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Regular Figures
''Regular Figures'' is a book on polyhedra and symmetric patterns, by Hungarian geometer László Fejes Tóth. It was published in 1964 by Pergamon in London and Macmillan in New York. Topics ''Regular Figures'' is divided into two parts, "Systematology of the Regular Figures" and "Genetics of the Regular Figures", each in five chapters. Although the first part represents older and standard material, much of the second part is based on a large collection of research works by Fejes Tóth, published over the course of approximately 25 years, and on his previous exposition of this material in a 1953 German-language text. The first part of the book covers many of the same topics as a previously published book, '' Regular Polytopes'' (1947), by H. S. M. Coxeter, but with a greater emphasis on group theory and the classification of symmetry groups. Its first three chapters describe the symmetries that two-dimensional geometric objects can have: the 17 wallpaper groups of the Euclidean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhedr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tammes Problem
In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the nephew of pioneering botanist Jantina Tammes) who posed the problem in his 1930 doctoral dissertation on the distribution of pores on pollen grains.Pieter Merkus Lambertus Tammes (1930): ''On the number and arrangements of the places of exit on the surface of pollen-grains'', University of Groningen Mathematicians independent of Tammes began studying circle packing on the sphere in the early 1940s; it was not until twenty years later that the problem became associated with his name. It can be viewed as a particular special case of the generalized Thomson problem of minimizing the total Coulomb force of electrons in a spherical arrangement. Thus far, solutions have been proven only for small numbers of circles: 3 through 14, and 24. There ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'', also widely referred to as ''Science Magazine'', is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet which contains an electronic version of ''Mathematical Reviews'' and additionally contains citation information for over 3.5 million items as of 2018. Reviews Mathematical Reviews was founded by Otto E. Neugebauer in 1940 as an alternative to the German journal ''Zentralblatt für Mathematik'', which Neugebauer had also founded a decade earlier, but which under the Nazis had begun censoring reviews by and of Jewish mathematicians. The goal of the new journal was to give reviews of every mathematical research publication. As of November 2007, the ''Mathematical Reviews'' database contained information on over 2.2 million articles. The authors of reviews are volunteers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Books About Polyhedra
This is a list of books about polyhedra. Polyhedral models Cut-out kits * ''Advanced Polyhedra 1: The Final Stellation'', . ''Advanced Polyhedra 2: The Sixth Stellation'', . ''Advanced Polyhedra 3: The Compound of Five Cubes'', . * ''More Mathematical Curiosities'', Tarquin, . ''Make Shapes 1'', . ''Make Shapes 2'', . * ''Cut and Assemble 3-D Star Shapes'', 1997. ''Easy-To-Make 3D Shapes in Full Color'', 2000. * Origami * *Reviews of ''3D Geometric Origami: Modular Origami Polyhedra'': * * * * ''Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality'', 2002.Reviews of ''Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality'': * * ''Beginner's Book of Modular Origami Polyhedra: The Platonic Solids'', 2008. ''Modular Origami Polyhedra'', also with Lewis Simon, 2nd ed., 1999.Reviews of ''Modular Origami Polyhedra'' (2nd ed.): * * * * ''A Plethora of Polyhedra in Origami'', Dover, 2002. Other model-making * 2nd ed., 1961. 3rd ed., Tarquin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patrick Du Val
Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Early life Du Val was born in Cheadle Hulme, Cheshire. He was the son of a cabinet maker, but his parents' marriage broke up. As a child, he suffered ill-health, in particular asthma, and was educated mostly by his mother. He was awarded a first class honours degree from the University of London External Programme in 1926, which he took by correspondence course. He was a talented linguist, for example teaching himself Norwegian so that he might read Peer Gynt. He also had a strong interest in history but his love of mathematics led him to pursue that as a career. His earliest publications show a leaning towards applied mathematics. His mother moved to a village near Cambridge and he became acquainted with Henry Baker, Lowndean P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Ambrose Rogers
Claude Ambrose Rogers FRS (1 November 1920 – 5 December 2005) was an English mathematician who worked in analysis and geometry. Research Much of his work concerns the Geometry of Numbers, Hausdorff Measures, Analytic Sets, Geometry and Topology of Banach Spaces, Selection Theorems and Finite-dimensional Convex Geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky–Rogers lemma and the Dvoretzky–Rogers theorem, both with Aryeh Dvoretzky. He constructed a counterexample to a conjecture related to the Busemann–Petty problem. In the geometry of numbers, the Rogers bound is a bound for dense packings of spheres. Awards and honours Rogers was elected a Fellow of the Royal Society (FRS) in 1959. He won the London Mathematical Society's De Morgan Medal The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Edge (mathematician)
William Leonard Edge FRSE (8 November 1904 – 27 September 1997) was a British mathematician most known for his work in finite geometry. Students knew him as WLE. Life Born in Stockport to schoolteacher parents (his father William Henry Edge being a headmaster), Edge attended Stockport Grammar School before winning a place at Trinity College, Cambridge in 1923 with an entrance scholarship, later graduating MA DSc. In 1928 Trinity College made him a Research Fellow and he was also an Allen Scholar. William Edge was a geometry student of H. F. Baker at Cambridge. Edge's dissertation extended Luigi Cremona’s 1868 delineation of the quadric ruled surfaces in projective 3-space RP3. Edge made a "systematic classification of the quintic and sextic ruled surfaces of three-dimensional projective space." In 1932 E. T. Whittaker invited Edge to lecture at University of Edinburgh. An anachronism, Edge never drove a motor car and disdained the mass-media of radio and television; he wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Urban Planning
Urban planning, also known as town planning, city planning, regional planning, or rural planning, is a technical and political process that is focused on the development and design of land use and the built environment, including air, water, and the infrastructure passing into and out of urban areas, such as transportation, communications, and distribution networks and their accessibility. Traditionally, urban planning followed a top-down approach in master planning the physical layout of human settlements. The primary concern was the public welfare, which included considerations of efficiency, sanitation, protection and use of the environment, as well as effects of the master plans on the social and economic activities. Over time, urban planning has adopted a focus on the social and environmental bottom-lines that focus on planning as a tool to improve the health and well-being of people while maintaining sustainability standards. Sustainable development was added as one of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Anaglyph 3D
Anaglyph 3D is the stereoscopic 3D effect achieved by means of encoding each eye's image using filters of different (usually chromatically opposite) colors, typically red and cyan. Anaglyph 3D images contain two differently filtered colored images, one for each eye. When viewed through the "color-coded" "anaglyph glasses", each of the two images reaches the eye it's intended for, revealing an integrated stereoscopic image. The visual cortex of the brain fuses this into the perception of a three-dimensional scene or composition. Anaglyph images have seen a recent resurgence due to the presentation of images and video on the Web, Blu-ray Discs, CDs, and even in print. Low cost paper frames or plastic-framed glasses hold accurate color filters that typically, after 2002, make use of all 3 primary colors. The current norm is red and cyan, with red being used for the left channel. The cheaper filter material used in the monochromatic past dictated red and blue for convenience and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jensen's Inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations. Jensen's inequality generalizes the statement that the secant line of a convex function lies ''above'' the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function (for ''t'' ∈ ,1, :t f(x_1) + (1-t) f(x_2), while t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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