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The Spider And The Fly Problem
400px, 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 geodesics problem with an unintuitive solution. 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. The shortest distance strictly abiding by the rules, 40 feet, is obtained by constructing an appropriate net of the room and connecting the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spider And Fly Problem
Spiders (order (biology), order Araneae) are air-breathing arthropods that have eight legs, chelicerae with fangs generally able to inject venom, and spinnerets that extrude spider silk, silk. They are the largest order of arachnids and rank seventh in total species diversity among all Order (biology), orders of organisms. Spiders are found worldwide on every continent except for Antarctica, and have become established in nearly every land habitat. , 50,356 spider species in 132 Family (biology), families have been recorded by Taxonomy (biology), 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 segmentation (biology), segments are fused into two Tagma (biology), tagmata, the cephalothorax or prosoma, and the opisthosoma, or abdomen, and joined by a small, cylindrical Gl ... [...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] |
Geodesics
In geometry, a geodesic () is a curve representing in some sense the 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 having vanishing ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron, whose polyhedral graph is the same as that of a cube. Special cases are a cube, with 6 squares as faces, a rectangular prism, rectangular cuboid or rectangular box, with 6 rectangles as faces, for both, cube and rectangular prism, adjacent faces meet in a right angle. General cuboids By Euler's formula the numbers of faces ''F'', of vertices ''V'', and of edges ''E'' of any convex polyhedron are related by the formula ''F'' + ''V'' = ''E'' + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges. Along with the rectangular cuboids, any parallelepiped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Net (polyhedron)
In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the 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 polyhedron to form a net must form a spanning tree of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lateral Thinking
Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. It involves ideas that may not be obtainable using only traditional step-by-step logic. The term was first used in 1967 by Maltese psychologist Edward de Bono in his book ''The Use of Lateral Thinking''. De Bono cites the Judgment of Solomon as an example of lateral thinking, where King Solomon resolves a dispute over the parentage of a child by calling for the child to be cut in half, and making his judgment according to the reactions that this order receives. Edward de Bono also links lateral thinking with humour, arguing it entails a switch-over from a familiar pattern to a new, unexpected one. It is this moment of surprise, generating laughter and new insight, which facilitates the ability to see a different thought pattern which initially was not obvious. According to de Bono, lateral thinking deliberately distances itself from the stand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dragline Silk
Spider silk is a protein fibre spun by spiders. Spiders use their silk to make Spider web, webs or other structures, which function as sticky nets to catch other animals, or as nests or cocoons to protect their offspring, or to wrap up prey. They can also use their silk to suspend themselves, to Ballooning (spider), float through the air, or to glide away from predators. Most spiders vary the thickness and stickiness of their silk for different uses. In some cases, spiders may even use silk as a source of food. While methods have been developed to collect silk from a spider by force, it is difficult to gather silk from many spiders compared to silk-spinning organisms such as Sericulture, silkworms. All spiders produce silk, and even in non-web building spiders, silk is intimately 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. O ... [...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 country's 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 ... [...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 scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also 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. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
