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Gino Fano
Gino Fano (5 January 18718 November 1952) was an Italians, Italian mathematician, best known as the founder of finite geometry. He was born to a wealthy Jewish family in Mantua, in Italy and died in Verona, also in Italy. Fano made various contributions on projective geometry, projective and algebraic geometry. His work in the foundations of geometry predates the similar, but more popular, work of David Hilbert by about a decade. He was the father of physicist Ugo Fano and electrical engineer Robert Fano and uncle to physicist and mathematician Giulio Racah. Mathematical work Fano was an early writer in the area of finite projective spaces. In his article on proving the independence of his set of axioms for Projective space, projective ''n''-space, among other things, he considered the consequences of having a Projective harmonic conjugate, fourth harmonic point be equal to its conjugate. This leads to a configuration of seven points and seven lines contained in a PG(3,2), finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mantua
Mantua ( ; ; Lombard language, Lombard and ) is a ''comune'' (municipality) in the Italian region of Lombardy, and capital of the Province of Mantua, eponymous province. In 2016, Mantua was designated as the "Italian Capital of Culture". In 2017, it was named as the "European Capital of Gastronomy", included in the Eastern Lombardy District (together with the cities of Bergamo, Brescia, and Cremona). In 2008, Mantua's ''centro storico'' (old town) and the nearby of Sabbioneta were declared by UNESCO to be a World Heritage Site. Mantua's historic power and influence under the House of Gonzaga, Gonzaga family between 1328 and 1708 made it one of the main artistic, culture, cultural, and especially musical hubs of Northern Italy and of Italy as a whole. It had one of the most splendid courts of Europe of the fifteenth, sixteenth, and early seventeenth centuries. Mantua is noted for its significant role in the history of opera; the city is also known for its architectural treasur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of Phenomenon, phenomena, and usually frame their understanding in mathematical terms. They work across a wide range of Physics#Research fields, research fields, spanning all length scales: from atom, sub-atomic and particle physics, through biological physics, to physical cosmology, cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: Experimental physics, experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, and Theoretical physics, theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benito Mussolini
Benito Amilcare Andrea Mussolini (29 July 188328 April 1945) was an Italian politician and journalist who, upon assuming office as Prime Minister of Italy, Prime Minister, became the dictator of Fascist Italy from the March on Rome in 1922 until Fall of the Fascist regime in Italy, his overthrow in 1943. He was also of Italian fascism from the establishment of the Italian Fasces of Combat in 1919, until Death of Benito Mussolini, his summary execution in 1945. He founded and led the National Fascist Party (PNF). As a dictator and founder of fascism, Mussolini inspired the List of fascist movements, international spread of fascism during the interwar period. Mussolini was originally a socialist politician and journalist at the Avanti! (newspaper), ''Avanti!'' newspaper. In 1912, he became a member of the National Directorate of the Italian Socialist Party (PSI), but was expelled for advocating military intervention in World War I. In 1914, Mussolini founded a newspaper, ''Il P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian Racial Laws
The Italian racial laws, otherwise referred to as the Racial Laws (), were a series of laws promulgated by the government of Benito Mussolini in Fascist Italy from 1938 to 1944 in order to enforce racial discrimination and segregation in the Kingdom of Italy. The main victims of the Racial Laws were Italian Jews and the African inhabitants of the Italian Empire. In the aftermath of Mussolini's fall from power and the invasion of Italy by Nazi Germany, the Badoglio government suppressed the laws in January 1944. In northern Italy, they remained in force and were made more severe in the territories ruled by the Italian Social Republic until the end of the Second World War. History The first and most important of the Racial Laws (''Leggi Razziali'') was the Regio Decreto 17 Novembre 1938, Nr. 1728. It restricted the civil rights of Italian Jews, banned books written by Jewish authors, and excluded Jews from public offices and higher education. Additional laws stripped Jew ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Group
In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures together and consequently they are not independent from each other. Topological groups were studied extensively in the period of 1925 to 1940. Haar and Weil (respectively in 1933 and 1940) showed that the integrals and Fourier series are special cases of a construct that can be defined on a very wide class of topological groups. Topological groups, along with continuous group actions, are used to study continuous symmetries, which have many applications, for example, in physics. In functional analysis, every topological vector space is an additive topological group with the additional property that scalar multiplication is continuous; consequently, many results from the theory of topological groups can be applied to functional analy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synthetic Geometry
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulates, and at present called axioms. After the 17th-century introduction by René Descartes of the coordinate method, which was called analytic geometry, the term "synthetic geometry" was coined to refer to the older methods that were, before Descartes, the only known ones. According to Felix Klein Synthetic geometry is that which studies figures as such, without recourse to formulae, whereas analytic geometry consistently makes use of such formulae as can be written down after the adoption of an appropriate system of coordinates. The first systematic approach for synthetic geometry is Euclid's ''Elements''. However, it appeared at the end of the 19th century that Euclid's postulates were not sufficient for characterizing geometry. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, Aerospace engineering, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including Algebraic geometry, algebraic, Differential geometry, differential, Discrete geometry, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PG(3,2)
In finite geometry, PG(3, 2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane, ''PG(2, 2)''. Elements It has 15 points, 35 lines, and 15 planes. Each point is contained in 7 lines and 7 planes. Each line is contained in 3 planes and contains 3 points. Each plane contains 7 points and 7 lines. These can be summarized in a rank 3 configuration matrix counting points, lines, and planes on the diagonal. The incidences are expressed off diagonal. The structure is self dual, swapping points and planes, expressed by rotating the configuration matrix 180 degrees. :\left begin15&7&7\\3&35&3\\7&7&15\end\right /math> It has the following properties: * Each plane is isomorphic to the Fano plane. * Every pair of distinct planes intersects in a line. * A line and a plane not containing the line intersect in exactly one point. has 20160 automorphisms. The number of automorphisms is given by finding the number of ways of selecting 4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Harmonic Conjugate
In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction: :Given three collinear points , let be a point not lying on their join and let any line through meet at respectively. If and meet at , and meets at , then is called the harmonic conjugate of with respect to and . The point does not depend on what point is taken initially, nor upon what line through is used to find and . This fact follows from Desargues theorem. In real projective geometry, harmonic conjugacy can also be defined in terms of the cross-ratio as . Cross-ratio criterion The four points are sometimes called a harmonic range (on the real projective line) as it is found that always divides the segment ''internally'' in the same proportion as divides ''externally''. That is: \overline:\overline = \overline:\overline \, . If these segments are now endowed with the ordinary metri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
