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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] |
Neusis Construction
In geometry, the neusis (; ; plural: ) 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'' (). 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 the scale division on the ruler. A second marking on the ruler (the blue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hendecagram
In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven Vertex (geometry), vertices. The name ''hendecagram'' combines a Greek numeral prefix, ''wikt:hendeca-, hendeca-'', with the Greek language, Greek suffix ''wikt:-gram, -gram''. The ''hendeca-'' prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning "11 (number), 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 Stellation#Stellating polygons, 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 produ ... [...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 Idealization (science philosophy), idealized ruler and a Compass (drawing tool), compass. 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 it 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' or ''corners''. 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. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain. A simple polygon is the boundary of a region of the plane that is called a ''solid polygon''. The interior of a solid polygon is its ''body'', also known as a ''polygonal region'' or ''polygonal area''. In contexts where one is concerned only with simple and solid polygons, a ''polygon'' may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polyg ... [...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'' or ''star polygon, star''. 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 polygon also h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loonie
The loonie (), 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. Beginning in December 2023, a new version featuring King Charles III entered circulation, to replace the version featuring Elizabeth II. The coin's outline is an 11-sided Reuleaux polygon. Its diameter of and its 11-sidedness match that of the already-circulating Susan B. Anthony dollar in the United States, and its thickness of is a close match to the latter's . Its gold colour differs from the silver-coloured Anthony dollar; however, ... [...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 Pierpont primes all have the form , when is a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius Coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaim Goodman-Strauss
Chaim Goodman-Strauss (born June 22, 1967 in Austin, Texas) is an American mathematician who works in convex geometry, especially aperiodic tiling. He retired from the faculty of the University of Arkansas and currently serves as outreach mathematician for the National Museum of Mathematics. He is co-author with John H. Conway and Heidi Burgiel 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 John Edwin Luecke. He joined the faculty at the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. 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. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Dollar
The Canadian dollar (currency symbol, symbol: $; ISO 4217, code: CAD; ) is the currency of Canada. It is abbreviated with the dollar sign $. There is no standard disambiguating form, but the abbreviations Can$, CA$ and C$ are frequently used for distinction from other dollar-denominated currencies (though C$ remains ambiguous with the Nicaraguan córdoba). It is divided into 100 cent (currency), cents (¢). Owing to the image of a common loon on its reverse, the dollar coin, and sometimes the unit of currency itself, may be metonymy, referred to as the ''loonie'' by English-speaking Canadians and foreign exchange traders and analysts. Accounting for approximately two per cent of all global reserves, the Canadian dollar is the fifth-most held reserve currency in the world, behind the United States dollar, US dollar, euro, Japanese yen, yen, and pound sterling, sterling. The Canadian dollar is popular with central banks because of Canada's relative economic soundness, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
