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Equilateral Polygon
In geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, an equilateral polygon does not need to also be equiangular (have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon does not need to be a convex polygon: it could be concave or even self-intersecting. Examples All regular polygons and edge-transitive polygons are equilateral. When an equilateral polygon is non-crossing and cyclic (its vertices are on a circle) it must be regular. An equilateral quadrilateral must be convex; this polygon is a rhombus (possibly a square). A convex equilateral pentagon can be described by two consecutive angles, which together determine the other angles. However, equilateral pentagons, and equilateral polygons with more than five sides, can also be concave, and if concave pentagons are allowed then two angles are no longer sufficient to determine the sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, 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 manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incircle
In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle (at vertex , for example) and the external bisectors of the other two. The center of this excircle is called the excenter relative to the vertex , or the excenter of . Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometriae Dedicata
''Geometriae Dedicata'' is a mathematical journal, founded in 1972, concentrating on geometry and its relationship to topology, group theory and the theory of dynamical systems. It was created on the initiative of Hans Freudenthal in Utrecht, the Netherlands.. It is published by Springer Netherlands. The Editors-in-Chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ... are John R. Parker and Jean-Marc Schlenker.Journal website References External links Springer site Mathematics journals Springer Science+Business Media academic journals {{math-journal-stub ... [...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] |
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. In more modern usage, the length d of a diameter is also called the diameter. In this sense one speaks of diameter rather than diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r. :d = 2r \qquad\text\qquad r = \frac. For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perimeter
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter. Formulas The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with \int_0^L \mathrms, where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise smooth plane curve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinhardt Polygon
In geometry, a Reinhardt polygon is an equilateral polygon inscribed in a Reuleaux polygon. As in the regular polygons, each vertex of a Reinhardt polygon participates in at least one defining pair of the diameter of the polygon. Reinhardt polygons with n sides exist, often with multiple forms, whenever n is not a power of two. Among all polygons with n sides, the Reinhardt polygons have the largest possible perimeter for their diameter, the largest possible width for their diameter, and the largest possible width for their perimeter. They are named after Karl Reinhardt, who studied them in 1922. Definition and construction A Reuleaux polygon is a convex shape with circular-arc sides, each centered on a vertex of the shape and all having the same radius; an example is the Reuleaux triangle. These shapes are curves of constant width. Some Reuleaux polygons have side lengths that are irrational multiples of each other, but if a Reuleaux polygon has sides that can be partitioned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reuleaux Polygon
In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. These shapes are named after their prototypical example, the Reuleaux triangle, which in turn, is named after 19th-century German engineer Franz Reuleaux. The Reuleaux triangle can be constructed from an equilateral triangle by connecting each two vertices by a circular arc centered on the third vertex, and Reuleaux polygons can be formed by a similar construction from any regular polygon with an odd number of sides, or from certain irregular polygons. Every curve of constant width can be accurately approximated by Reuleaux polygons. They have been applied in coinage shapes. Construction If P is a convex polygon with an odd number of sides, in which each vertex is equidistant to the two opposite vertices and closer to all other vertices, then replacing each side of P by an arc centered at its opposite vertex produces a Reuleaux polygon. As a special case, this construction i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinhardt 15-gons
Reinhardt may refer to: * Reinhardt University, Waleska, Georgia, USA People * Reinhardt (surname) * Reinhardt Kristensen, Danish invertebrate biologist * Reinhardt Rahr, American politician Fictional characters * Reinhardt (''Overwatch''), a character from the 2016 video game * Reinhardt, a character from '' Fire Emblem: Thracia 776'' See also * Reinhard * Reinhart Reinhart is a given name or surname, and may refer to: Surname *Anna Barbara Reinhart (1730–1796), Swiss mathematician * Annie Reinhart (1942–2004), American politician from Missouri * Art Reinhart (1899–1946), Major League Baseball pitc ... * Rinehart * Operation Reinhard, a particularly deadly part of the Holocaust {{Disambig, given name Germanic given names German masculine given names Dutch masculine given names ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crux Mathematicorum
''Crux Mathematicorum'' is a scientific journal of mathematics published by the Canadian Mathematical Society. It contains mathematical problems for secondary school and undergraduate students. , its editor-in-chief is Kseniya Garaschuk. The journal was established in 1975, under the name ''Eureka'', by the Carleton-Ottawa Mathematics Association, with Léo Sauvé as its first editor-in-chief. It took the name ''Crux Mathematicorum'' with its fourth volume, in 1978, to avoid confusion with another journal ''Eureka'' published by the Cambridge University Mathematical Society. The Canadian Mathematical Society took over the journal in 1985, and soon afterwards G.W. (Bill) Sands became its new editor. Bruce L. R. Shawyer took over as editor in 1996. In 1997 it merged with another journal founded in 1988, ''Mathematical Mayhem'', to become ''Crux Mathematicorum with Mathematical Mayhem''. Jim Totten became editor in 2003, and Václav (Vazz) Linek replaced him in 2008. Ross Honsberger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagon
In geometry, a hexagon (from Ancient Greek, Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple polygon, simple (non-self-intersecting) hexagon is 720°. Regular hexagon A ''regular polygon, regular hexagon'' has Schläfli symbol and can also be constructed as a Truncation (geometry), truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral polygon, equilateral and equiangular polygon, equiangular. It is bicentric polygon, bicentric, meaning that it is both cyclic polygon, cyclic (has a circumscribed circle) and tangential polygon, tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed figure, inscribed circle). All internal angles are 120 degree (angle), degrees. A regular hexago ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonardo (journal)
''Leonardo'' is a peer-reviewed academic journal published by the MIT Press covering the application of contemporary science and technology to the arts and music. History ''Leonardo'' journal was established in 1968 by artist and scientist Frank Malina in Paris, France. ''Leonardo'' has published writings by artists who work with science- and technology-based art media for 50 years. Journal operations were moved to the San Francisco Bay Area by Frank's son Roger Malina, an astronomer and space scientist, who took over operations of the journal upon Frank Malina's death in 1981. In 1982, the International Society for the Arts Sciences and Technology (Leonardo/ISAST) was founded to further the aims of ''Leonardo'' by providing avenues of communication for artists working in contemporary media. The society also publishes ''Leonardo Music Journal'', the ''Leonardo Electronic Almanac'', ''Leonardo Reviews'', and the ''Leonardo Book Series''. All publications are produced in collabor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
