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David Smith (amateur Mathematician)
David Smith is an amateur mathematician and retired print technician from Bridlington, England, who is best known for his discoveries related to aperiodic monotiles that helped to solve the einstein problem. Einstein tile Initial discovery Smith discovered a 13-sided polygon in November 2022 whilst using a software package called ''PolyForm Puzzle Solver'' to experiment with different shapes. After further experimentation using cardboard cut-outs, he realised that the shape appeared to tessellate but seemingly without ever achieving a regular pattern. Contacting experts Smith contacted Craig S. Kaplan from the University of Waterloo to alert him to this potential discovery of an aperiodic monotile. They nicknamed the newly discovered shape "the hat", because of its resemblance to a fedora. Kaplan proceeded to further inspect the polykite shape. During this time, Smith informed Kaplan that he had discovered yet another shape, which he nicknamed "the turtle", that appeared to have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith Aperiodic Monotiling
Smith may refer to: People * Metalsmith, or simply smith, a craftsman fashioning tools or works of art out of various metals * Smith (given name) * Smith (surname), a family name originating in England, Scotland and Ireland ** List of people with surname Smith * Smith (artist) (born 1985), French visual artist Arts and entertainment * Smith (band), an American rock band 1969–1971 * ''Smith'' (EP), by Tokyo Police Club, 2007 * ''Smith'' (play), a 1909 play by W. Somerset Maugham * ''Smith'' (1917 film), a British silent film based on the play * ''Smith'' (1939 film), a short film * ''Smith!'', a 1969 Disney Western film * ''Smith'' (TV series), a 2006 American drama * ''Smith'', a 1932 novel by Warwick Deeping * ''Smith'', a 1967 novel by Leon Garfield and a 1970 TV adaptation Places North America * Smith, Indiana, U.S. * Smith, Kentucky, U.S. * Smith, Nevada, U.S. * Smith, South Carolina, U.S. * Smith Village, Oklahoma, U.S. * Smith Park (Middletown, Connecticut), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bridlington
Bridlington is a coastal town and a civil parish on the Holderness Coast of the North Sea in the East Riding of Yorkshire, England. It is about north of Hull and east of York. The Gypsey Race enters the North Sea at its harbour. The 2011 Census gave a parish population of 35,369. As a sea-fishing port, it is known for shellfish, and is the largest lobster port in Europe, with over 300 tonnes of the crustaceans landed there each year. It has been termed the "Lobster Capital of Europe". Alongside manufacturing, retail and service firms, its main trade is summer tourism. It is twinned with Millau, France, and until 2020 was twinned with Bad Salzuflen, Germany. It holds one of the UK's coastal weather stations. The Priory Church of St Mary and associated Bayle (or gate) are Grade I listed buildings on the site of an Augustinian Priory. History Archaeological evidence shows habitation in the Bronze Age and in Roman Britain. The settlement after the Norman conquest was called '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aperiodic Set Of Prototiles
A set of prototiles is aperiodic if copies of the prototiles can be assembled to create tilings, such that all possible tessellation patterns are non- periodic. The ''aperiodicity'' referred to is a property of the particular set of prototiles; the various resulting tilings themselves are just non-periodic. A given set of tiles, in the Euclidean plane or some other geometric setting, ''admits a tiling'' if non-overlapping copies of the tiles in the set can be fitted together to cover the entire space. A given set of tiles might admit periodic tilings — that is, tilings that remain invariant after being shifted by a translation (for example, a lattice of square tiles is periodic). It is not difficult to design a set of tiles that admits non-periodic tilings as well as periodic tilings. (For example, randomly arranged tilings using a 2×2 square and 2×1 rectangle are typically non-periodic.) However, an aperiodic set of tiles can ''only'' produce non-periodic tilings. Infinit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Problem
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles, that is, a shape that can tessellate space, but only in a nonperiodic way. Such a shape is called an "einstein" (not to be confused with the physicist Albert Einstein), a play on the German words ''ein Stein'', meaning ''one tile''. Depending on the particular definitions of nonperiodicity and the specifications of what sets may qualify as tiles and what types of matching rules are permitted, the problem is either open or solved. The einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral. Such anisohedral tiles were found by Karl Reinhardt in 1928, but these anisohedral tiles all tile space periodically. Proposed solutions In 1988, Peter Schmitt discovered a singl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its ''edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Craig S
__NOTOC__ Craig may refer to: Geology *Craig (landform), a rocky hill or mountain often having large casims or sharp intentations. People (and fictional characters) * Craig (surname) *Craig (given name) Places Scotland * Craig, Angus, aka Barony of Craigie United States *Craig, Alaska, a city * Craig, Colorado, a city * Craig, Indiana, an unincorporated place *Craig, Iowa, a city *Craig, Missouri, a city *Craig, Montana, an unincorporated place *Craig, Nebraska, a village *Craig, Ohio, an unincorporated community *Craig County, Virginia *Craig County, Oklahoma *Craig Township (other) (two places) Other uses *Craig (song) *Craig Electronics, a consumer electronics company * Craig Broadcast Systems, later Craig Media and finally Craig Wireless, a defunct Canadian media and communication company *Clan Craig, a Scottish clan *Craig tube A Craig tube is an item of apparatus used in small-scale (up to about 100 mg) preparative and analytical chemistry, particularly for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Waterloo
The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario, Canada. The main campus is on of land adjacent to "Uptown" Waterloo and Waterloo Park. The university also operates three satellite campuses and four affiliated university colleges. The university offers academic programs administered by six faculties and thirteen faculty-based schools. Waterloo operates the largest post-secondary co-operative education program in the world, with over 20,000 undergraduate students enrolled in the university's co-op program. Waterloo is a member of the U15, a group of research-intensive universities in Canada. The institution originates from the Waterloo College Associate Faculties, established on 4 April 1956; a semi-autonomous entity of Waterloo College, which was an affiliate of the University of Western Ontario. This entity formally separated from Waterloo College and was incorporated as a university with the pass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aperiodic Monotile
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles, that is, a shape that can tessellate space, but only in a nonperiodic way. Such a shape is called an "einstein" (not to be confused with the physicist Albert Einstein), a play on the German words ''ein Stein'', meaning ''one tile''. Depending on the particular definitions of nonperiodicity and the specifications of what sets may qualify as tiles and what types of matching rules are permitted, the problem is either open or solved. The einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral. Such anisohedral tiles were found by Karl Reinhardt in 1928, but these anisohedral tiles all tile space periodically. Proposed solutions In 1988, Peter Schmitt discovered a single ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fedora
A fedora () is a hat with a soft brim and indented crown.Kilgour, Ruth Edwards (1958). ''A Pageant of Hats Ancient and Modern''. R. M. McBride Company. It is typically creased lengthwise down the crown and "pinched" near the front on both sides. Fedoras can also be creased with teardrop crowns, diamond crowns, center dents, and others, and the positioning of pinches can vary. The typical crown height is . The term ''fedora'' was in use as early as 1891. Its popularity soared, and eventually it eclipsed the similar-looking homburg. The fedora hat's brim is usually around wide, but can be wider, can be left raw-edged (left as cut), finished with a sewn overwelt or underwelt, or bound with a trim-ribbon. ''Stitched edge'' means that there is one or more rows of stitching radiating inward toward the crown. The Cavanagh edge is a welted edge with invisible stitching to hold it in place and is a very expensive treatment that can no longer be performed by modern hat factories. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge became an important trading centre during the Roman and Viking ages, and there is archaeological evidence of settlement in the area as early as the Bronze Age. The first town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is most famous as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chapel, Cavendish Laboratory, and the Cambridge University Library, one of the largest legal deposit libraries in the world. The city's skyline is dominated by several college buildings, along with the spire of the Our Lady and the English Marty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaim Goodman-Strauss
Chaim Goodman-Strauss (born June 22, 1967 in Austin TX) is an American mathematician who works in convex geometry, especially aperiodic tiling. He is on the faculty of the University of Arkansas and is a co-author with John H. Conway of ''The Symmetries of Things'', a comprehensive book surveying the mathematical theory of patterns. Education and career Goodman-Strauss received both his B.S. (1988) and Ph.D. (1994) in mathematics from the University of Texas at Austin.Chaim Goodman-Strauss The College Board His doctoral advisor was John Edwin Luecke. He joined the faculty at the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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