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Giovanni Fagnano
Giovanni Francesco Fagnano dei Toschi (born 31 January 1715 in Senigallia, died 14 May 1797 in Senigallia) was an Italian churchman and mathematician, the son of Giulio Carlo de' Toschi di Fagnano, also a mathematician. Religious career Fagnano was ordained as a priest. In 1752 he became canon, and in 1755 he was appointed archdeacon of the cathedral of Senigallia. Mathematics Fagnano is known for Fagnano's problem, the problem of inscribing a minimum-perimeter triangle within an acute triangle. As Fagnano showed, the solution is the orthic triangle, whose vertices are the points where the altitudes of the original triangle cross its sides. Another property of the orthic triangle, also proven by Fagnano, is that its angle bisectors are the altitudes of the original triangle. Fagnano also partially solved the problem of finding the geometric median of sets of four points in the Euclidean plane; this is the point minimizing the sum of its distances to the four given points. As Fag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senigallia
Senigallia (or Sinigaglia in Old Italian, Romagnol: ''S’nigaja'') is a ''comune'' and port town on Italy's Adriatic coast. It is situated in the province of Ancona in the Marche region and lies approximately 30 kilometers north-west of the provincial capital city Ancona. Senigallia's small port is located at the mouth of the river Misa. It is one of the endpoints of the Massa-Senigallia Line, one of the most important dividing lines (isoglosses) in the classification of the Romance languages. History Senigallia was first settled in the 4th century BC by the gallic tribe of the Senones who first settled this coastal area. In 284 BC, the settlement was taken over by Romans, who established the colony ''Sena Gallica'' there''. "''Sena''"'' is probably a corrupted form of "Senones" and "Gallica''"'' (meaning "Gaulish") distinguished it from ''Saena'' (Siena) in Etruria. In the prelude to the Battle of the Metaurus between Romans and Carthaginians in 207 BC, ''Sena Gallica'' was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Plane
In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions of parallel lines, and also metrical notions of distance, circles, and angle measurement. The set \mathbb^2 of pairs of real numbers (the real coordinate plane) augmented by appropriate structure often serves as the canonical example. History Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other topics. Later, the plane was described in a so-called '' Cartesian coordinate system'', a coordinate system that specifies each point uniquely in a plane by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18th-century Italian Mathematicians
The 18th century lasted from January 1, 1701 ( MDCCI) to December 31, 1800 ( MDCCC). During the 18th century, elements of Enlightenment thinking culminated in the American, French, and Haitian Revolutions. During the century, slave trading and human trafficking expanded across the shores of the Atlantic, while declining in Russia, China, and Korea. Revolutions began to challenge the legitimacy of monarchical and aristocratic power structures, including the structures and beliefs that supported slavery. The Industrial Revolution began during mid-century, leading to radical changes in human society and the environment. Western historians have occasionally defined the 18th century otherwise for the purposes of their work. For example, the "short" 18th century may be defined as 1715–1789, denoting the period of time between the death of Louis XIV of France and the start of the French Revolution, with an emphasis on directly interconnected events. To historians who expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian Mathematicians
Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Italian, regional variants of the Italian language ** Languages of Italy, languages and dialects spoken in Italy ** Italian culture, cultural features of Italy ** Italian cuisine, traditional foods ** Folklore of Italy, the folklore and urban legends of Italy ** Mythology of Italy, traditional religion and beliefs Other uses * Italian dressing, a vinaigrette-type salad dressing or marinade * Italian or Italian-A, alternative names for the Ping-Pong virus, an extinct computer virus See also * * * Italia (other) * Italic (other) * Italo (other) * The Italian (other) * Italian people (other) Italian people may refer to: * in terms of ethnicity: all ethnic Italians, in and outside of Italy * in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1797 Deaths
Events January–March * January 3 – The Treaty of Tripoli, a peace treaty between the United States and Ottoman Tripolitania, is signed at Algiers (''see also'' 1796). * January 7 – The parliament of the Cisalpine Republic adopts the Italian green-white-red tricolour as the official flag (this is considered the birth of the flag of Italy). * January 13 – Action of 13 January 1797, part of the War of the First Coalition: Two British Royal Navy frigates, HMS ''Indefatigable'' and HMS ''Amazon'', drive the French 74-gun ship of the line '' Droits de l'Homme'' aground on the coast of Brittany, with over 900 deaths. * January 14 – War of the First Coalition – Battle of Rivoli: French forces under General Napoleon Bonaparte defeat an Austrian army of 28,000 men, under ''Feldzeugmeister'' József Alvinczi, near Rivoli (modern-day Italy), ending Austria's fourth and final attempt to relieve the fortress city of Mantua. * January 26 & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1715 Births
Events For dates within Great Britain and the British Empire, as well as in the Russian Empire, the "old style" Julian calendar was used in 1715, and can be converted to the "new style" Gregorian calendar (adopted in the British Empire in 1752 and in Russia in 1923) by adding 11 days. January–March * January 13 – A fire in London, described by some as the worst since the Great Fire of London (1666) almost 50 years earlier, starts on Thames Street when fireworks prematurely explode "in the house of Mr. Walker, an oil man"; more than 100 houses are consumed in the blaze, which continues over to Tower Street before it is controlled. * January 22 – Voting begins for the British House of Commons and continues for the next 46 days in different constituencies on different days. * February 11 – Tuscarora War: The Tuscarora and their allies sign a peace treaty with the Province of North Carolina, and agree to move to a reservation near Lake Mattamusk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radon Point
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of ''d'' + 2 points in R''d'' can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex hulls is called a Radon point of the set. For example, in the case ''d'' = 2, any set of four points in the Euclidean plane can be partitioned in one of two ways. It may form a triple and a singleton, where the convex hull of the triple (a triangle) contains the singleton; alternatively, it may form two pairs of points that form the endpoints of two intersecting line segments. Proof and construction Consider any set X=\\subset \mathbf^d of ''d'' + 2 points in ''d''-dimensional space. Then there exists a set of multipliers ''a''1, ..., ''a''''d'' + 2, not all of which are zero, solving the system of linear equations : \sum_^ a_i x_i=0,\quad \sum_^ a_i=0, because there are ''d'' + 2 unknow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, derived from greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A, B, C and D is sometimes denoted as \square ABCD. Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ''ABCD'' add up to 360 degrees of arc, that is :\angle A+\angle B+\angle C+\angle D=360^. This is a special case of the ''n''-gon interior angle sum formula: ''S'' = (''n'' − 2) × 180°. All non-self-crossing quadrilaterals tile the plane, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve. The intersection of all the convex sets that contain a given subset of Euclidean space is called the convex hull of . It is the smallest convex set containing . A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Median
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the ''L''1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation. The special case of the problem for three points in the plane (that is, = 3 and = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giulio Carlo De' Toschi Di Fagnano
Giulio Carlo, Count Fagnano, Marquis de Toschi (26 September 1682 — 18 May 1766) was an Italian mathematician. He was probably the first to direct attention to the theory of elliptic integrals. Fagnano was born in Senigallia (at the time spelled "Sinigaglia"), and also died there. Life Giulio Fagnano was born to Francesco Fagnano and Camilla Bartolini in Senigallia (at the time spelled "Sinigaglia") in 1682. Fagnano had twelve children. One, Giovanni Fagnano, was also well-known as a mathematician. Another of Fagnano's children became a Benedictine nun. In 1721, Fagnano was made a count by Louis XV; in 1723, he was appointed ''gonfaloniere'' of Senigallia and elected to the Royal Society of London; in 1745 he was made a marquis of Sant' Onofrio. Mathematical work Fagnano made his higher studies at the Collegio Clementino in Rome, and there won great distinction — except in mathematics, to which his aversion was extreme. Only after his college course did he take up the stu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Bisector
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a ''bisector''. The most often considered types of bisectors are the ''segment bisector'' (a line that passes through the midpoint of a given segment) and the ''angle bisector'' (a line that passes through the apex of an angle, that divides it into two equal angles). In three-dimensional space, bisection is usually done by a plane, also called the ''bisector'' or ''bisecting plane''. Perpendicular line segment bisector Definition *The perpendicular bisector of a line segment is a line, which meets the segment at its midpoint perpendicularly. The Horizontal intersector of a segment AB also has the property that each of its points X is equidistant from the segment's endpoints: (D)\quad , XA, = , XB, . The proof follows from and Pythagoras' theorem: :, XA, ^2=, XM, ^2+, MA, ^2=, XM, ^2+, MB, ^2=, XB, ^2 \; . Property (D) is usually used for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
