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75 (number)
75 (seventy-five) is the natural number following 74 and preceding 76. __TOC__ In mathematics 75 is a self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number. It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75... 75 is the count of the number of weak orderings on a set of four items. Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra. In other fields Seventy-five is: *The atomic number of rhenium *The age limit for Canadian senators [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal numbers'', and numbers used for ordering are called '' ordinal numbers''. Natural numbers are sometimes used as labels, known as '' nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
46 (number)
46 (forty-six) is the natural number following 45 and preceding 47. In mathematics Forty-six is * a Wedderburn-Etherington number, * an enneagonal number * a centered triangular number. * the number of parallelogram polyominoes with 6 cells. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that cannot be expressed as a sum of two abundant numbers. It is also the sixteenth semiprime. Since it is possible to find sequences of 46+1 consecutive integers such that each inner member shares a factor with either the first or the last member, 46 is an Erdős–Woods number. In science * The atomic number of palladium. * The number of human chromosomes. * The approximate molar mass of ethanol (46.07 g mol) Astronomy * Messier object M46, a magnitude 6.5 open cluster in the constellation Puppis. * The New General Cataloguebr>objectNGC 46, a star in the constellation Pisces. In music * Japanese idol group franchis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, fashion, gastronomy, and science. For its leading role in the arts and sciences, as well as its very early system of street lighting, in the 19th century it became known as "the City of Light". Like London, prior to the Second World War, it was also sometimes called the capital of the world. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an estimated population of 12,262,544 in 2019, or about 19% of the population of France, making the region France's primate city. The Paris Region had a GDP of €739 billion ($743 billion) in 2019, which is the highest in Europe. According to the Economis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Departments Of France
In the administrative divisions of France, the department (french: département, ) is one of the three levels of government under the national level (" territorial collectivities"), between the administrative regions and the communes. Ninety-six departments are in metropolitan France, and five are overseas departments, which are also classified as overseas regions. Departments are further subdivided into 332 arrondissements, and these are divided into cantons. The last two levels of government have no autonomy; they are the basis of local organisation of police, fire departments and, sometimes, administration of elections. Each department is administered by an elected body called a departmental council ( ing. lur.. From 1800 to April 2015, these were called general councils ( ing. lur.. Each council has a president. Their main areas of responsibility include the management of a number of social and welfare allowances, of junior high school () buildings and technical st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canon De 75 Modèle 1897
The French 75 mm field gun was a quick-firing field artillery piece adopted in March 1898. Its official French designation was: Matériel de 75mm Mle 1897. It was commonly known as the French 75, simply the 75 and Soixante-Quinze (French for "seventy-five"). The French 75 was designed as an anti-personnel weapon system for delivering large volumes of time-fused shrapnel shells on enemy troops advancing in the open. After 1915 and the onset of trench warfare, other types of battlefield use demanding impact-detonated high-explosive shells prevailed. By 1918 the 75s became the main agents of delivery for toxic gas shells. The 75s also became widely used as truck mounted anti-aircraft artillery. They were the main armament of the Saint-Chamond tank in 1918. When World War II broke out the French were still using the “75” against lightly armored tanks like the Panzer III and IV. The French 75 is widely regarded as the first modern artillery piece.Priscilla Mary Roberts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senate Of Canada
The Senate of Canada (french: region=CA, Sénat du Canada) is the upper house of the Parliament of Canada. Together with the Crown and the House of Commons, they comprise the bicameral legislature of Canada. The Senate is modelled after the British House of Lords with members appointed by the governor general on the advice of the prime minister. The explicit basis on which appointment is made and the chamber's size is set, at 105 members, is by province or territory assigned to 'divisions'. The Constitution divides provinces of Canada geographically among four regions, which are represented equally. Senatorial appointments were originally for life; since 1965, they have been subject to a mandatory retirement age of 75. While the Senate is the upper house of parliament and the House of Commons is the lower house, this does not imply the former is more powerful than the latter. It merely entails that its members and officers outrank the members and officers of the Commons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhenium
Rhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-gray, heavy, third-row transition metal in group 7 of the periodic table. With an estimated average concentration of 1 part per billion (ppb), rhenium is one of the rarest elements in the Earth's crust. Rhenium has the third-highest melting point and highest boiling point of any stable element at 5869 K. Rhenium resembles manganese and technetium chemically and is mainly obtained as a by-product of the extraction and refinement of molybdenum and copper ores. Rhenium shows in its compounds a wide variety of oxidation states ranging from −1 to +7. Discovered by Walter Noddack, Ida Tacke and Otto Berg in 1925, rhenium was the last stable element to be discovered. It was named after the river Rhine in Europe, from which the earliest samples had been obtained and worked commercially. Nickel-based superalloys of rhenium are used in combustion chambers, turbine blades, and exhaust nozzle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Polyhedron Compound
In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e. the symmetry group of the compound acts transitively on the compound's vertices. The uniform polyhedron compounds were first enumerated by John Skilling in 1976, with a proof that the enumeration is complete. The following table lists them according to his numbering. The prismatic compounds of prisms ( UC20 and UC21) exist only when , and when and are coprime. The prismatic compounds of antiprisms ( UC22, UC23, UC24 and UC25) exist only when , and when and are coprime. Furthermore, when , the antiprisms degenerate into tetrahedra with digon In geometry, a digon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antiprism
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are triangles, rather than quadrilaterals. The dual polyhedron of an -gonal antiprism is an -gonal trapezohedron. History At the intersection of modern-day graph theory and coding theory, the triangulation of a set of points have interested mathematicians since Isaac Newton, who fruitlessly sought a mathematical proof of the kissing number problem in 1694. The existence of antiprisms was discussed, and their name was coined by Johannes Kepler, though it is possible that they were previously known to Archimedes, as they satisfy the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prism (geometry)
In geometry, a prism is a polyhedron comprising an polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. Like many basic geometric terms, the word ''prism'' () was first used in Euclid's Elements. Euclid defined the term in Book XI as “a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms”. However, this definition has been criticized for not being specific enough in relation to the nature of the bases, which caused confusion among later geometry writers. Oblique prism An oblique prism is a prism in which the joining edges and faces are ''not perpendicular'' to the base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Polyhedron
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: *Polyhedra which self-intersect in a repetitive way. *Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way. Mathematically these figures are examples of star domains. Mathematical studies of star polyhedra are usually concerned with regular, uniform polyhedra, or the duals of the uniform polyhedra. All these stars are of the self-intersecting kind. Self-intersecting star polyhedra Regular star polyhedra The regular star polyhedra are self-intersecting polyhedra. They may either have self-intersecting faces, or self-intersecting vertex figures. There are four regular star polyhedra, known as the Kepler–Poinsot polyhedra. The Schläfli symbol implies faces with ''p'' sides, and vertex figures with ''q'' sides. Two of them have pen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Polyhedra
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent. Uniform polyhedra may be regular (if also face- and edge-transitive), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular (if neither edge- nor face-transitive). The faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra. There are two infinite classes of uniform polyhedra, together with 75 other polyhedra: *Infinite classes: **prisms, **antiprisms. * Convex exceptional: ** 5 Platonic solids: regular convex polyhedra, ** 13 Archimedean solids: 2 quasiregular and 11 semiregular convex polyhedra. * Star (nonconvex) exceptional: ** 4 Kepler–Poinsot polyhedra: regular nonconvex polyhedra, ** 53 uniform star polyhedra: 14 quasiregular and 39 semiregular. Hence 5 + 13 + 4 + 53 = 75. There are also many degen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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