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Carnot's Theorem (conics)
Carnot's theorem (named after Lazare Carnot) describes a relation between conic sections and triangle A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...s. In a triangle ABC with points C_A, C_B on the side AB, A_B, A_C on the side BC and B_C, B_A on the side AC those six points are located on a common conic section if and only if the following equation holds: : \frac\cdot \frac\cdot \frac\cdot \frac \cdot \frac\cdot \frac=1 . References *Huub P.M. van Kempen''On Some Theorems of Poncelet and Carnot'' Forum Geometricorum, Volume 6 (2006), pp. 229–234. *Lorenz Halbeisen, Norbert Hungerbühler, Juan Läuchli: ''Mit harmonischen Verhältnissen zu Kegelschnitten: Perlen der klassischen Geometrie''. Springer 2016, {{ISBN, 9783662530344, pp. 40, 168–173 (German) External links ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carnot Conic
Carnot may refer to: People * Carnot Posey (1818–1863), American lawyer and military officer People with the surname *Lazare Carnot (1753-1823), French mathematician and politician of the French Revolution *Louis Carnot (born 2001), French French footballer *Nicolas Léonard Sadi Carnot (1796-1832), French military scientist and physicist; son of Lazare Carnot * Hippolyte Carnot (1801-1888), French politician; son of Lazare Carnot * Marie François Sadi Carnot (1837-1894), French politician; President of France from 1887 to 1894 and son of Hippolyte Carnot *Marie-Adolphe Carnot (1839-1920), French mining engineer and chemist; son of Hippolyte Carnot *Paul Carnot (1869-1957), French physician; son of Marie-Adolphe Carnot * Stéphane Carnot (born 1972), former French footballer Places *Carnot, Central African Republic, a city * Carnot, Wisconsin, United States *Carnot-Moon, Pennsylvania, United States Other uses *Carnot cycle, in thermodynamics * Carnot heat engine, an idealise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lazare Carnot
Lazare Nicolas Marguerite, Count Carnot (; 13 May 1753 – 2 August 1823) was a French mathematician, physicist and politician. He was known as the "Organizer of Victory" in the French Revolutionary Wars and Napoleonic Wars. Education and early life Carnot was born on 13 May 1753 in the village of Nolay, in Burgundy, as the son of a local judge and royal notary, Claude Carnot and his wife, Marguerite Pothier. He was the second oldest of seven children. At the age of fourteen, Lazare and his brother were enrolled at the ''Collège d'Autun'', where he focused on the study of philosophy and the classics. He held a strong belief in stoic philosophy and was deeply influenced by Roman civilization. When he turned fifteen, he left school in Autun to strengthen his philosophical knowledge and study under the Society of the Priests of Saint Sulpice. During his short time with them, he studied logic, mathematics and theology under the Abbe Bison. After being impressed with Lazare's work a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Section
In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a ''focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''eccentricity''. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-Collinearity, collinear, determine a unique triangle and simultaneously, a unique Plane (mathematics), plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
