|
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. It cannot exist as a solid object in ordinary three-dimensional Euclidean space, although its surface can be embedded isometrically (bent but not stretched) in five-dimensional Euclidean space. 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, the mathematician and Nobel Prize laureate 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 wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waterfall (M
A waterfall is any point in a river or stream where water flows over a vertical drop or a series of steep drops. Waterfalls also occur where meltwater drops over the edge of a tabular iceberg or ice shelf. Waterfalls can be formed in several ways, but the most common method of formation is that a river courses over a top layer of resistant bedrock before falling onto softer rock, which Erosion, erodes faster, leading to an increasingly high fall. Waterfalls have been studied for their impact on species living in and around them. Humans have had a distinct relationship with waterfalls since prehistory, travelling to see them, exploring and naming them. They can present head of navigation, formidable barriers to navigation along rivers. Waterfalls are religious sites in many cultures. Since the 18th century, they have received increased attention as tourist destinations, sources of hydropower, andparticularly since the mid-20th centuryas subjects of research. Definition and te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangles
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated withi ... [...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 graphical projection, projection of a three-dimensional object but cannot exist as a solid object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline. Notable examples Notable impossible objects include: Explanations Impossible objects can be unsettling because of our natural desire to interpret 2D drawings as three-dimensional objects. This is why a drawing of a Necker cube would most likely be seen as a cube, rather than "two squares connected with diagonal lines, a square surrounded by irregular planar figures, or any other planar figure". Looking at different parts of an impossible object makes one reassess the 3D nature of the object, which confuses the mind. In most cases the imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics 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, Torsion (mechanics), 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 List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, 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 to ... [...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 type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... 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 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] |
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, 120-Cell," Notices of the AMS, January 2001, pp. 17–24. In 2012, he became a fellow of the American Mathematical Society. Works Books Stillwell is the author of many textbooks and other books on mathematics including: *''Classical Topology and Combinatorial Group Theory'', 1980, *2012 pbk reprint of 1993 ... [...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 an openly accessible, free database which includes 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 Institute .... External links * Perception journals Vision Neuroscience journals English-language journals Academic journals established in 1972 SAGE Publishing academic journals {{psychology-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Stairs
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' ... [...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 (perception), 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impossible Trident
An impossible trident, also known as an impossible fork, blivet, poiuyt, or devil's tuning fork,Brooks Masterton, John M. Kennedy"Building the Devil's Tuning Fork" ''Perception'', 1975, vol. 4, pp. 107-109 is a drawing of an impossible object (undecipherable figure), a kind of an optical illusion. It appears to have three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end. In 1964, D.H. Schuster reported that he noticed an ambiguous figure of a new kind in the advertising section of an aviation journal. He dubbed it a "three-stick clevis". He described the novelty as follows: "Unlike other ambiguous drawings, an actual shift in visual fixation is involved in its perception and resolution." The word "poiuyt" appeared on the March 1965 cover of ''Mad (magazine), Mad'' magazine bearing the four-eyed Alfred E. Neuman balancing the impossible fork on his finger with caption "Introducing 'The Mad Poiuyt' " (the last six letters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
