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Hexaflexagon
In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be ''flexed'' or folded in certain ways to reveal faces besides the two that were originally on the back and front. Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon. In hexaflexagon theory (that is, concerning flexagons with six sides), flexagons are usually defined in terms of ''pats''. Two flexagons are equivalent if one can be transformed to the other by a series of pinches and rotations. Flexagon equivalence is an equivalence relation. History Discovery and introduction The discovery of the first flexagon, a trihexaflexagon, is credited to the British mathematician Arthur H. Stone, while ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trihexaflexagon Example
In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be ''flexed'' or folded in certain ways to reveal faces besides the two that were originally on the back and front. Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon. In hexaflexagon theory (that is, concerning flexagons with six sides), flexagons are usually defined in terms of ''pats''. Two flexagons are equivalent if one can be transformed to the other by a series of pinches and rotations. Flexagon equivalence is an equivalence relation. History Discovery and introduction The discovery of the first flexagon, a trihexaflexagon, is credited to the British mathematician Arthur H. Stone, whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE. The Möbius strip is a non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. Every non-orientable surface contains a Möbius strip. As an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: a clockwise half-twist is different from a counterclockwise half-twist, and it can also be embedded with odd numbers of twists greater than one, or with a knotted centerline. Any two embeddings with the same knot for the centerline and the same number and direction of twists are topologically equivalent. All of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Harold Stone
Arthur Harold Stone (30 September 1916 – 6 August 2000) was a British mathematician born in London, who worked at the universities of Manchester and Rochester, mostly in topology. His wife was American mathematician Dorothy Maharam. Stone studied at Trinity College, Cambridge. His first paper dealt with squaring the square, he proved the Erdős–Stone theorem with Paul Erdős and is credited with the discovery of the first two flexagons, a trihexaflexagon and a hexahexaflexagon while he was a student at Princeton University in 1939. His Ph.D. thesis, ''Connectedness and Coherence'', was written in 1941 under the direction of Solomon Lefschetz. He served as a referee for ''The American Mathematical Monthly'' journal in the 1980s. The Stone metrization theorem has been named after him, and he was a member of a group of mathematicians who published pseudonymously as Blanche Descartes. He is not to be confused with American mathematician Marshall Harvey Stone. See also *Ha ... [...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] |
Pittsburgh
Pittsburgh ( ) is a city in the Commonwealth (U.S. state), Commonwealth of Pennsylvania, United States, and the county seat of Allegheny County, Pennsylvania, Allegheny County. It is the most populous city in both Allegheny County and Western Pennsylvania, the List of municipalities in Pennsylvania#Municipalities, second-most populous city in Pennsylvania behind Philadelphia, and the List of United States cities by population, 68th-largest city in the U.S. with a population of 302,971 as of the 2020 United States census, 2020 census. The city anchors the Pittsburgh metropolitan area of Western Pennsylvania; its population of 2.37 million is the largest in both the Ohio Valley and Appalachia, the Pennsylvania metropolitan areas, second-largest in Pennsylvania, and the List of metropolitan statistical areas, 27th-largest in the U.S. It is the principal city of the greater Pittsburgh–New Castle–Weirton combined statistical area that extends into Ohio and West Virginia. Pitts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trefoil Knot
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory. The trefoil knot is named after the three-leaf clover (or trefoil) plant. Descriptions The trefoil knot can be defined as the curve obtained from the following parametric equations: :\begin x &= \sin t + 2 \sin 2t \\ y &= \cos t - 2 \cos 2t \\ z &= -\sin 3t \end The (2,3)-torus knot is also a trefoil knot. The following parametric equations give a (2,3)-torus knot lying on torus (r-2)^2+z^2 = 1: :\begin x &= (2+\cos 3t) \cos 2t \\ y &= (2+\cos 3t )\sin 2t \\ z &= \sin 3t \end Any continuous deformation of the curve above is also considered a trefoil knot. Specifically, any curve isotopic to a trefoil knot is also considered to be a trefoil. In addition, the mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recycling Symbol
The universal recycling symbol ( or in Unicode) is internationally recognized for symbol for recycling activity. The symbol's creation originates on the first Earth Day in 1970, where the logo depicted is a Möbius strip. The public domain status of the symbol has been challenged before, but attempts have been unsuccessful. Many variations on the logo had been created since its creation. History Worldwide attention to environmental issues led to the first Earth Day in 1970. Container Corporation of America, a large producer of recycled paperboard, sponsored a contest for art and design students at high schools and colleges across the country to raise awareness of environmental issues. It was won by Gary Anderson (designer), Gary Anderson, then a 23-year-old college student at the University of Southern California, whose entry was the image now known as the universal recycling symbol. The symbol is not trademarked and is in the public domain. The public-domain status of the symb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Himber
Richard Himber (born Herbert Richard Imber; February 20, 1899 – December 11, 1966) was an American bandleader, composer, violinist, magician and practical joker. Early life He was born as Herbert Richard Imber in Newark, New Jersey to the owner of a chain of meat stores. His parents gave him violin lessons, but when they found him performing in a seedy Newark dive, they took the instrument away from him and sent him to military school. In 1915, he stole away into New York City, where Sophie Tucker heard him play and hired him as a novelty act to play with her and the ''Five Kings of Syncopation'' where Himber was the highlight of the cabaret act. He worked his way through Vaudeville and down Tin Pan Alley. He managed Rudy Vallee's orchestra service, which sent out bands for private parties and society functions. A suave salesman and irrepressible idea man, he soon had his own band booking agency. In 1932, he acquired the first known "vanity" telephone number, ''R-HIMBER'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubik's Magic
Rubik's Magic, like the Rubik's Cube, is a mechanical puzzle invented by Ernő Rubik and first manufactured by Matchbox in the mid-1980s. The puzzle consists of eight black square tiles (changed to red squares with goldish rings in 1997) arranged in a 2 × 4 rectangle; diagonal grooves on the tiles hold wires that connect them, allowing them to be folded onto each other and unfolded again in two perpendicular directions (assuming that no other connections restrict the movement) in a manner similar to a Jacob's ladder toy. The front side of the puzzle shows, in the initial state, three separate, rainbow-coloured rings; the back side consists of a scrambled picture of three interconnected rings. The goal of the game is to fold the puzzle into a heart-like shape and unscramble the picture on the back side, thus interconnecting the rings. Numerous ways to accomplish this exist, and experienced players can transform the puzzle from its initial into the solved state in less than 2 sec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
