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Penrose Triangle
The Penrose triangle, also known as the Penrose tribar, the impossible tribar, or the impossible triangle, is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing, but cannot exist as a solid object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, prominent Nobel Prize-winning mathematician Sir Roger Penrose, who described it as "impossibility in its purest form". It is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. Description The tribar/triangle appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form. The beams may be broken, forming cubes or cuboids. This combination of proper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Water Wheel
A water wheel is a machine for converting the energy of flowing or falling water into useful forms of power, often in a watermill. A water wheel consists of a wheel (usually constructed from wood or metal), with a number of blades or buckets arranged on the outside rim forming the driving car. Water wheels were still in commercial use well into the 20th century but they are no longer in common use. Uses included milling flour in gristmills, grinding wood into pulp for papermaking, hammering wrought iron, machining, ore crushing and pounding fibre for use in the manufacture of cloth. Some water wheels are fed by water from a mill pond, which is formed when a flowing stream is dammed. A channel for the water flowing to or from a water wheel is called a mill race. The race bringing water from the mill pond to the water wheel is a headrace; the one carrying water after it has left the wheel is commonly referred to as a tailrace. Waterwheels were used for various purposes from ag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impossible Objects
An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two- dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline. Notable examples Notable impossible objects include: * Borromean rings — although conventionally drawn as three linked circles in three-dimensional space, any realization must be non-circular * Impossible cube — invented by M.C. Escher for ''Belvedere'', a lithograph in which a boy seated at the foot of the building holds an impossible cube. * Penrose stairs – created by Oscar Reutersvärd and later independently devised and popularised by Lionel Penrose and his mathematician son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
British Journal Of Psychology
The ''British Journal of Psychology'' is a quarterly peer-reviewed psychology journal. It was established in 1904 and is published by Wiley-Blackwell on behalf of the British Psychological Society. The editor-in-chief is Stefan R. Schweinberger (University of Jena). According to the ''Journal Citation Reports'', the journal has a 2018 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 3.308, ranking it 20th out of 137 journals in the category "Psychology, Multidisciplinary". References External links * Psychology journals British Psychological Society academic journals Publications established in 1904 Quarterly journals English-language journals Wiley-Blackwell academic journals {{Psychology-journal-stub ... [...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 famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it is the oldest continuously published magazine in the United States. ''Scientific American'' is owned by Springer Nature, which in turn 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 newspaper was released 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 device for buoying vessels by Abraham Lincoln, and the universal joint which now can be found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Stillwell
John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University. Biography He was born in Melbourne, Australia and lived there until he went to the Massachusetts Institute of Technology for his doctorate. He received his PhD from MIT in 1970, working under Hartley Rogers, Jr who had himself worked under Alonzo Church. From 1970 until 2001 he taught at Monash University back in Australia and in 2002 began teaching in San Francisco. Honors In 2005, Stillwell was the recipient of the Mathematical Association of America's prestigious Chauvenet Prize for his article “The Story of the 120-Cell,” Notices of the AMS, January 2001, pp. 17–24. In 2012 he became a fellow of the American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perception (journal)
''Perception'' is a peer-reviewed scientific journal specialising in the psychology of vision and perception. Founded by Richard Gregory, it is available in print form and online. It publishes primary research from any discipline within the sensory sciences. The journal is indexed in PubMed PubMed is a free search engine accessing primarily the MEDLINE database of references and abstracts on life sciences and biomedical topics. The United States National Library of Medicine (NLM) at the National Institutes of Health maintain the .... External links * Perception journals Vision Neuroscience journals English-language journals Publications established in 1972 SAGE Publishing academic journals {{psychology-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mobius Strip
Moebius, Möbius or Mobius may refer to: People * August Ferdinand Möbius (1790–1868), German mathematician and astronomer * Theodor Möbius (1821–1890), German philologist * Karl Möbius (1825–1908), German zoologist and ecologist * Paul Julius Möbius (1853–1907), German neurologist * Dieter Moebius (1944–2015), German/Swiss musician * Mark Mobius (born 1936), emerging markets investments pioneer * Jean Giraud (1938–2012), French comics artist who used the pseudonym Mœbius Fictional characters * Mobius M. Mobius, a character in Marvel Comics * Mobius, also known as the Anti-Monitor, a supervillain in DC Comics Mathematics * Möbius energy, a particular knot energy * Möbius strip, an object with one surface and one edge * Möbius function, an important multiplicative function in number theory and combinatorics ** Möbius transform, transform involving the Möbius function ** Möbius inversion formula, in number theory * Möbius transformation, a particular ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Steps
The Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Oscar Reutersvärd in 1937 and later independently discovered and made popular by Lionel Penrose and his son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three-dimensional Euclidean geometry but possible in some non-Euclidean geometry like in nil geometry. The "continuous staircase" was first presented in an article that the Penroses wrote in 1959, based on the so-called "triangle of Penrose" published by Roger Penrose in the ''British Journal of Psychology'' in 1958. M.C. Escher then discovered the Penrose stairs in the following year and made his now famous lithograph ''Klimmen en dalen'' (''Ascending and Descending'') i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Hares
The three hares (or three rabbits) is a circular motif or meme appearing in sacred sites from East Asia, the Middle East and to the churches of Devon, England (as the " Tinners' Rabbits"), and historical synagogues in Europe. It is used as an architectural ornament, a religious symbol, and in other modern works of art or a logo for adornment (including tattoos), jewelry, and a coat of arms on an escutcheon. It is viewed as a puzzle, a topology problem or a visual challenge, and has been rendered as sculpture, drawing, and painting. The symbol features three hares or rabbits chasing each other in a circle. Like the triskelion, the triquetra, and their antecedents (e.g., the triple spiral), the symbol of the three hares has a threefold rotational symmetry. Each of the ears is shared by two hares, so that only three ears are shown. Although its meaning is apparently not explained in contemporary written sources from any of the medieval cultures where it is found, it is thought to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shepard Elephant
The Shepard elephant, also known as L'egs-istential Quandary or the impossible elephant is an optical illusion, of the type impossible object, based on figure-ground confusion. As its creator Roger Shepard explains: The elephant…belongs to a class of objects that are truly impossible in that the object itself cannot be globally segregated from the nonobject or background. Parts of the object (in this case the elephant’s legs) become the background, and vice versa. History Shepard first published this optical paradox in his 1990 book ''Mind Sights'' (page 79) giving it the name "''L'egs-istential Quandary''". It is the first entry in his chapter on "Figure-ground impossibilities". The pen-and-ink drawing is based on a dream Shepard had in 1974, and on the pencil sketch he made when he woke up. Interpretation The image is widely reproduced and discussed. Brad Honeycutt, author of ''Exceptional Eye Tricks'', calls the Shepard elephant "one of the most famous and classic op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
