The cover regularly features mathematical visualizations. The ''Notices'' is self-described to be the world's most widely read mathematical journal. As the membership journal of the American Mathematical Society, the ''Notices'' is sent to the approximately 30,000 AMS members worldwide, one-third of whom reside outside the United States. By publishing high-level exposition, the ''Notices'' provides opportunities for mathematicians to find out what is going on in the field. Each is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catenary
In physics and geometry, a catenary ( , ) is the curve that an idealized hanging chain or wire rope, cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, which it is not. The curve appears in the design of certain types of Catenary arch, arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings. The catenary is also called the alysoid, chainette,#MathWorld, MathWorld or, particularly in the materials sciences, an example of a funicular curve, funicular. Rope statics describes catenaries in a classic statics problem involving a hanging rope. Mathematically, the catenary curve is the Graph of a function, graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a minimal surface of revolution. A ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kette Kettenkurve Catenary 2008 PD
Kette is a town and commune in Cameroon. In 2019, a 160 kilometer road connecting Kette to Sembé was completed. The road costed 100 billion CFA franc, and the opening ceremony was attended by president Denis Sassou Nguesso. See also * Communes of Cameroon The Divisions of Cameroon are the third-level units of administration in Cameroon. They are organised by divisions and sub divisions of each province (now Regions). As of 2005 (and since 1996) there are 2 urban communities (Douala and Ya ... References Site de la primature – Élections municipales 2002 Contrôle de gestion et performance des services publics communaux des villes camerounaises Thèse de Donation Avele, Université Montesquieu Bordeaux IV * Charles Nanga, La réforme de l’administration territoriale au Cameroun à la lumière de la loi constitutionnelle n° 96/06 du 18 janvier 1996', Mémoire ENA. Populated places in East Region (Cameroon) Communes of Cameroon {{Cameroon-geo-stu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catenary Arch
A catenary arch is a type of architectural arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient times. It forms an underlying principle to the overall system of vaults and buttresses in stone vaulted Gothic cathedrals and in Renaissance domes. It is not a parabolic arch, although the non- circumferential curves used in arch designs (parabola, catenary, and weighted catenary) look similar, and match at shallow profiles, so a catenary is often misclassified as a parabola (per Galileo, "the angingchain fits its parabola almost perfectly"). In history The 17th-century scientist Robert Hooke wrote: "''Ut pendet continuum flexile, sic stabit contiguum rigidum inversum''", or, "As hangs a flexible cable so, inverted, stand the touching pieces of an arch." A note written by Thomas Jefferson in 1788 reads, "I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspect Ratio
The aspect ratio of a geometry, geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape format, landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal Fraction (mathematics), fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses The term is most commonly used with reference to: * Graphic / image ** Aspect ratio (image), Image aspect ratio ** Display aspect ratio ** Pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gateway Arch
The Gateway Arch is a monument in St. Louis, Missouri, United States. Clad in stainless steel and built in the form of a weighted catenary Catenary arch, arch, it is the world's tallest arch and List of tallest buildings in Missouri, Missouri's tallest accessible structure. Some sources consider it the tallest human-made monument in the Western Hemisphere. Built as a monument to the westward expansion of the United States and officially dedicated to "the American people", the Arch, commonly referred to as "The Gateway to the West", is a National Historic Landmark in Gateway Arch National Park and has become a popular tourist destination, as well as an internationally recognized symbol of St. Louis. The Arch was designed by the Finnish-American architect Eero Saarinen in 1947, and construction began on February 12, 1963, and was completed on October 28, 1965, at an overall cost of $13 million (equivalent to $ in ). The monument opened to the public on June 10, 1967. It is lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Missouri
Missouri (''see #Etymology and pronunciation, pronunciation'') is a U.S. state, state in the Midwestern United States, Midwestern region of the United States. Ranking List of U.S. states and territories by area, 21st in land area, it borders Iowa to the north, Illinois, Kentucky and Tennessee to the east, Arkansas to the south and Oklahoma, Kansas, and Nebraska to the west. In the south are the Ozarks, a forested highland, providing timber, minerals, and recreation. At 1.5 billion years old, the St. Francois Mountains are among the oldest in the world. The Missouri River, after which the state is named, flows through the center and into the Mississippi River, which makes up the eastern border. With over six million residents, it is the List of U.S. states and territories by population, 19th-most populous state of the country. The largest urban areas are St. Louis, Kansas City, Missouri, Kansas City, Springfield, Missouri, Springfield, and Columbia, Missouri, Columbia. The Cap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Suspension Bridge
A simple suspension bridge (also rope bridge, swing bridge (in New Zealand), suspended bridge, hanging bridge and catenary bridge) is a primitive type of bridge in which the deck of the bridge lies on two parallel load-bearing cables that are anchored at either end. They have no towers or piers. The cables follow a shallow downward catenary arc which moves in response to dynamic loads on the bridge deck. The arc of the deck and its large movement under load make such bridges unsuitable for vehicular traffic. Simple suspension bridges are restricted in their use to foot traffic. For safety, they are built with stout handrail cables, supported on short piers at each end, and running parallel to the load-bearing cables. Sometime these may be the primary load-bearing element, with the deck suspended below. Simple suspension bridges are considered the most efficient and sustainable design in rural regions, especially for river crossings that lie in non-floodplain topography such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
