|
Napoleon's Theorem
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle. The triangle thus formed is called the inner or outer ''Napoleon triangle''. The difference in the areas of the outer and inner Napoleon triangles equals the area of the original triangle. The theorem is often attributed to Napoleon Bonaparte (1769–1821). Some have suggested that it may date back to W. Rutherford's 1825 question published in ''The Ladies' Diary'', four years after the French emperor's death, but the result is covered in three questions set in an examination for a Gold Medal at the University of Dublin in October, 1820, whereas Napoleon died the following May. Proofs In the figure above, ABC is the original triangle. AZB, BXC, and CYA are equilateral triangles constructed on its sides' exteriors, and points L, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Napoleon's Theorem
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle. The triangle thus formed is called the inner or outer ''Napoleon triangle''. The difference in the areas of the outer and inner Napoleon triangles equals the area of the original triangle. The theorem is often attributed to Napoleon Bonaparte (1769–1821). Some have suggested that it may date back to W. Rutherford's 1825 question published in ''The Ladies' Diary'', four years after the French emperor's death, but the result is covered in three questions set in an examination for a Gold Medal at the University of Dublin in October, 1820, whereas Napoleon died the following May. Proofs In the figure above, ABC is the original triangle. AZB, BXC, and CYA are equilateral triangles constructed on its sides' exteriors, and points L, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Napoleon Barlotti
Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who rose to prominence during the French Revolution and led successful campaigns during the Revolutionary Wars. He was the ''de facto'' leader of the French Republic as First Consul from 1799 to 1804, then Emperor of the French from 1804 until 1814 and again in 1815. Napoleon's political and cultural legacy endures to this day, as a highly celebrated and controversial leader. He initiated many liberal reforms that have persisted in society, and is considered one of the greatest military commanders in history. His wars and campaigns are studied by militaries all over the world. Between three and six million civilians and soldiers perished in what became known as the Napoleonic Wars. Napoleon was born on the island of Corsica, not long after ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete & Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * ''Zentralblatt MATH'' * ''Science Citation Index'' * ''Current Contents''/Engineering, Computing and Technology Notable articles The articles by Gil Kalai with a proof of a subexponential upper bound on the diameter of a polyhedron and by Samuel Ferguson on the Kepler conjecture, both published in Discrete & Computational geometry, earned their author the Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e .... References External link ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral In Hexagon 1
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Principal properties Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that: *The area is A=\frac a^2, *The perimeter is p=3a\,\! *The radius of the circumscribed circle is R = \frac *The radius of the inscribed circle is r=\frac a or r=\frac *The geometric center of the triangle is the center of the circumscribed and inscribed circles *The altitude (height) from any side is h=\frac a Denoting the radius of the circumscribed circle as ''R'', we can determine using trigonometry that: *The area of the triangle is \mathrm=\fracR^2 Many of these quantities have simple re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Geometry
In classical 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 defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weitzenböck's Inequality
In mathematics, Weitzenböck's inequality, named after Roland Weitzenböck, states that for a triangle of side lengths a, b, c, and area \Delta, the following inequality holds: : a^2 + b^2 + c^2 \geq 4\sqrt\, \Delta. Equality occurs if and only if the triangle is equilateral. Pedoe's inequality is a generalization of Weitzenböck's inequality. The Hadwiger–Finsler inequality is a strengthened version of Weitzenböck's inequality. Geometric interpretation and proof Rewriting the inequality above allows for a more concrete geometric interpretation, which in turn provides an immediate proof. : \fraca^2 + \fracb^2 + \fracc^2 \geq 3\, \Delta. Now the summands on the left side are the areas of equilateral triangles erected over the sides of the original triangle and hence the inequation states that the sum of areas of the equilateral triangles is always greater than or equal to threefold the area of the original triangle. : \Delta_a + \Delta_b + \Delta_c \geq 3\, \Delta. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Kelland
Philip Kelland PRSE FRS (17 October 1808 – 8 May 1879) was an English mathematician. He was known mainly for his great influence on the development of education in Scotland. Life Kelland was born in 1808 the son of Philip Kelland (d.1847), curate in Dunster, Somerset, England. He was educated at Sherborne, and an undergraduate at Queens' College, Cambridge, where he was tutored privately by English mathematician William Hopkins and graduated in 1834 as senior wrangler and first Smith's prizeman. He was ordained in the Church of England. From 1834 to 1838, he was a fellow of Queens' College, Cambridge. Kelland was elected Fellow of the Royal Society in 1838 and Fellow of the Royal Society of Edinburgh in 1839. He served as Secretary of the RSE 1843-4, Vice-President 1857–77 and President 1878-9. He won their Keith Medal for the period 1849–51. He lived his final years at 20 Clarendon Crescent in western Edinburgh. Kelland is buried in Warriston Cemetery in the north of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Tait (physicist)
Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote with Lord Kelvin, and his early investigations into knot theory. His work on knot theory contributed to the eventual formation of topology as a mathematical discipline. His name is known in graph theory mainly for Tait's conjecture. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles. Early life Tait was born in Dalkeith on 28 April 1831 the only son of Mary Ronaldson and John Tait, secretary to the 5th Duke of Buccleuch. He was educated at Dalkeith Grammar School then Edinburgh Academy. He studied Mathematics and Physics at the University of Edinburgh, and then went to Peterhouse, Cambridge, graduating as senior wrangler and first Smith's prizeman in 1852. As a fellow and lecturer of his college he remain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centroid
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in ''n''-dimensional Euclidean space. In geometry, one often assumes uniform mass density, in which case the ''barycenter'' or ''center of mass'' coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin. In physics, if variations in gravity are considered, then a ''center of gravity'' can be defined as the weighted mean of all points weighted by their specific weight. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center. History The term "centroid" is of recent coinage (1814). It is used as a substitute for the older te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raymond Clare Archibald
Raymond Clare Archibald (7 October 1875 – 26 July 1955) was a prominent Canadian-American mathematician. He is known for his work as a historian of mathematics, his editorships of mathematical journals and his contributions to the teaching of mathematics. Biography Raymond Clare Archibald was born in South Branch, Stewiacke, Nova Scotia on 7 October 1875. He was the son of Abram Newcomb Archibald (1849–1883) and Mary Mellish Archibald (1849–1901). He was the fourth cousin twice removed of the famous Canadian-American astronomer and mathematician Simon Newcomb. Archibald graduated in 1894 from Mount Allison College with B.A. degree in mathematics and teacher's certificate in violin. After teaching mathematics and violin for a year at the Mount Allison Ladies' College he went to Harvard where he received a B.A. 1896 and a M.A. in 1897. He then traveled to Europe where he attended the Humboldt University of Berlin during 1898 and received a Ph.D. cum laude from the Univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Magazine
The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Oxford Dictionary of National Biography, Oxford University Press, Sept 2004; online edn, May 2006, accessed 17 Feb 2010 in 1822 Richard Taylor became joint editor and it has been published continuously by Taylor & Francis ever since. Early history The name of the journal dates from a period when "natural philosophy" embraced all aspects of science. The very first paper published in the journal carried the title "Account of Mr Cartwright's Patent Steam Engine". Other articles in the first volume include "Methods of discovering whether Wine has been adulterated with any Metals prejudicial to Health" and "Description of the Apparatus used by Lavoisier to produce Water from its component Parts, Oxygen and Hydrogen". 19th century Early in the nineteenth century, classic papers by Humphry Davy, M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
