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35-666: [REDACTED] Look up xi in Wiktionary, the free dictionary. XI may refer to: 11 (number) , XI in Roman numerals First XI of a cricket or football team XI monogram , an early Christian symbol XI (album) , an album by Metal Church X.I., a fictional supercomputer in the video game Terminal Velocity Northern Ireland, ISO 3166-1 alpha-2 country code used for tax purposes See also [ edit ] Xi (disambiguation) 11 (disambiguation) Topics referred to by

70-560: A Mersenne prime is 11. 11 is part of a pair of Brown numbers . Only three such pairs of numbers are known. Rows in Pascal's triangle can be seen as representation of powers of 11. An 11-sided polygon is called a hendecagon , or undecagon . A regular hendecagon is the polygon with the fewest number of sides that is not able to be constructed with a straightedge, compass, and angle trisector . The Mathieu group M 11 {\displaystyle \mathrm {M} _{11}}

105-402: A bassoon , not counting the whisper key. (A few bassoons have a 12th thumb key.) In sports, there are 11 players on an association football (soccer) team, 11 players on an American football team during play, 11 players on a cricket team on the field, and 11 players in a field hockey team. In the game of blackjack , an ace can count as either one or 11, whichever is more advantageous for

140-398: A polygon ( / ˈ p ɒ l ɪ ɡ ɒ n / ) 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

175-494: A given perimeter, the one with the largest area is regular (and therefore cyclic). Many specialized formulas apply to the areas of regular polygons . The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by This radius is also termed its apothem and is often represented as a . The area of a regular n -gon in terms of the radius R of its circumscribed circle can be expressed trigonometrically as: The area of

210-401: A regular n -gon inscribed in a unit-radius circle, with side s and interior angle α , {\displaystyle \alpha ,} can also be expressed trigonometrically as: The area of a self-intersecting polygon can be defined in two different ways, giving different answers: Using the same convention for vertex coordinates as in the previous section, the coordinates of

245-399: A simple formula for the polygon's area based on the numbers of interior and boundary grid points: the former number plus one-half the latter number, minus 1. In every polygon with perimeter p and area A , the isoperimetric inequality p 2 > 4 π A {\displaystyle p^{2}>4\pi A} holds. For any two simple polygons of equal area,

280-459: Is a 2-dimensional example of the more general polytope in any number of dimensions. There are many more generalizations of polygons defined for different purposes. The word polygon derives from the Greek adjective πολύς ( polús ) 'much', 'many' and γωνία ( gōnía ) 'corner' or 'angle'. It has been suggested that γόνυ ( gónu ) 'knee' may be the origin of gon . Polygons are primarily classified by

315-439: Is commonly called the shoelace formula or surveyor's formula . The area A of a simple polygon can also be computed if the lengths of the sides, a 1 , a 2 , ..., a n and the exterior angles , θ 1 , θ 2 , ..., θ n are known, from: The formula was described by Lopshits in 1963. If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives

350-459: 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 polygons and other self-intersecting polygons . Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon ), even when the chain does not lie in a single plane. A polygon

385-609: Is different from Wikidata All article disambiguation pages All disambiguation pages 11 (number) "Eleven" derives from the Old English ęndleofon , which is first attested in Bede 's late 9th-century Ecclesiastical History of the English People . It has cognates in every Germanic language (for example, German elf ), whose Proto-Germanic ancestor has been reconstructed as * ainalifa- , from

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420-451: Is large, this approaches one half. Or, each vertex inside the square mesh connects four edges (lines). The imaging system calls up the structure of polygons needed for the scene to be created from the database. This is transferred to active memory and finally, to the display system (screen, TV monitors etc.) so that the scene can be viewed. During this process, the imaging system renders polygons in correct perspective ready for transmission of

455-429: 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

490-515: Is the maximal subgroup Mathieu group M 12 {\displaystyle \mathrm {M} _{12}} , where 11 is also its largest prime factor. In chemistry, Group 11 of the Periodic Table of the Elements ( IUPAC numbering) consists of the three coinage metals copper , silver , and gold known from antiquity, and roentgenium , a recently synthesized superheavy element. 11

525-472: Is the first compound number in many other languages: Chinese 十一 shí yī , Korean 열하나 yeol hana or 십일 ship il . The number 11 (alongside its multiples 22 and 33) are master numbers in numerology , especially in New Age . Grimes, James. "Eleven" . Numberphile . Brady Haran . Archived from the original on 2017-10-15 . Retrieved 2016-01-03 . Polygon In geometry ,

560-548: Is the number of spacetime dimensions in M-theory . Apollo 11 was the first crewed spacecraft to land on the Moon . In our solar system, the Sun has a sunspot cycle 's periodicity that is approximately 11 years. The interval of an octave plus a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale . Regarding musical instruments , there are 11 thumb keys on

595-439: Is the smallest of twenty-six sporadic groups . It has order 7920 = 2 4 ⋅ 3 2 ⋅ 5 ⋅ 11 = 8 ⋅ 9 ⋅ 10 ⋅ 11 {\displaystyle 7920=2^{4}\cdot 3^{2}\cdot 5\cdot 11=8\cdot 9\cdot 10\cdot 11} , with 11 as its largest prime factor. M 11 {\displaystyle \mathrm {M} _{11}}

630-461: The Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. However, if the polygon is simple and cyclic then the sides do determine the area. Of all n -gons with given side lengths, the one with the largest area is cyclic. Of all n -gons with

665-613: The Giant's Causeway in Northern Ireland , or at the Devil's Postpile in California . In biology , the surface of the wax honeycomb made by bees is an array of hexagons , and the sides and base of each cell are also polygons. In computer graphics , a polygon is a primitive used in modelling and rendering. They are defined in a database, containing arrays of vertices (the coordinates of

700-666: The eleventh hour means the last possible moment to take care of something, and often implies a situation of urgent danger or emergency (see Doomsday clock ). "The eleventh hour" is a phrase in the Parable of the Workers in the Vineyard in the Bible. While 11 has its own name in Germanic languages such as English, German, or Swedish, and some Latin-based languages such as Spanish, Portuguese, and French, it

735-456: The geometrical vertices , as well as other attributes of the polygon, such as color, shading and texture), connectivity information, and materials . Any surface is modelled as a tessellation called polygon mesh . If a square mesh has n + 1 points (vertices) per side, there are n squared squares in the mesh, or 2 n squared triangles since there are two triangles in a square. There are ( n + 1) / 2( n ) vertices per triangle. Where n

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770-488: The regular star pentagon is also known as the pentagram . To construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows. The "kai" term applies to 13-gons and higher and was used by Kepler , and advocated by John H. Conway for clarity of concatenated prefix numbers in the naming of quasiregular polyhedra , though not all sources use it. Polygons have been known since ancient times. The regular polygons were known to

805-526: The ancient Greeks, with the pentagram , a non-convex regular polygon ( star polygon ), appearing as early as the 7th century B.C. on a krater by Aristophanes , found at Caere and now in the Capitoline Museum . The first known systematic study of non-convex polygons in general was made by Thomas Bradwardine in the 14th century. In 1952, Geoffrey Colin Shephard generalized the idea of polygons to

840-453: The centroid of a solid simple polygon are In these formulas, the signed value of area A {\displaystyle A} must be used. For triangles ( n = 3 ), the centroids of the vertices and of the solid shape are the same, but, in general, this is not true for n > 3 . The centroid of the vertex set of a polygon with n vertices has the coordinates The idea of a polygon has been generalized in various ways. Some of

875-426: The complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons . Polygons appear in rock formations, most commonly as the flat facets of crystals , where the angles between the sides depend on the type of mineral from which the crystal is made. Regular hexagons can occur when the cooling of lava forms areas of tightly packed columns of basalt , which may be seen at

910-833: The more important include: The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek -derived numerical prefix with the suffix -gon , e.g. pentagon , dodecagon . The triangle , quadrilateral and nonagon are exceptions. Beyond decagons (10-sided) and dodecagons (12-sided), mathematicians generally use numerical notation, for example 17-gon and 257-gon. Exceptions exist for side counts that are easily expressed in verbal form (e.g. 20 and 30), or are used by non-mathematicians. Some special polygons also have their own names; for example

945-552: The notation ( x n , y n ) = ( x 0 , y 0 ) will also be used. If the polygon is non-self-intersecting (that is, simple ), the signed area is or, using determinants where Q i , j {\displaystyle Q_{i,j}} is the squared distance between ( x i , y i ) {\displaystyle (x_{i},y_{i})} and ( x j , y j ) . {\displaystyle (x_{j},y_{j}).} The signed area depends on

980-525: The number of sides. Polygons may be characterized by their convexity or type of non-convexity: The property of regularity may be defined in other ways: a polygon is regular if and only if it is both isogonal and isotoxal, or equivalently it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon . Euclidean geometry is assumed throughout. Any polygon has as many corners as it has sides. Each corner has several angles. The two most important ones are: In this section,

1015-423: The ordering of the vertices and of the orientation of the plane. Commonly, the positive orientation is defined by the (counterclockwise) rotation that maps the positive x -axis to the positive y -axis. If the vertices are ordered counterclockwise (that is, according to positive orientation), the signed area is positive; otherwise, it is negative. In either case, the area formula is correct in absolute value . This

1050-566: The player. In the mockumentary film This Is Spinal Tap , the idiomatic phrase up to eleven is coined to allude to going beyond the limitations of a system, in this case music amplifier volume levels. The stylized maple leaf on the Flag of Canada has 11 points. The CA$ one-dollar loonie is in the shape of an 11-sided hendecagon , and clocks depicted on Canadian currency , like the Canadian 50-dollar bill , show 11:00. Being one hour before 12:00,

1085-523: The prefix * aina- (adjectival " one ") and suffix * -lifa- , of uncertain meaning. It is sometimes compared with the Lithuanian vienúolika , though -lika is used as the suffix for all numbers from 11 to 19 (analogously to "-teen"). The Old English form has closer cognates in Old Frisian , Saxon , and Norse , whose ancestor has been reconstructed as * ainlifun . This

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1120-426: The processed data to the display system. Although polygons are two-dimensional, through the system computer they are placed in a visual scene in the correct three-dimensional orientation. In computer graphics and computational geometry , it is often necessary to determine whether a given point P = ( x 0 , y 0 ) {\displaystyle P=(x_{0},y_{0})} lies inside

1155-401: The same term [REDACTED] This disambiguation page lists articles associated with the title XI . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=XI&oldid=1217014465 " Category : Disambiguation pages Hidden categories: Short description

1190-417: The vertices of the polygon under consideration are taken to be ( x 0 , y 0 ) , ( x 1 , y 1 ) , … , ( x n − 1 , y n − 1 ) {\displaystyle (x_{0},y_{0}),(x_{1},y_{1}),\ldots ,(x_{n-1},y_{n-1})} in order. For convenience in some formulas,

1225-408: Was formerly thought to be derived from Proto-Germanic * tehun (" ten "); it is now sometimes connected with * leikʷ- or * leip- ("left; remaining"), with the implicit meaning that "one is left" after counting to ten. 11 is a prime number , and a super-prime . 11 forms a twin prime with 13 , and sexy pair with 5 and 17. The first prime exponent that does not yield

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