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73-457: Danish Dance Theatre was founded in 1981 as "New Danish Dance Theatre” by the English/Norwegian choreographer Randi Patterson in collaboration with Anette Abildgaard, Ingrid Buchholtz, Mikala Barnekow and soon after Warren Spears . They were passionate choreographers who did a great job of putting modern dance on the cultural map. The English-born ballet dancer and choreographer Tim Rushton

146-438: A n ) n = − ∞ ∞ {\textstyle {(a_{n})}_{n=-\infty }^{\infty }} is a bi-infinite sequence , and can also be written as ( … , a − 1 , a 0 , a 1 , a 2 , … ) {\textstyle (\ldots ,a_{-1},a_{0},a_{1},a_{2},\ldots )} . In cases where

219-464: A n ) . {\textstyle (a_{n}).} Here A is the domain, or index set, of the sequence. Sequences and their limits (see below) are important concepts for studying topological spaces. An important generalization of sequences is the concept of nets . A net is a function from a (possibly uncountable ) directed set to a topological space. The notational conventions for sequences normally apply to nets as well. The length of

292-431: A coherent whole.” Choreography consisting of ordinary motor activities, social dances, commonplace movements or gestures, or athletic movements may lack a sufficient amount of authorship to qualify for copyright protection. A recent lawsuit was brought by professional dancer and choreographer Kyle Hanagami, who sued Epic Games, alleging that the video game developer copied a portion of Hanagami’s copyrighted dance moves in

365-663: A distance from L {\displaystyle L} less than d {\displaystyle d} . For example, the sequence a n = n + 1 2 n 2 {\textstyle a_{n}={\frac {n+1}{2n^{2}}}} shown to the right converges to the value 0. On the other hand, the sequences b n = n 3 {\textstyle b_{n}=n^{3}} (which begins 1, 8, 27, ...) and c n = ( − 1 ) n {\displaystyle c_{n}=(-1)^{n}} (which begins −1, 1, −1, 1, ...) are both divergent. If

438-462: A function from an arbitrary index set. For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite , as in these examples, or infinite , such as the sequence of all even positive integers (2, 4, 6, ...). The position of an element in

511-599: A function of n . Nevertheless, holonomic sequences play an important role in various areas of mathematics. For example, many special functions have a Taylor series whose sequence of coefficients is holonomic. The use of the recurrence relation allows a fast computation of values of such special functions. Not all sequences can be specified by a recurrence relation. An example is the sequence of prime numbers in their natural order (2, 3, 5, 7, 11, 13, 17, ...). There are many different notions of sequences in mathematics, some of which ( e.g. , exact sequence ) are not covered by

584-416: A limit if the elements of the sequence become closer and closer to some value L {\displaystyle L} (called the limit of the sequence), and they become and remain arbitrarily close to L {\displaystyle L} , meaning that given a real number d {\displaystyle d} greater than zero, all but a finite number of the elements of the sequence have

657-483: A natural number N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} we have If ( a n ) {\displaystyle (a_{n})} is a sequence of complex numbers rather than a sequence of real numbers, this last formula can still be used to define convergence, with the provision that | ⋅ | {\displaystyle |\cdot |} denotes

730-1080: A new, more naturalistic style of choreography, including by Russian choreographer Michel Fokine (1880-1942) and Isadora Duncan (1878-1927), and since then styles have varied between realistic representation and abstraction. Merce Cunningham , George Balanchine , and Sir Frederick Ashton were all influential choreographers of classical or abstract dance, but Balanchine and Ashton, along with Martha Graham , Leonide Massine , Jerome Robbins and others also created representational works. Isadora Duncan loved natural movement and improvisation . The work of Alvin Ailey (1931-1989), an African-American dancer, choreographer, and activist, spanned many styles of dance, including ballet, jazz , modern dance, and theatre. Dances are designed by applying one or both of these fundamental choreographic methods: Several underlying techniques are commonly used in choreography for two or more dancers: Movements may be characterized by dynamics, such as fast, slow, hard, soft, long, and short. Today,

803-415: A recurrence relation is Recamán's sequence , defined by the recurrence relation with initial term a 0 = 0. {\displaystyle a_{0}=0.} A linear recurrence with constant coefficients is a recurrence relation of the form where c 0 , … , c k {\displaystyle c_{0},\dots ,c_{k}} are constants . There

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876-400: A sequence are discussed after the examples. The prime numbers are the natural numbers greater than 1 that have no divisors but 1 and themselves. Taking these in their natural order gives the sequence (2, 3, 5, 7, 11, 13, 17, ...). The prime numbers are widely used in mathematics , particularly in number theory where many results related to them exist. The Fibonacci numbers comprise

949-440: A sequence converges, then the value it converges to is unique. This value is called the limit of the sequence. The limit of a convergent sequence ( a n ) {\displaystyle (a_{n})} is normally denoted lim n → ∞ a n {\textstyle \lim _{n\to \infty }a_{n}} . If ( a n ) {\displaystyle (a_{n})}

1022-404: A sequence is defined as the number of terms in the sequence. A sequence of a finite length n is also called an n -tuple . Finite sequences include the empty sequence  ( ) that has no elements. Normally, the term infinite sequence refers to a sequence that is infinite in one direction, and finite in the other—the sequence has a first element, but no final element. Such a sequence

1095-467: A sequence is its rank or index ; it is the natural number for which the element is the image. The first element has index 0 or 1, depending on the context or a specific convention. In mathematical analysis , a sequence is often denoted by letters in the form of a n {\displaystyle a_{n}} , b n {\displaystyle b_{n}} and c n {\displaystyle c_{n}} , where

1168-463: A sequence is to list all its elements. For example, the first four odd numbers form the sequence (1, 3, 5, 7). This notation is used for infinite sequences as well. For instance, the infinite sequence of positive odd integers is written as (1, 3, 5, 7, ...). Because notating sequences with ellipsis leads to ambiguity, listing is most useful for customary infinite sequences which can be easily recognized from their first few elements. Other ways of denoting

1241-409: A sequence of integers whose pattern can be easily inferred. In these cases, the index set may be implied by a listing of the first few abstract elements. For instance, the sequence of squares of odd numbers could be denoted in any of the following ways. Moreover, the subscripts and superscripts could have been left off in the third, fourth, and fifth notations, if the indexing set was understood to be

1314-450: A sequence of sequences: ( ( a m , n ) n ∈ N ) m ∈ N {\textstyle ((a_{m,n})_{n\in \mathbb {N} })_{m\in \mathbb {N} }} denotes a sequence whose m th term is the sequence ( a m , n ) n ∈ N {\textstyle (a_{m,n})_{n\in \mathbb {N} }} . An alternative to writing

1387-565: Is monotonically decreasing if each consecutive term is less than or equal to the previous one, and is strictly monotonically decreasing if each is strictly less than the previous. If a sequence is either increasing or decreasing it is called a monotone sequence. This is a special case of the more general notion of a monotonic function . The terms nondecreasing and nonincreasing are often used in place of increasing and decreasing in order to avoid any possible confusion with strictly increasing and strictly decreasing , respectively. If

1460-474: Is a divergent sequence, then the expression lim n → ∞ a n {\textstyle \lim _{n\to \infty }a_{n}} is meaningless. A sequence of real numbers ( a n ) {\displaystyle (a_{n})} converges to a real number L {\displaystyle L} if, for all ε > 0 {\displaystyle \varepsilon >0} , there exists

1533-463: Is a general method for expressing the general term a n {\displaystyle a_{n}} of such a sequence as a function of n ; see Linear recurrence . In the case of the Fibonacci sequence, one has c 0 = 0 , c 1 = c 2 = 1 , {\displaystyle c_{0}=0,c_{1}=c_{2}=1,} and the resulting function of n

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1606-411: Is a simple classical example, defined by the recurrence relation with initial terms a 0 = 0 {\displaystyle a_{0}=0} and a 1 = 1 {\displaystyle a_{1}=1} . From this, a simple computation shows that the first ten terms of this sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, and 34. A complicated example of a sequence defined by

1679-401: Is a strictly increasing sequence of positive integers. Some other types of sequences that are easy to define include: An important property of a sequence is convergence . If a sequence converges, it converges to a particular value known as the limit . If a sequence converges to some limit, then it is convergent . A sequence that does not converge is divergent . Informally, a sequence has

1752-464: Is bi-infinite. This sequence could be denoted ( 2 n ) n = − ∞ ∞ {\textstyle {(2n)}_{n=-\infty }^{\infty }} . A sequence is said to be monotonically increasing if each term is greater than or equal to the one before it. For example, the sequence ( a n ) n = 1 ∞ {\textstyle {(a_{n})}_{n=1}^{\infty }}

1825-409: Is called a lower bound . If a sequence is both bounded from above and bounded from below, then the sequence is said to be bounded . A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the remaining elements. For instance, the sequence of positive even integers (2, 4, 6, ...) is a subsequence of

1898-465: Is called a singly infinite sequence or a one-sided infinite sequence when disambiguation is necessary. In contrast, a sequence that is infinite in both directions—i.e. that has neither a first nor a final element—is called a bi-infinite sequence , two-way infinite sequence , or doubly infinite sequence . A function from the set Z of all integers into a set, such as for instance the sequence of all even integers ( ..., −4, −2, 0, 2, 4, 6, 8, ... ),

1971-418: Is called an index , and the set of values that it can take is called the index set . It is often useful to combine this notation with the technique of treating the elements of a sequence as individual variables. This yields expressions like ( a n ) n ∈ N {\textstyle (a_{n})_{n\in \mathbb {N} }} , which denotes a sequence whose n th element

2044-408: Is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family , defined as

2117-416: Is easily discernible by inspection. Other examples are sequences of functions , whose elements are functions instead of numbers. The On-Line Encyclopedia of Integer Sequences comprises a large list of examples of integer sequences. Other notations can be useful for sequences whose pattern cannot be easily guessed or for sequences that do not have a pattern such as the digits of π . One such notation

2190-612: Is educated at the Royal Swedish Ballet School and has a master's degree in Contemporary Performing Arts from the University of Gothenburg. Pontus Lidberg has created works for several leading companies, including New York City Ballet, Paris Opera Ballet, Royal Danish Ballet, Wiener Staatsballett and Martha Graham Dance Company. For Danish Dance Company he has created the following works: Sirene, Kentaur (winner of

2263-406: Is given by Binet's formula . A holonomic sequence is a sequence defined by a recurrence relation of the form where c 1 , … , c k {\displaystyle c_{1},\dots ,c_{k}} are polynomials in n . For most holonomic sequences, there is no explicit formula for expressing a n {\displaystyle a_{n}} as

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2336-503: Is given by the variable a n {\displaystyle a_{n}} . For example: One can consider multiple sequences at the same time by using different variables; e.g. ( b n ) n ∈ N {\textstyle (b_{n})_{n\in \mathbb {N} }} could be a different sequence than ( a n ) n ∈ N {\textstyle (a_{n})_{n\in \mathbb {N} }} . One can even consider

2409-431: Is in contrast to the definition of sequences of elements as functions of their positions. To define a sequence by recursion, one needs a rule, called recurrence relation to construct each element in terms of the ones before it. In addition, enough initial elements must be provided so that all subsequent elements of the sequence can be computed by successive applications of the recurrence relation. The Fibonacci sequence

2482-404: Is monotonically increasing if and only if a n + 1 ≥ a n {\textstyle a_{n+1}\geq a_{n}} for all n ∈ N . {\displaystyle n\in \mathbf {N} .} If each consecutive term is strictly greater than (>) the previous term then the sequence is called strictly monotonically increasing . A sequence

2555-500: Is replaced by the expression dist ⁡ ( a n , L ) {\displaystyle \operatorname {dist} (a_{n},L)} , which denotes the distance between a n {\displaystyle a_{n}} and L {\displaystyle L} . If ( a n ) {\displaystyle (a_{n})} and ( b n ) {\displaystyle (b_{n})} are convergent sequences, then

2628-536: Is taken from the dance techniques of ballet , contemporary dance , jazz dance , hip hop dance , folk dance , techno , K-pop , religious dance, pedestrian movement, or combinations of these. The word choreography literally means "dance-writing" from the Greek words "χορεία" (circular dance, see choreia ) and "γραφή" (writing). It first appeared in the American English dictionary in the 1950s, and "choreographer"

2701-807: Is the longest-running choreography competition in the world (started c.  1982 ), organised by the Ballett Gesellschaft Hannover e.V. It took place online during the COVID-19 pandemic in 2020 and 2021, returning to the stage at the Theater am Aegi in 2022. Gregor Zöllig, head choreographer of dance at the Staatstheater Braunschweig was appointed artistic director of the competition in 2020. The main conditions of entry are that entrants must be under 40 years of age, and professionally trained. The competition has been run in collaboration with

2774-568: Is to write down a general formula for computing the n th term as a function of n , enclose it in parentheses, and include a subscript indicating the set of values that n can take. For example, in this notation the sequence of even numbers could be written as ( 2 n ) n ∈ N {\textstyle (2n)_{n\in \mathbb {N} }} . The sequence of squares could be written as ( n 2 ) n ∈ N {\textstyle (n^{2})_{n\in \mathbb {N} }} . The variable n

2847-595: The Tanja Liedtke Foundation since her death in 2008, and from 2021 a new production prize has been awarded by the foundation, to complement the five other production awards. The 2021 and 2022 awards were presented by Marco Goecke , then director of ballet at the Staatstheater Hannover . There are a number of other international choreography competitions, mostly focused on modern dance. These include: The International Online Dance Competition (IODC)

2920-441: The codomain of the sequence is fixed by context, for example by requiring it to be the set R of real numbers, the set C of complex numbers, or a topological space . Although sequences are a type of function, they are usually distinguished notationally from functions in that the input is written as a subscript rather than in parentheses, that is, a n rather than a ( n ) . There are terminological differences as well:

2993-427: The convergence properties of sequences. In particular, sequences are the basis for series , which are important in differential equations and analysis . Sequences are also of interest in their own right, and can be studied as patterns or puzzles, such as in the study of prime numbers . There are a number of ways to denote a sequence, some of which are more useful for specific types of sequences. One way to specify

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3066-422: The design itself. A choreographer is one who creates choreographies by practising the art of choreography, a process known as choreographing . It most commonly refers to dance choreography . In dance, choreography. may also refer to the design itself, which is sometimes expressed by means of dance notation . Dance choreography is sometimes called dance composition . Aspects of dance choreography include

3139-411: The limit of a sequence of rational numbers (e.g. via its decimal expansion , also see completeness of the real numbers ). As another example, π is the limit of the sequence (3, 3.1, 3.14, 3.141, 3.1415, ...), which is increasing. A related sequence is the sequence of decimal digits of π , that is, (3, 1, 4, 1, 5, 9, ...). Unlike the preceding sequence, this sequence does not have any pattern that

3212-420: The natural numbers . In the second and third bullets, there is a well-defined sequence ( a k ) k = 1 ∞ {\textstyle {(a_{k})}_{k=1}^{\infty }} , but it is not the same as the sequence denoted by the expression. Sequences whose elements are related to the previous elements in a straightforward way are often defined using recursion . This

3285-518: The "arranger of dance as a theatrical art", with one well-known master being of the late 18th century being Jean-Georges Noverre , with others following and developing techniques for specific types of dance, including Gasparo Angiolini , Jean Dauberval , Charles Didelot , and Salvatore Viganò . Ballet eventually developed its own vocabulary in the 19th century, and romantic ballet choreographers included Carlo Blasis , August Bournonville , Jules Perrot and Marius Petipa . Modern dance brought

3358-435: The 17th and 18th centuries, social dance became more separated from theatrical dance performances. During this time the word choreography was applied to the written record of dances, which later became known as dance notation , with the meaning of choreography shifting to its current use as the composition of a sequence of movements making up a dance performance. The ballet master or choreographer during this time became

3431-781: The Lumen Prize Nordic Award), Roaring Twenties, Ikaros, and Paysage Soudain La Nuit (restoration with dancers from A Costa Danza, Cuba and Dansk Danseteater) for Copenhagen Summer Dance. Marina Mascarell was appointed artistic director of Danish Dance Theater on April 1. 2023. She was born in Oliva, Spain and is a well-established choreographer. House choreographer at Korzo Theater in The Hague 2011-21, Associated Artist at Mercat de les Flors in Barcelona since 2019, and founder and artistic director of

3504-593: The MEI(s) Foundation. Marina Mascarell has created works for e.g. Nederlands Dans Theater 1 and 2, GöteborgOperans Dansekompani, Biennale de la Danse de Lyon with Lyon Opera Ballet, Skånes Dansteater, Dance Forum Tapei and The Australian Ballet, Sydney. She also collaborates with other artists in visual arts, film, music and theatre. Throughout her career, she has been recognized and awarded with numerous awards, e.g. BNG Excellent Dance Award 2015. Her first performance for Danish Dance Theatre “Køter” premiered in 2024 and

3577-686: The Reumert of the Year in 1999 for "Busy Being Blue", in 2005 for "Kridt", in 2006 for "Requiem" and in 2008 for "Labyrinth". In 2010, Danish Dance Theatre received Årets Reumert for best dance performance with “Frost” choreographed by Tina Tarpgaard. In 2012, Tim Rushton received the Bikuben’s Honorary Award. Other prizes include the award of Teaterkatten in November 2006 as best producer. In 2007 Danish Arts Foundation’s Prize for special works of art, in 2006 for

3650-486: The beautiful national stage, e.g. at Takkelloftet, where Danish Dance Theatre several times a year presents work, as well as access to the big stage at The Royal Danish Playhouse. In addition to the company’s intensive national and international touring activities, the company has great success with its yearly open-air performance Copenhagen Summer Dance that takes place at the harbor of Copenhagen. The company's former artistic director and chief choreographer Tim Rushton (MBE)

3723-638: The company's new artistic director. Since 2017, Danish Dance Company has had its permanent base at the Royal Opera House on Holmen , Copenhagen . The administrative, technical staff, and dancers are all at home here. The company is an independent institution with its own finances and framework agreement with the Ministry of Culture. The collaboration with the Royal Danish Theatre offers the opportunity to add more spectacular, modern dance performances to

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3796-441: The complex modulus, i.e. | z | = z ∗ z {\displaystyle |z|={\sqrt {z^{*}z}}} . If ( a n ) {\displaystyle (a_{n})} is a sequence of points in a metric space , then the formula can be used to define convergence, if the expression | a n − L | {\displaystyle |a_{n}-L|}

3869-528: The compositional use of organic unity , rhythmic or non-rhythmic articulation, theme and variation, and repetition. The choreographic process may employ improvisation for the purpose of developing innovative movement ideas. In general, choreography is used to design dances that are intended to be performed as concert dance . The art of choreography involves the specification of human movement and form in terms of space, shape, time and energy, typically within an emotional or non-literal context. Movement language

3942-422: The copyright claims after the district court concluded that his two-second, four-beat sequence of dance steps was not protectable under copyright law. Sequence In mathematics , a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set , it contains members (also called elements , or terms ). The number of elements (possibly infinite )

4015-432: The definitions and notations introduced below. In this article, a sequence is formally defined as a function whose domain is an interval of integers . This definition covers several different uses of the word "sequence", including one-sided infinite sequences, bi-infinite sequences, and finite sequences (see below for definitions of these kinds of sequences). However, many authors use a narrower definition by requiring

4088-697: The domain of a sequence in the subscript is to indicate the range of values that the index can take by listing its highest and lowest legal values. For example, the notation ( k 2 ) ) k = 1 10 {\textstyle (k^{2}){\vphantom {)}}_{k=1}^{10}} denotes the ten-term sequence of squares ( 1 , 4 , 9 , … , 100 ) {\displaystyle (1,4,9,\ldots ,100)} . The limits ∞ {\displaystyle \infty } and − ∞ {\displaystyle -\infty } are allowed, but they do not represent valid values for

4161-433: The domain of a sequence to be the set of natural numbers . This narrower definition has the disadvantage that it rules out finite sequences and bi-infinite sequences, both of which are usually called sequences in standard mathematical practice. Another disadvantage is that, if one removes the first terms of a sequence, one needs reindexing the remainder terms for fitting this definition. In some contexts, to shorten exposition,

4234-474: The index, only the supremum or infimum of such values, respectively. For example, the sequence ( a n ) n = 1 ∞ {\textstyle {(a_{n})}_{n=1}^{\infty }} is the same as the sequence ( a n ) n ∈ N {\textstyle (a_{n})_{n\in \mathbb {N} }} , and does not contain an additional term "at infinity". The sequence (

4307-434: The integer sequence whose elements are the sum of the previous two elements. The first two elements are either 0 and 1 or 1 and 1 so that the sequence is (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...). Other examples of sequences include those made up of rational numbers , real numbers and complex numbers . The sequence (.9, .99, .999, .9999, ...), for instance, approaches the number 1. In fact, every real number can be written as

4380-731: The main rules for choreography are that it must impose some kind of order on the performance, within the three dimensions of space as well the fourth dimension of time and the capabilities of the human body. In the performing arts , choreography applies to human movement and form. In dance , choreography is also known as dance choreography or dance composition. Choreography is also used in a variety of other fields, including opera , cheerleading , theatre , marching band , synchronized swimming , cinematography , ice skating , gymnastics , fashion shows , show choir , cardistry , video game production, and animated art . The International Choreographic Competition Hannover, Hanover , Germany,

4453-553: The performance: “Requiem”. In 2008 Danish Theater Association's honorary award. In 2009 Wilhelm Hansen Foundation’s Honorary Award. In 2011 Friends of the Ballet’s Honorary Award. Tim Rushton is now choreographer and artistic director of Kompagni B, the Royal Danish Ballet's Youth Company. The Swedish choreographer, dancer and filmmaker Pontus Lidberg was Danish Dance Theatre’s artistic director from 2018 to 2022. He

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4526-417: The popular game Fortnite. Hanagami published a YouTube video in 2017 featuring a dance he choreographed to the song "How Long" by Charlie Puth, and Hanagami claimed that Fortnight's "It's Complicated" "emote" copied a portion of his "How High" choreography. Hanagami's asserted claims for direct and contributory copyright infringement and unfair competition. Fortnite-maker Epic Games ultimately won dismissal of

4599-628: The positive integers (1, 2, 3, ...). The positions of some elements change when other elements are deleted. However, the relative positions are preserved. Formally, a subsequence of the sequence ( a n ) n ∈ N {\displaystyle (a_{n})_{n\in \mathbb {N} }} is any sequence of the form ( a n k ) k ∈ N {\textstyle (a_{n_{k}})_{k\in \mathbb {N} }} , where ( n k ) k ∈ N {\displaystyle (n_{k})_{k\in \mathbb {N} }}

4672-426: The sequence of real numbers ( a n ) is such that all the terms are less than some real number M , then the sequence is said to be bounded from above . In other words, this means that there exists M such that for all n , a n ≤ M . Any such M is called an upper bound . Likewise, if, for some real m , a n ≥ m for all n greater than some N , then the sequence is bounded from below and any such m

4745-457: The set of indexing numbers is understood, the subscripts and superscripts are often left off. That is, one simply writes ( a k ) {\textstyle (a_{k})} for an arbitrary sequence. Often, the index k is understood to run from 1 to ∞. However, sequences are frequently indexed starting from zero, as in In some cases, the elements of the sequence are related naturally to

4818-477: The subscript n refers to the n th element of the sequence; for example, the n th element of the Fibonacci sequence F {\displaystyle F} is generally denoted as F n {\displaystyle F_{n}} . In computing and computer science , finite sequences are usually called strings , words or lists , with the specific technical term chosen depending on

4891-494: The type of object the sequence enumerates and the different ways to represent the sequence in computer memory . Infinite sequences are called streams . The empty sequence ( ) is included in most notions of sequence. It may be excluded depending on the context. A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions , spaces , and other mathematical structures using

4964-543: The value of a sequence at the lowest input (often 1) is called the "first element" of the sequence, the value at the second smallest input (often 2) is called the "second element", etc. Also, while a function abstracted from its input is usually denoted by a single letter, e.g. f , a sequence abstracted from its input is usually written by a notation such as ( a n ) n ∈ A {\textstyle (a_{n})_{n\in A}} , or just as (

5037-480: Was a new staging of the original performance created for GöteborgOperans Danskompani in 2015. The performance toured around Denmark and is included in Danish Dance Theatre’s repertoire. Choreography Choreography is the art or practice of designing sequences of movements of physical bodies (or their depictions) in which motion or form or both are specified. Choreography may also refer to

5110-705: Was born in England and trained at the Royal Ballet Upper School, Covent Garden, London. He was employed as a ballet dancer at the Deutsche Oper am Rhein 1982-1986, Malmö Stadsteater 1985-1987, and the Royal Ballet 1987-1992, where he finished his dancing career to become a full time choreographer. During his time as head of Danish Dance Theatre, Tim Rushton was nominated 10 times for the Reumert Award and received

5183-548: Was first used as a credit for George Balanchine in the Broadway show On Your Toes in 1936. Before this, stage credits and movie credits used phrases such as "ensembles staged by", "dances staged by", or simply "dances by" to denote the choreographer. In Renaissance Italy , dance masters created movements for social dances which were taught, while staged ballets were created in a similar way. In 16th century France, French court dances were developed in an artistic pattern. In

5256-519: Was introduced in 2020 in response to the COVID-19 pandemic, with a Grand Prix worth US$ 1,000 . Section 102(a)(4) of the Copyright Act provides protection in “choreographic works” that were created after January 1, 1978, and are fixed in a tangible medium of expression. Under copyright law, choreography is “the composition and arrangement of a related series of dance movements and patterns organized into

5329-511: Was the company's artistic director from 2001 to 2018. He started by working with a permanent ensemble of full-time dancers, and as from 2010 the company is subsidiary recipient under the Danish government’s Finance Act. The Swedish choreographer, dancer and filmmaker Pontus Lidberg was artistic director from 2018 to 2022. In April 2022, the Spanish dancer and choreographer Marina Mascarell was appointed as

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