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The Spider And The Fly Problem
upright=1.3, Isometric projection and net of naive (1) and optimal (2) solutions of the spider and the fly problem The spider and the fly problem is a recreational mathematics problem with an unintuitive solution, asking for a shortest path or geodesic between two points on the surface of a cuboid. It was originally posed by Henry Dudeney. Problem In the typical version of the puzzle, an otherwise empty cuboid room 30 feet long, 12 feet wide and 12 feet high contains a spider and a fly. The spider is 1 foot below the ceiling and horizontally centred on one 12′×12′ wall. The fly is 1 foot above the floor and horizontally centred on the opposite wall. The problem is to find the minimum distance the spider must crawl along the walls, ceiling and/or floor to reach the fly, which remains stationary. Solutions A naive solution is for the spider to remain horizontally centred, and crawl up to the ceiling, across it and down to the fly, giving a distance of 42 feet. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spider And Fly Problem
Spiders (order Araneae) are air-breathing arthropods that have eight limbs, chelicerae with fangs generally able to inject venom, and spinnerets that extrude silk. They are the largest order of arachnids and rank seventh in total species diversity among all orders of organisms. Spiders are found worldwide on every continent except Antarctica, and have become established in nearly every land habitat. , 53,034 spider species in 136 families have been recorded by taxonomists. However, there has been debate among scientists about how families should be classified, with over 20 different classifications proposed since 1900. Anatomically, spiders (as with all arachnids) differ from other arthropods in that the usual body segments are fused into two tagmata, the cephalothorax or prosoma, and the opisthosoma, or abdomen, and joined by a small, cylindrical pedicel. However, as there is currently neither paleontological nor embryological evidence that spiders ever had a separate thor ... [...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 and 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 mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic
In geometry, a geodesic () is a curve representing in some sense the locally shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a " straight line". The noun '' geodesic'' and the adjective '' geodetic'' come from ''geodesy'', the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of havi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboid
In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six Face (geometry), faces; it has eight Vertex (geometry), vertices and twelve Edge (geometry), edges. A ''rectangular cuboid'' (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a Convex polyhedron, convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the Dihedral angle, angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles. Along with the rectangular cuboids, ''parallelepiped'' is a cuboid with six parallelogram faces. ''Rhombohedron'' is a cuboid with six rhombus faces. A ''square fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Dudeney
Henry Ernest Dudeney (10 April 1857 – 23 April 1930) was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the foremost creators of mathematical puzzles. Early life Dudeney was born in the village of Mayfield, East Sussex, England, one of six children of Gilbert and Lucy Dudeney. His grandfather, John Dudeney, was well known as a self-taught mathematician and shepherd; his initiative was much admired by his grandson. Dudeney learned to play chess at an early age, and continued to play frequently throughout his life. This led to a marked interest in mathematics and the composition of puzzles. Chess problems in particular fascinated him during his early years. Career Although Dudeney spent his career in the Civil Service, he continued to devise various problems and puzzles. Dudeney's first puzzle contributions were submissions to newspapers and magazines, often under the pseudonym of "Sphinx." Much of this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Net (polyhedron)
In geometry, a net of a polyhedron is an arrangement of non-overlapping Edge (geometry), edge-joined polygons in the plane (geometry), plane which can be folded (along edges) to become the face (geometry), faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard. An early instance of polyhedral nets appears in the works of Albrecht Dürer, whose 1525 book ''A Course in the Art of Measurement with Compass and Ruler'' (''Unterweysung der Messung mit dem Zyrkel und Rychtscheyd '') included nets for the Platonic solids and several of the Archimedean solids. These constructions were first called nets in 1543 by Augustin Hirschvogel. Existence and uniqueness Many different nets can exist for a given polyhedron, depending on the choices of which edges are joined and which are separated. The edges that are cut from a convex poly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lateral Thinking
Lateral thinking is a manner of Problem solving, solving problems using an indirect and creativity, creative approach via reasoning that is not immediately obvious. Synonymous to thinking outside the box, it involves ideas that may not be obtainable using only traditional step-by-step logic. The cutting of the Gordian Knot is a classical example. The term was first used in 1967 by Maltese psychologist Edward de Bono who used the Judgement of Solomon, the Nine dots puzzle, Nine Dots Puzzle, and the sewing machine (automating the work rather than adding more workers) as examples, among many others, of lateral thinking. Lateral thinking deliberately distances itself from Vertical Thinking, the traditional method for problem solving. De Bono argues lateral thinking entails a switch-over from a familiar pattern to a new, unexpected one. Such insight sometimes takes the form of humour but can also be cultivated. Critics have characterized lateral thinking as a pseudo-science, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dragline Silk
Spider silk is a protein fibre or silk spun by spiders. Spiders use silk to make webs or other structures that function as adhesive traps to catch prey, to entangle and restrain prey before biting, to transmit tactile information, or as nests or cocoons to protect their offspring. They can use the silk to suspend themselves from height, to float through the air, or to glide away from predators. Most spiders vary the thickness and adhesiveness of their silk according to its use. In some cases, spiders may use silk as a food source. While methods have been developed to collect silk from a spider by force, gathering silk from many spiders is more difficult than from silk-spinning organisms such as silkworms. All spiders produce silk, although some spiders do not make webs. Silk is tied to courtship and mating. Silk produced by females provides a transmission channel for male vibratory courtship signals, while webs and draglines provide a substrate for female sex pheromones. Obs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was a leading authority on Lewis Carroll; '' The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies.Martin Gardner obituary (2010) He had a lifelong interest in magic and illusion and in 1999, ''MAGIC'' magazine named him as one of the "10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Hurwitz
Adolf Hurwitz (; 26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, mathematical analysis, analysis, geometry and number theory. Early life He was born in Hildesheim, then part of the Kingdom of Hanover, to a Jewish family and died in Zürich, in Switzerland. His father Salomon Hurwitz, a merchant, was not wealthy. Hurwitz's mother, Elise Wertheimer, died when he was three years old. Family records indicate that he had siblings and cousins, but their names have yet to be confirmed except for an older brother, Julius, with whom he developed an arithmetical theory for complex continued fractions circa 1890. Hurwitz entered the in Hildesheim in 1868. He was taught mathematics there by Hermann Schubert. Schubert persuaded Hurwitz's father to allow him to attend university, and arranged for Hurwitz to study with Felix Klein at Munich. Salomon Hurwitz could not afford to send his son to university, but his friend, Mr. Edwards, assisted financially. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Von Mises
Richard Martin Edler von Mises (; 19 April 1883 – 14 July 1953) was an Austrian scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon McKay Professor of Aerodynamics and Applied Mathematics at Harvard University. He described his work in his own words shortly before his death as: Although best known for his mathematical work, von Mises also contributed to the philosophy of science as a neo-positivist and empiricist, following the line of Ernst Mach. Historians of the Vienna Circle of logical empiricism recognize a "first phase" from 1907 through 1914 with Philipp Frank, Hans Hahn, and Otto Neurath. His older brother, Ludwig von Mises, held an opposite point of view with respect to positivism and epistemology. His brother developed ''praxeology'', an ''a priori'' view. During his time in Istanbul, Mises maintained close contact with Philipp Frank, a lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Prize-winners being featured since its inception. In print since 1845, it is the oldest continuously published magazine in the United States. ''Scientific American'' is owned by Springer Nature, which is a subsidiary of Holtzbrinck Publishing Group. History ''Scientific American'' was founded by inventor and publisher Rufus Porter (painter), Rufus Porter in 1845 as a four-page weekly newspaper. The first issue of the large-format New York City newspaper was released on August 28, 1845. Throughout its early years, much emphasis was placed on reports of what was going on at the United States Patent and Trademark Office, U.S. Patent Office. It also reported on a broad range of inventions including perpetual motion machines, an 1860 devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
