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Hendecagon
In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name ''hendecagon'', from Greek ''hendeka'' "eleven" and ''–gon'' "corner", is often preferred to the hybrid ''undecagon'', whose first part is formed from Latin ''undecim'' "eleven".) Regular hendecagon A '' regular hendecagon'' is represented by Schläfli symbol . A regular hendecagon has internal angles of 147. degrees (=147 \tfrac degrees). The area of a regular hendecagon with side length ''a'' is given by. :A = \fraca^2 \cot \frac \simeq 9.36564\,a^2. As 11 is not a Fermat prime, the regular hendecagon is not constructible with compass and straightedge. Because 11 is not a Pierpont prime, construction of a regular hendecagon is still impossible even with the usage of an angle trisector. Close approximations to the regular hendecagon can be constructed. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a unit circl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hendecagonal Prism
In geometry, the hendecagonal prism is one in an infinite set of convex prisms formed by square sides and two regular polygon caps, in this case two hendecagon In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name ''hendecagon'', from Greek ''hendeka'' "eleven" and ''–gon'' "corner", is often preferred to the hybrid ''undecagon'', whose first part is f ...s. So, it has 2 hendecagons and 11 squares as its faces. Related polyhedra External links * Prismatoid polyhedra {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hendecagram
In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name ''hendecagram'' combines a Greek numeral prefix, '' hendeca-'', with the Greek suffix ''-gram''. The ''hendeca-'' prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning " eleven". The ''-gram'' suffix derives from γραμμῆς (''grammēs'') meaning a line. Regular hendecagrams There are four regular hendecagrams, which can be described by the notation , , , and ; in this notation, the number after the slash indicates the number of steps between pairs of points that are connected by edges. These same four forms can also be considered as stellations of a regular hendecagon. Since 11 is prime, all hendecagrams are star polygons and not compound figures. Construction As with all odd regular polygons and star polygons whose orders are not products of distinct Fermat primes, the regular hendecagrams cannot be constructed with compass and straigh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compass And Straightedge
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neusis Construction
In geometry, the neusis (; ; plural: grc, νεύσεις, neuseis, label=none) is a geometric construction method that was used in antiquity by Greek mathematicians. Geometric construction The neusis construction consists of fitting a line element of given length () in between two given lines ( and ), in such a way that the line element, or its extension, passes through a given point . That is, one end of the line element has to lie on , the other end on , while the line element is "inclined" towards . Point is called the pole of the neusis, line the directrix, or guiding line, and line the catch line. Length is called the ''diastema'' ( el, διάστημα, lit=distance). A neusis construction might be performed by means of a marked ruler that is rotatable around the point (this may be done by putting a pin into the point and then pressing the ruler against the pin). In the figure one end of the ruler is marked with a yellow eye with crosshairs: this is the origin of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loonie
The loonie (french: huard), formally the Canadian one-dollar coin, is a gold-coloured Canadian coin that was introduced in 1987 and is produced by the Royal Canadian Mint at its facility in Winnipeg. The most prevalent versions of the coin show a common loon, a bird found throughout Canada, on the reverse and Queen Elizabeth II, the nation's head of state at the time of the coin's issue, on the obverse. Various commemorative and specimen-set editions of the coin with special designs replacing the loon on the reverse have been minted over the years. The coin's outline is an 11-sided Reuleaux polygon. Its diameter of 26.5 mm and its 11-sidedness matched that of the already-circulating Susan B. Anthony dollar in the United States, and its thickness of 1.95 mm was a close match to the latter's 2.0 mm. Its gold colour differed from the silver-coloured Anthony dollar; however, the succeeding Sacagawea and Presidential dollars matched the loonie's overall hue. Othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either convex polygon, convex, star polygon, star or Skew polygon, skew. In the limit (mathematics), limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a Line (geometry), straight line), if the edge length is fixed. General properties ''These properties apply to all regular polygons, whether convex or star polygon, star.'' A regular ''n''-sided polygon has rotational symmetry of order ''n''. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Together with the property of equal-length sides, this implies that every regular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierpont Prime
In number theory, a Pierpont prime is a prime number of the form 2^u\cdot 3^v + 1\, for some nonnegative integers and . That is, they are the prime numbers for which is 3-smooth. They are named after the mathematician James Pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. The same characterization applies to polygons that can be constructed using ruler, compass, and angle trisector, or using paper folding. Except for 2 and the Fermat primes, every Pierpont prime must be 1 modulo 6. The first few Pierpont primes are: It has been conjectured that there are infinitely many Pierpont primes, but this remains unproven. Distribution A Pierpont prime with is of the form 2^u+1, and is therefore a Fermat prime (unless ). If is positive then must also be positive (because 3^v+1 would be an even number greater than 2 and therefore not prime), and therefore the non-Fermat Piermont primes all have the form , when is a posi ... [...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 |
Directed Edge
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Dollar
The Canadian dollar ( symbol: $; code: CAD; french: dollar canadien) is the currency of Canada. It is abbreviated with the dollar sign $, there is no standard disambiguating form, but the abbreviation Can$ is often suggested by notable style guides for distinction from other dollar-denominated currencies. It is divided into 100 cents (¢). Owing to the image of a common loon on its reverse, the dollar coin, and sometimes the unit of currency itself, are sometimes referred to as the ''loonie'' by English-speaking Canadians and foreign exchange traders and analysts. Accounting for approximately 2% of all global reserves, the Canadian dollar is the fifth-most held reserve currency in the world, behind the U.S. dollar, the euro, the yen and sterling. The Canadian dollar is popular with central banks because of Canada's relative economic soundness, the Canadian government's strong sovereign position, and the stability of the country's legal and political systems. Histo ... [...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] |
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