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Mathematical Models (Cundy And Rollett), Mathematical Models
A mathematical model may mean a description of a physical system using mathematical concepts and language. "Mathematical model" may also refer to: *Model theory, a branch of mathematical logic, in which a model is an abstract structure that satisfies a set of logical sentences *Physical models of mathematical objects, created for instructional or artistic purposes, including: ** Polyhedron model, a physical model of a polyhedron ** ''Mathematical Models'' (Cundy and Rollett), a book about constructing models of mathematical objects for secondary-school education ** ''Mathematical Models'' (Fischer), a book of photographs and commentary on university collections of physical models of mathematical objects See also *Model (other) A model is an informative representation of an object, person or system, and serves as a substitute for the original. For example: * Machine learning model, a type of a mathematical model of reality in the context of machine learning * Model (perso . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their Structure (mathematical logic), models (those Structure (mathematical logic), structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be definable set, defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron Model
A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material. Since there are 75 uniform polyhedra, including the five regular convex polyhedra, five polyhedral compounds, four Kepler-Poinsot polyhedra, and thirteen Archimedean solids, constructing or collecting polyhedron models has become a common mathematical recreation. Polyhedron models are found in mathematics classrooms much as globes in geography classrooms. Polyhedron models are notable as three-dimensional proof-of-concepts of geometric theories. Some polyhedra also make great centerpieces, tree toppers, Holiday decorations, or symbols. The Merkaba religious symbol, for example, is a stellated octahedron. Constructing large models offer challenges in engineering structural design. Construction Construction begins by choosing a ''size'' of the model, either the ''length'' of its edges or the ''hei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Models (Cundy And Rollett)
''Mathematical Models'' is a book on the construction of physical models of mathematical objects for educational purposes. It was written by Martyn Cundy and A. P. Rollett, and published by the Clarendon Press in 1951, with a second edition in 1961. Tarquin Publications published a third edition in 1981. The vertex configuration of a uniform polyhedron, a generalization of the Schläfli symbol that describes the pattern of polygons surrounding each vertex, was devised in this book as a way to name the Archimedean solids, and has sometimes been called the ''Cundy–Rollett symbol'' as a nod to this origin. Topics The first edition of the book had five chapters, including its introduction which discusses model-making in general and the different media and tools with which one can construct models. The media used for the constructions described in the book include "paper, cardboard, plywood, plastics, wire, string, and sheet metal". The second chapter concerns plane geometry, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Models (Fischer)
''Mathematical Models: From the Collections of Universities and Museums – Photograph Volume and Commentary'' is a book on the physical models of concepts in mathematics that were constructed in the 19th century and early 20th century and kept as instructional aids at universities. It credits Gerd Fischer as editor, but its photographs of models are also by Fischer. It was originally published by Vieweg+Teubner Verlag for their bicentennial in 1986, both in German (titled ''Mathematische Modelle. Aus den Sammlungen von Universitäten und Museen. Mit 132 Fotografien. Bildband und Kommentarband'') and (separately) in English translation, in each case as a two-volume set with one volume of photographs and a second volume of mathematical commentary. Springer Spektrum reprinted it in a second edition in 2017, as a single dual-language volume. Topics The work consists of 132 full-page photographs of mathematical models, divided into seven categories, and seven chapters of mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
