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Paradox Of Loyd And Schlömilch
The chessboard paradoxGreg N. Frederickson: ''Dissections: Plane and Fancy''. Cambridge University Press, 2003, , chapter 23, pp. 268–277 in particular pp. 271–274 Colin Foster: "Slippery Slopes". In: ''Mathematics in School'', vol. 34, no. 3 (May, 2005), pp. 33–34JSTOR or paradox of Loyd and SchlömilchFranz Lemmermeyer: ''Mathematik à la Carte: Elementargeometrie an Quadratwurzeln mit einigen geschichtlichen Bemerkungen''. Springer 2014, , pp95–96(German) is a falsidical paradox based on an optical illusion. A chessboard or a square with a side length of 8 units is cut into four pieces. Those four pieces are used to form a rectangle with side lengths of 13 and 5 units. Hence the combined area of all four pieces is 64 area units in the square but 65 area units in the rectangle, this seeming contradiction is due an optical illusion as the four pieces don't fit exactly in the rectangle, but leave a small barely visible gap around the rectangle's diagonal. The paradox is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albrecht Beutelspacher
Albrecht Beutelspacher (born 5 June 1950) is a German mathematician and founder of the Mathematikum. He is a professor emeritus of the University of Giessen, where he held the chair for geometry and discrete mathematics from 1988 to 2018. Biography Beutelspacher studied 1969-1973 math, physics and philosophy at the University of Tübingen and received his PhD 1976 from the University of Mainz. His PhD advisor was Judita Cofman. From 1982-1985 he was an associate professor at the University of Mainz and from 1985-1988 he worked for a research department of the Siemens. From 1988 to 2018 he was a tenured professor for geometry and discrete mathematics at the University of Giessen. He became a well-known popularizer of mathematics in Germany by authoring several books in the field of popular science and recreational math and by founding Germany's first math museum, the Mathematikum. He received several awards for his contributions to popularizing mathematics. He has a math column ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recreational Mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics. Topics Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Paradoxes
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. In the Canadian curriculum, there are six basic strands in Elementary Mathematics: Number, Algebra, Data, Spatial Sense, Financial Literacy, and Social emotional learning skills and math processes. These six strands are the focus of Mathematics education from grade 1 through grade 8. In secondary school, the main topics in elementary mathematics from grade nine until grade ten are: Number Sense and algebra, Linear Relations, Measurement and Geometry. Once students enter grade eleven and twelve students begin university and college preparation classes, which include: Functions, Calculus & Vectors, Advanced Functions, and Data Management. Strands of elementary mathematics Number Sense and Numeration Number Sense is an understanding of numbers and operations. In the 'Number Sense and Numeration' strand students develop an understanding of numbers by being taught ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Illusions
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; their categorization is difficult because the underlying cause is often not clear but a classification proposed by Richard Gregory is useful as an orientation. According to that, there are three main classes: physical, physiological, and cognitive illusions, and in each class there are four kinds: Ambiguities, distortions, paradoxes, and fictions. A classical example for a physical distortion would be the apparent bending of a stick half immerged in water; an example for a physiological paradox is the motion aftereffect (where, despite movement, position remains unchanged). An example for a physiological fiction is an afterimage. Three typical cognitive distortions are the Ponzo, Poggendorff, and Müller-Lyer illusion. Physical illusions are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Missing Square Puzzle
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle, but one has a 1×1 hole in it. Solution The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, nor would either truly be 13x5 if it were, because what appears to be the hypotenuse is bent. In other words, the "hypotenuse" does not maintain a consistent slope, even though it may appear that way to the human eye. A true 13×5 triangle cannot be created from the given component parts. The four figures (the yellow, red, blue and green shapes) total 32 units of area. The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Carroll
Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet and mathematician. His most notable works are ''Alice's Adventures in Wonderland'' (1865) and its sequel ''Through the Looking-Glass'' (1871). He was noted for his facility with word play, logic, and fantasy. His poems ''Jabberwocky'' (1871) and ''The Hunting of the Snark'' (1876) are classified in the genre of literary nonsense. Carroll came from a family of high-church Anglicanism, Anglicans, and developed a long relationship with Christ Church, Oxford, where he lived for most of his life as a scholar and teacher. Alice Liddell, the daughter of Christ Church's dean Henry Liddell, is widely identified as the original inspiration for ''Alice in Wonderland'', though Carroll always denied this. An avid puzzler, Carroll created the word ladder puzzle (which he then called "Doublets"), which he published in his weekly column for ''Vanity Fair ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Victor Schlegel
Victor Schlegel (4 March 1843 – 22 November 1905) was a German mathematician. He is remembered for promoting the geometric algebra of Hermann Grassmann and for a method of visualizing polytopes called Schlegel diagrams. In the nineteenth century there were various expansions of the traditional field of geometry through the innovations of hyperbolic geometry, non-Euclidean geometry and algebraic geometry. Hermann Grassmann was one of the more advanced innovators with his anticipation of linear algebra and multilinear algebra that he called "Extension theory" (''Ausdehnungslehre''). As recounted by David E. Rowe in 2010: :The most important new convert was Victor Schlegel, Grassmann’s colleague at Stettin Gymnasium from 1866 to 1868. Afterward Schlegel accepted a position as Oberlehrer at the Gymnasium in Waren, a small town in Mecklenburg. In 1872 Schlegel published the first part of his ''System der Raumlehre'' which used Grassmann’s methods to develop plane geometry. Schleg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edmé Gilles Guyot
The name Edmé may refer to: *Edmé Bouchardon (1698–1762), French sculptor *Edmé Boursault (1638–1701), French writer and dramatist * Edme Castaing (1796–1823), French physician *Edmé-Louis Daubenton (1732–1786), French naturalist * Gaston Audiffret-Pasquier (1823–1905), born Edme-Armand-Gaston d'Audiffret-Pasquier, French politician *Edme Étienne Borne Desfourneaux (1767–1849), French general *Edme Gaulle (1762–1841), French sculptor *Edme Henry (1760–1841), Canadian politician * Edme François Jomard (1777–1862), French engineer and cartographer * Edme-Jean Leclaire (1801–1872), French economist *Edme Mariotte (1620–1684), French physicist *Edme Mongin (1668–1746), French bishop and orator *Edmé Samson (1810–1891), French ceramist *Edmé-Martin Vandermaesen (1767–1813), French general in the Napoleonic Wars *Edmé Félix Alfred Vulpian (1826–1887), French physician People named Edmée * Edmée Daenen (born 1985), Belgian singer *Edmee Janss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hooper's Paradox
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an area of only 30 units. Explanation Upon close inspection one can notice that the triangles of the dissected shape are not identical to the triangles in the rectangle. The length of the shorter side at the right angle measures 2 units in the original shape but only 1.8 units in the rectangle. This means, the real triangles of the original shape overlap in the rectangle. The overlapping area is a parallelogram, the diagonals and sides of which can be computed via the Pythagorean theorem. : d_1=\sqrt=\sqrt : d_2=\sqrt=\sqrt : s_1=\sqrt=\sqrt : s_2=\sqrt=\sqrt The area of this parallelogram can determined using Heron's formula for triangles. This yields : s=\frac=\frac for the halved circumference of the triangle (half of the parallelogram) and with that for the area of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hooper Paradox
The word hooper is an archaic English term for a person who aided a cooper in the building of barrels by creating the hoop for the barrel. Hooper may also refer to: Place names in the United States: * Hooper, Colorado, town in Alamosa County, Colorado * Hooper, Georgia, an unincorporated community * Hooper, Nebraska, town in Dodge County, Nebraska * Hooper, Utah, place in Weber County, Utah * Hooper Bay, Alaska, town in Alaska * Hooper Township, Dodge County, Nebraska Other: * ''Hooper'' (film), 1978 comedy film starring Burt Reynolds * Hooper (mascot), the mascot for the National Basketball Association team, Detroit Pistons * Hooper (coachbuilder), a British coachbuilder fitting bodies to many Rolls-Royce and Daimler cars * USS ''Hooper'' (DE-1026), a destroyer escort in the US Navy * Hooper Ratings, an early audience measurement in early radio and television * Hooper, someone who practices dance form of Hooping People with the surname Hooper: * Hooper (surname) See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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