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Hexastix
Hexastix is a symmetric arrangement of non-intersecting prisms, that when extended infinitely, fill exactly 3/4 of space. The prisms in a hexastix arrangement are all parallel to 4 directions on the body-centered cubic lattice. In '' The Symmetries of Things'', John Horton Conway, Heidi Burgiel, and Chaim Goodman-Strauss named this structure hexastix. Applications The hexastix arrangement has found use in mathematics, crystallography, reticular chemistry, puzzle design, and art. Michael O'Keeffe (chemist) and associates define this structure as one of the 6 possible invariant cubic rod packing arrangements. O’Keefe classifies this arrangement as the ''Γ'' or Garnet rod packing, and describes it as the densest possible cubic rod packing. Rod packings are used to classify chains of atoms in crystal structures, and in the develop of materials like metal–organic frameworks. It has been proposed that stratum corneum’s structure could be modeled using the hexastix cylinder packi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stick Puzzle
Stick puzzles are a type of combination puzzle that uses multiple sticks or 'polysticks' (which can be one-dimensional objects) to assemble two- or three-dimensional configurations. Polysticks are configurations of joined or unjoined thin (ideally one-dimensional) 'sticks'. The sticks may be; line segments on paper, matchsticks, pieces of straw, wire or similar. A special class of stick puzzles are 'matchstick puzzles', where all parts used are sticks (usually matchsticks) rather than polysticks. Some trick puzzles can only be solved when one assumes that the sticks actually have measurements in more than one dimension. Three-dimensional arrangements like tetrastix can also be made from matchsticks. Examples of stick puzzles * Matchstick puzzles * Burr puzzle * Hexastix Hexastix is a symmetric arrangement of non-intersecting prisms, that when extended infinitely, fill exactly 3/4 of space. The prisms in a hexastix arrangement are all parallel to 4 directions on the body-centere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burr Puzzle
A burr puzzle is an interlocking puzzle consisting of notched sticks, combined to make one three-dimensional, usually symmetrical unit. These puzzles are traditionally made of wood, but versions made of plastic or metal can also be found. Quality burr puzzles are usually precision-made for easy sliding and accurate fitting of the pieces. In recent years the definition of "burr" is expanding, as puzzle designers use this name for puzzles not necessarily of stick-based pieces. History The term "burr" is first mentioned in a 1928 book by Edwin Wyatt, but the text implies that it was commonly used before. The term is attributed to the finished shape of many of these puzzles, resembling a seed burr. The origin of burr puzzles is unknown. The first known record appears in a 1698 engraving used as a title page of Chambers's Cyclopaedia. Later records can be found in German catalogs from the late 18th century and early 19th century. There are claims of the burr being a Chinese inventio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrastix
In geometry, it is possible to fill 3/4 of the volume of three-dimensional Euclidean space by three sets of infinitely-long square prisms aligned with the three coordinate axes, leaving cubical voids; John Horton Conway, Heidi Burgiel and Chaim Goodman-Strauss have named this structure tetrastix. Applications The motivation for some of the early studies of this structure was for its applications in the crystallography of crystal structures formed by rod-shaped molecules. Shrinking the square cross-sections of the prisms slightly causes the remaining space, consisting of the cubical voids, to become linked up into a single polyhedral set, bounded by axis-parallel faces. Polyhedra constructed in this way from finitely many prisms provide examples of axis-parallel polyhedra with n vertices and faces that require \Omega(n^) pieces when subdivided into convex pieces; they have been called Thurston polyhedra, after William Thurston, who suggested using these shapes for this lower bound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrastix
In geometry, it is possible to fill 3/4 of the volume of three-dimensional Euclidean space by three sets of infinitely-long square prisms aligned with the three coordinate axes, leaving cubical voids; John Horton Conway, Heidi Burgiel and Chaim Goodman-Strauss have named this structure tetrastix. Applications The motivation for some of the early studies of this structure was for its applications in the crystallography of crystal structures formed by rod-shaped molecules. Shrinking the square cross-sections of the prisms slightly causes the remaining space, consisting of the cubical voids, to become linked up into a single polyhedral set, bounded by axis-parallel faces. Polyhedra constructed in this way from finitely many prisms provide examples of axis-parallel polyhedra with n vertices and faces that require \Omega(n^) pieces when subdivided into convex pieces; they have been called Thurston polyhedra, after William Thurston, who suggested using these shapes for this lower bound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stratum Corneum
The stratum corneum (Latin for 'horny layer') is the outermost layer of the epidermis. The human stratum corneum comprises several levels of flattened corneocytes that are divided into two layers: the ''stratum disjunctum'' and ''stratum compactum''. The skin's protective acid mantle and lipid barrier sit on top of the stratum disjunctum. The stratum disjunctum is the uppermost and loosest layer of skin. The stratum compactum is the comparatively deeper, more compacted and more cohesive part of the stratum corneum. The corneocytes of the stratum disjunctum are larger, more rigid and more hydrophobic than that of the stratum compactum. The stratum corneum is the dead tissue that performs protective and adaptive physiological functions including mechanical shear, impact resistance, water flux and hydration regulation, microbial proliferation and invasion regulation, initiation of inflammation through cytokine activation and dendritic cell activity, and selective permeability to exc ... [...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 . He joined the faculty at the |
Crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word "crystallography" is derived from the Greek word κρύσταλλος (''krystallos'') "clear ice, rock-crystal", with its meaning extending to all solids with some degree of transparency, and γράφειν (''graphein'') "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. denote a direction vector (in real space). * Coordinates in ''angle brackets'' or ''chevrons'' such as <100> denote a ''family'' of directions which are related by symmetry operations. In the cubic crystal system for example, would mean 00 10 01/nowiki> or the negative of any of those directions. * Miller indices in ''parentheses'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael O'Keeffe (chemist)
Michael O’Keeffe (born April 3, 1934) is a British-American chemist. He is currently Regents’ Professor Emeritus in the School of Molecular Sciences at Arizona State University. As a scientist, he is particularly known for his contributions to the field of reticular chemistry. In 2019, he received the Gregori Aminoff Prize in Crystallography from the Royal Swedish Academy of Sciences. Early life and education Michael O’Keeffe was born in Bury St Edmunds, Suffolk, England, on the 3rd April, 1934. He was one of four children born to Dr. E. Joseph O’Keeffe, an immigrant from Ireland, and his mother Marjorie G. O’Keeffe (née Marten). From 1942 to 1951 he attended Prior Park College (Bath) and then from 1951 to 1957 the University of Bristol: B.Sc. in chemistry (1954), Ph.D. (1958, mentor Frank S. Stone). He spent 1958-1959 at Philips Natuurkundig Laboratorium (group of Evert W. Gorter) then did postdoctoral research at Indiana University (mentor Walter J. Moore). 1960 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Groups In Three Dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries. Symmetry groups of geometric objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetries. All isometries of a bounded (finite) 3D object have one or more common fixed points. We follow the usual convention by choosing the origin as one of them. The symmetry group of an object is sometimes also called its full symmetry group, as opposed to its proper symmetry group, the intersection of its full symmetry group with E+(3), which consists of all ''direct isometries'', i.e., isometries preserving orientation. For a bounded object, the proper sy ... [...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] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius College, Camb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stewart Coffin
Stewart Coffin is an American puzzle maker. According to Ars Technica, he is considered to be one of the "best designers of polyhedral interlocking puzzles in the world." Biography Coffin majored in electrical engineering in college at the University of Massachusetts at Amherst where he graduated in 1953. He worked at the Lincoln Laboratory at the Massachusetts Institute of Technology (MIT) building computers from 1953 through 1958. In 1964, he left electronics to start building canoes and other boats. He and his family moved to a farm in Lincoln, Massachusetts. Coffin currently lives in Carlisle, Massachusetts, where he moved to in 2021. He has three daughters, all of whom are very good at solving his puzzles. Work Coffin began creating puzzles in 1968, after quitting the design and manufacture of canoes and kayaks. One of the puzzles he created, made of 12 hexagonal sticks and cast in epoxy, was brought to school by one of his three daughters. This event led to Coffin meetin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
