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Icons Of Mathematics
''Icons of Mathematics: An Exploration of Twenty Key Images'' is a book on elementary geometry for a popular audience. It was written by Roger B. Nelsen and Claudi Alsina, and published by the Mathematical Association of America in 2011 as volume 45 of their Dolciani Mathematical Expositions book series. Topics Each of the book's 20 chapters begins with an iconic mathematical diagram, and discusses an interrelated set of topics inspired by that diagram, including results in geometry, their proofs and visual demonstrations, background material, biographies of mathematicians, historical illustrations and quotations, and connections to real-world applications. The topics include: *The geometry of circles and triangles, star polygons, Platonic solids, and figurate numbers *The Pythagorean theorem, Thales's theorem on right triangles in semicircles, and geometric interpretations of the arithmetic mean, geometric mean, and harmonic mean *Dido's problem on surrounding as large an area a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icons Of Mathematics
''Icons of Mathematics: An Exploration of Twenty Key Images'' is a book on elementary geometry for a popular audience. It was written by Roger B. Nelsen and Claudi Alsina, and published by the Mathematical Association of America in 2011 as volume 45 of their Dolciani Mathematical Expositions book series. Topics Each of the book's 20 chapters begins with an iconic mathematical diagram, and discusses an interrelated set of topics inspired by that diagram, including results in geometry, their proofs and visual demonstrations, background material, biographies of mathematicians, historical illustrations and quotations, and connections to real-world applications. The topics include: *The geometry of circles and triangles, star polygons, Platonic solids, and figurate numbers *The Pythagorean theorem, Thales's theorem on right triangles in semicircles, and geometric interpretations of the arithmetic mean, geometric mean, and harmonic mean *Dido's problem on surrounding as large an area a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dido's Problem
In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n by its volume \operatorname(S), :\operatorname(S)\geq n \operatorname(S)^ \, \operatorname(B_1)^, where B_1\subset\R^n is a unit sphere. The equality holds only when S is a sphere in \R^n. On a plane, i.e. when n=2, the isoperimetric inequality relates the square of the circumference of a closed curve and the area of a plane region it encloses. ''Isoperimetric'' literally means "having the same perimeter". Specifically in \R ^2, the isoperimetric inequality states, for the length ''L'' of a closed curve and the area ''A'' of the planar region that it encloses, that : L^2 \ge 4\pi A, and that equality holds if and only if the curve is a circle. The isoperimetric problem is to determine a plane figure of the largest possible area whose bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Popular Mathematics Books
Popularity or social status is the quality of being well liked, admired or well known to a particular group. Popular may also refer to: In sociology * Popular culture * Popular fiction * Popular music * Popular science * Populace, the total population of a certain place ** Populism, a political philosophy, based on the idea that the common people are being exploited. * Informal usage or custom, as in popular names, as opposed to formal or scientific nomenclature Companies * Popular, Inc., also known as ''Banco Popular'', a financial services company * Popular Holdings, a Singapore-based educational book company * The Popular (department store), a chain of department stores in El Paso, Texas, from 1902 to 1995 * ''The Popular Magazine'', an American literary magazine that ran for 612 issues from November 1903 to October 1931 Media Music * "Popular" (Darren Hayes song) (2004), on the album ''The Tension and the Spark'' * "Popular" (Eric Saade song) (2011), on the al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tatami
A is a type of mat used as a flooring material in traditional Japanese-style rooms. Tatamis are made in standard sizes, twice as long as wide, about 0.9 m by 1.8 m depending on the region. In martial arts, tatami are the floor used for training in a dojo and for competition. Tatami are covered with a weft-faced weave of (common rush), on a warp of hemp or weaker cotton. There are four warps per weft shed, two at each end (or sometimes two per shed, one at each end, to cut costs). The (core) is traditionally made from sewn-together rice straw, but contemporary tatami sometimes have compressed wood chip boards or extruded polystyrene foam in their cores, instead or as well. The long sides are usually with brocade or plain cloth, although some tatami have no edging. History The term ''tatami'' is derived from the verb , meaning 'to fold' or 'to pile'. This indicates that the early tatami were thin and could be folded up when not used or piled in layers.Kodansha Encyclope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yin And Yang
Yin and yang ( and ) is a Chinese philosophy, Chinese philosophical concept that describes opposite but interconnected forces. In Chinese cosmology, the universe creates itself out of a primary chaos of material energy, organized into the cycles of yin and yang and formed into objects and lives. Yin is the receptive and yang the active principle, seen in all forms of change and difference such as the annual cycle (winter and summer), the landscape (north-facing shade and south-facing brightness), sexual coupling (female and male), the formation of both men and women as characters and sociopolitical history (disorder and order). Taiji (philosophy), Taiji or Tai chi () is a Chinese cosmological term for the "Supreme Ultimate" state of undifferentiated absolute and infinite potential, the oneness before duality, from which yin and yang originate. It can be compared with the old ''Wuji (philosophy), wuji'' (, "without pole"). In the cosmology pertaining to yin and yang, the mate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:Spiral ''American Heritage Dictionary of the English Language'', Houghton Mifflin Company, Fourth Edition, 2009. # a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point. # a three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis; a . The first definition describes a |
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (geometry), scaling (enlarging or reducing), possibly with additional translation (geometry), translation, rotation (mathematics), rotation and reflection (mathematics), reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruence (geometry), congruent to the result of a particular uniform scaling of the other. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. If two angles of a triangle h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rep-tile
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Martin Gardner in his "Mathematical Games" column in the May 1963 issue of ''Scientific American''. In 2012 a generalization of rep-tiles called self-tiling tile sets was introduced by Lee Sallows in ''Mathematics Magazine''. Terminology A rep-tile is labelled rep-''n'' if the dissection uses ''n'' copies. Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling. A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile. If the dissection uses ''n'' copies, the shape is said to be irrep-''n''. If all these sub-tiles are of different sizes then the tiling is additionally described as perfect. A shape that is rep-''n'' or irrep-''n'' is tri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon Triangulation
In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is . Triangulations may be viewed as special cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs. Polygon triangulation without extra vertices Over time, a number of algorithms have been proposed to triangulate a polygon. Special cases It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding diagonals from one vertex to all other non-nearest neighbor vertices. The total number of ways to triangulate a convex ''n''-gon by non-intersecting diagonals is the (''n''−2)nd Catalan number, which equals :\frac, a formula found by Leonhard Euler. A monotone polygon can be triangulated in linear time with either the algorithm of A. Fournier and D.Y. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve Of Constant Width
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. Standard examples are the circle and the Reuleaux triangle. These curves can also be constructed using circular arcs centered at crossings of an arrangement of lines, as the involutes of certain curves, or by intersecting circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line, and if the line crosses perpendicularly it does so at both crossings, separated by the width. By Barbier's theorem, the body's perimeter is exactly times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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