Westminster is an area of central London within the City of Westminster, part of the West End, on the north bank of the River Thames. Historically the area lay within St Margarets parish, City & Liberty of Westminster and it has been the home of the permanent institutions of Englands government continuously since about 1200 and is now the seat of British government. In a government context, Westminster often refers to the Parliament of the United Kingdom, the closest tube stations are Westminster, St Jamess Park on the Jubilee and District lines. Within the area is Westminster School, a public school which grew out of the Abbey. Bounding Westminster to the north is Green Park, a Royal Park of London, the area has a substantial resident population, indeed most of its listed buildings are residential. A proportion of residents are people of limited means, living in council, large Victorian homes and barracks exist nearer to Buckingham Palace. The name describes an area no more than 1 mile from Westminster Abbey, the settlement grew up around the palace and abbey, as a service area for them.
The need for a church, St Margarets Westminster for the servants of the palace. It became larger and in the Georgian period became connected through urban development with the City along the Strand. It did not become a local government unit until created as a civil parish. Indeed, the Cathedral and diocesan status of the church lasted only from 1539 to 1556, as such it is first known to have had two Members of Parliament in 1545 as a new Parliamentary Borough, centuries after the City of London and Southwark were enfranchised. The historic core of Westminster is the former Thorney Island on which Westminster Abbey was built, the abbey became the traditional venue of the coronation of the kings and queens of England from that of Harold Godwinson onwards. From about 1200, near the abbey, the Palace of Westminster became the royal residence, marked by the transfer of royal treasury. Later the palace housed the developing Parliament and Englands law courts, thus London developed two focal points, the City of London and Westminster.
The monarchs moved to St James Palace and the Palace of Whitehall a little towards the north-east, the main law courts have since moved to the Royal Courts of Justice. The Westminster area formed part of the City and Liberty of Westminster in Middlesex, the ancient parish was St Margaret, after 1727 this became the civil parish of St Margaret and St John, the latter a new church required for the increasing population. The area around Westminster Abbey formed the extra-parochial Close of the Collegiate Church of St Peter surrounded by —, until 1900 the local authority was the combined vestry of St Margaret and St John, which was based at Westminster City Hall in Caxton Street from 1883. The Liberty of Westminster, governed by the Westminster Court of Burgesses, included St Martin in the Fields, Westminster had its own quarter sessions, but the Middlesex sessions had jurisdiction
Darth Vader, known by his birth name Anakin Skywalker, is a fictional character in the Star Wars franchise. The character was created by George Lucas and has been portrayed by numerous actors and his appearances span the first six Star Wars films, as well as Rogue One, and his character is heavily referenced in Star Wars, The Force Awakens. He is an important character in the Star Wars expanded universe of television series, video games, novels and comic books. Originally a Jedi prophesied to bring balance to the Force, he falls to the side of the Force and serves the evil Galactic Empire at the right hand of his Sith master. He is the father of Luke Skywalker and Princess Leia Organa, grandfather of Kylo Ren, Darth Vader has become one of the most iconic villains in popular culture, and has been listed among the greatest villains and fictional characters ever. The American Film Institute listed him as the third greatest movie villain in history on 100 Years. 100 Heroes and Villains, behind Hannibal Lecter and Norman Bates, other critics consider him a tragic hero, citing his original motivations for the greater good before his fall to the dark side.
After the success of the original Star Wars, series creator George Lucas hired science fiction author Leigh Brackett to write the sequel with him and they held story conferences and, by late November 1977, Lucas had produced a handwritten treatment. The treatment is similar to the film, except that Vader does not reveal he is Lukes father. In the first draft that Brackett would write from this, Lukes father appears as a ghost to instruct Luke, Lucas was disappointed with the script, but Brackett died of cancer before he could discuss it with her. With no writer available, Lucas had to write the next draft himself, in this draft, he made use of a new plot twist, Vader claiming to be Lukes father. According to Lucas, he found this draft enjoyable to write, the new plot element of Lukes parentage had drastic effects on the series. Anakin battled Kenobi on the site of a volcano and was badly wounded, Kenobi hid Luke on Tatooine while the Galactic Republic became the tyrannical Galactic Empire and Vader systematically hunted down and killed the Jedi.
This change in character would provide a springboard to the Tragedy of Darth Vader storyline that underlies the prequel trilogy, after deciding to create the prequel trilogy, Lucas indicated the series would be a tragic one depicting Anakins fall to the dark side. He saw that the prequels could form the beginning of one story that started with Anakins childhood. This was the step towards turning the film series into a saga. For the first prequel, Star Wars, Episode I – The Phantom Menace, Movie trailers focused on Anakin and a one-sheet poster showing him casting Vaders shadow informed otherwise unknowing audiences of the characters eventual fate. The movie ultimately achieved a goal of introducing audiences to Anakin
London /ˈlʌndən/ is the capital and most populous city of England and the United Kingdom. Standing on the River Thames in the south east of the island of Great Britain and it was founded by the Romans, who named it Londinium. Londons ancient core, the City of London, largely retains its 1. 12-square-mile medieval boundaries. London is a global city in the arts, education, fashion, healthcare, professional services and development, tourism. It is crowned as the worlds largest financial centre and has the fifth- or sixth-largest metropolitan area GDP in the world, London is a world cultural capital. It is the worlds most-visited city as measured by international arrivals and has the worlds largest city airport system measured by passenger traffic, London is the worlds leading investment destination, hosting more international retailers and ultra high-net-worth individuals than any other city. Londons universities form the largest concentration of education institutes in Europe. In 2012, London became the first city to have hosted the modern Summer Olympic Games three times, London has a diverse range of people and cultures, and more than 300 languages are spoken in the region.
Its estimated mid-2015 municipal population was 8,673,713, the largest of any city in the European Union, Londons urban area is the second most populous in the EU, after Paris, with 9,787,426 inhabitants at the 2011 census. The citys metropolitan area is the most populous in the EU with 13,879,757 inhabitants, the city-region therefore has a similar land area and population to that of the New York metropolitan area. London was the worlds most populous city from around 1831 to 1925, Other famous landmarks include Buckingham Palace, the London Eye, Piccadilly Circus, St Pauls Cathedral, Tower Bridge, Trafalgar Square, and The Shard. The London Underground is the oldest underground railway network in the world, the etymology of London is uncertain. It is an ancient name, found in sources from the 2nd century and it is recorded c.121 as Londinium, which points to Romano-British origin, and hand-written Roman tablets recovered in the city originating from AD 65/70-80 include the word Londinio. The earliest attempted explanation, now disregarded, is attributed to Geoffrey of Monmouth in Historia Regum Britanniae and this had it that the name originated from a supposed King Lud, who had allegedly taken over the city and named it Kaerlud.
From 1898, it was accepted that the name was of Celtic origin and meant place belonging to a man called *Londinos. The ultimate difficulty lies in reconciling the Latin form Londinium with the modern Welsh Llundain, which should demand a form *lōndinion, from earlier *loundiniom. The possibility cannot be ruled out that the Welsh name was borrowed back in from English at a date, and thus cannot be used as a basis from which to reconstruct the original name. Until 1889, the name London officially applied only to the City of London, two recent discoveries indicate probable very early settlements near the Thames in the London area
Southwark is a district of Central London and part of the London Borough of Southwark. Situated 1.5 miles east of Charing Cross, it one of the oldest parts of London. It historically formed an ancient borough in the county of Surrey, made up of a number of parishes, as an inner district of London, Southwark experienced rapid depopulation during the late-19th and early-20th centuries. It is now at a stage of regeneration and is the county town of Greater London which is the location of the City Hall offices of the Greater London Authority. Southwark had a population of 30,119 in 2011, Southwark is recorded in the 1086 Domesday Book as Sudweca. The name means southern defensive work and is formed from the Old English sūth, the southern location is in reference to the City of London to the north, Southwark being at the southern end of London Bridge. The ancient borough of Southwark was simply as The Borough—or Borough—and this name. Southwark was referred to as the Ward of Bridge Without when administered by the City.
Southwark is on a marshy area south of the River Thames. Recent excavation has revealed prehistoric activity including evidence of ploughing, burial mounds. The area was originally a series of islands in the River Thames and this formed the best place to bridge the Thames and the area became an important part of Londinium owing its importance to its position as the endpoint of the Roman London Bridge. Two Roman roads, Stane Street and Watling Street, met at Southwark in what is now Borough High Street, archaeological work at Tabard Street in 2004 discovered a plaque with the earliest reference to London from the Roman period on it. Londinium was abandoned at the end of the Roman occupation in the fifth century. Archaeologically, evidence of settlement is replaced by a largely featureless soil called the Dark Earth which probably represents an urban area abandoned, Southwark appears to recover only during the time of King Alfred and his successors. Sometime about 886 AD, the burh of Southwark was created and it was probably fortified to defend the bridge and hence the re-emerging City of London to the north.
He failed to force the bridge during the Norman conquest of England, Southwark appears in the Domesday Book of 1086 as held by several Surrey manors. Southwarks value to the King was £16, much of Southwark was originally owned by the church—the greatest reminder of monastic London is Southwark Cathedral, originally the priory of St Mary Overie. During the early Middle Ages, Southwark developed and was one of the four Surrey towns which returned Members of Parliament for the first commons assembly in 1295
London Borough of Southwark
The London Borough of Southwark /ˈsʌðərk/ in south London, England forms part of Inner London and is connected by bridges across the River Thames to the City of London. It was created in 1965 when three smaller council areas amalgamated under the London Government Act 1963, all districts of the area are within the London postal district. It is governed by Southwark London Borough Council, Dulwich is home to the Dulwich Picture Gallery and the Imperial War Museum is in Elephant and Castle. The area was first settled in the Roman period but the name Southwark dates from the 9th century, the London Borough of Southwark was formed in 1965 from the former area of the Metropolitan Borough of Southwark, the Metropolitan Borough of Camberwell, and the Metropolitan Borough of Bermondsey. The borough borders the City of London and the London Borough of Tower Hamlets to the north, the London Borough of Lambeth to the west, to the south are the London Borough of Bromley and the London Borough of Croydon.
At the 2001 census Southwark had a population of 244,866, Southwark is ethnically 63% white, 16% black African and 8% black Caribbean. The area is the home of many Nigerian, South African, Tower Bridge, the Millennium Bridge, Blackfriars Bridge, Southwark Bridge and London Bridge all connect the City of London to the borough. The skyscraper Shard London Bridge is currently the tallest building in the EU, the Tate Modern art gallery, Shakespeares Globe Theatre, the Imperial War Museum and Borough Market are within the borough. At one mile wide, Burgess Park is Southwarks largest green space, Southwark has many notable places of Christian worship, Roman Catholic and independent non-conformist. These include Charles Spurgeons Metropolitan Tabernacle, Southwark Cathedral, St Georges Cathedral, Londons Norwegian Church and Finnish Church and the Swedish Seamens Church are all in Rotherhithe. St George the Martyr is the oldest church in Greater London dedicated to Englands Patron Saint, the other redundant church is Francis Bedfords in Trinity Church Square, now a recording studio, Henry Wood Hall.
Whilst Christianity is the dominant religion of the borough, several religious minorities are active, according to the 2001 Census, approximately 28% of Southwark identified as non-religious, or chose not to state their faith. Charles Dickens set several of his novels in the old borough where he lived as a young man, the site of The Tabard inn, the White Hart inn and the George Inn which survives. The rebuilt Globe Theatre and its exhibition on the Bankside remind us of the areas being the birthplace of classical theatre, there is the remains of the Rose Theatre. In 2007 the Unicorn Theatre for Children was opened on Tooley Street with both the Southwark Playhouse and the Union Theatre having premises in Bermondsey Street, the Menier Chocolate Factory combines a theatre and exhibition space. The Bankside Gallery is the headquarters of the Royal Watercolour Society, the Golden Hinde replica is at St Mary Overie Dock and nearby are the remains of the medieval Winchester Palace which is a scheduled ancient monument.
Peckham Library, designed by Will Alsop won the Stirling Prize for modern architecture, the museum was closed by Southwark council in 2008. MOCA, London, as curated by the artist Michael Petry, is a museum located in Peckham Rye dedicated to exposing and showcasing new cutting-edge artists
Tower Bridge is a combined bascule and suspension bridge in London built in 1886–1894. The bridge crosses the River Thames close to the Tower of London and has become a symbol of London. Tower Bridge is one of five London bridges now owned and maintained by the Bridge House Estates and it is the only one of the Trusts bridges not to connect the City of London directly to the Southwark bank, as its northern landfall is in Tower Hamlets. The vertical components of the forces in the sections and the vertical reactions of the two walkways are carried by the two robust towers. The bascule pivots and operating machinery are housed in the base of each tower, before its restoration in the 2010s, the bridges colour scheme dated from 1977, when it was painted red and blue for Queen Elizabeth IIs Silver Jubilee. Its colours were restored to blue and white. The nearest National Rail stations are at Fenchurch Street and London Bridge, in the second half of the 19th century, an advertisement in the East End of London led to a hiring for a new river crossing downstream of London Bridge.
A Special Bridge or Subway Committee was formed in 1877, chaired by Sir Albert Joseph Altman and it opened the design of the crossing to public competition. Over 50 designs were submitted, including one from civil engineer Sir Joseph Bazalgette, an Act of Parliament was pasesd in 1885 authorising the bridges construction. It specified the opening span must give a clear width of 61 metres, construction had to be in a Gothic style. Barry designed a bridge with two bridge towers built on piers. The central span was split into two equal bascules or leaves, which could be raised to allow traffic to pass. The two side-spans were suspension bridges, with the suspension rods anchored both at the abutments and through rods contained within the bridges upper walkways, E W Crutwell was the resident engineer for the construction. Two massive piers, containing over 70,000 tons of concrete, were sunk into the riverbed to support the construction, over 11,000 tons of steel provided the framework for the towers and walkways.
This was clad in Cornish granite and Portland stone, both to protect the steelwork and to give the bridge a pleasing appearance. Jones died in 1886 and George D. Stevenson took over the project, the total cost of construction was £1,184,000. The bridge was opened on 30 June 1894 by The Prince of Wales. The bridge connected Iron Gate, on the bank of the river, with Horselydown Lane, on the south – now known as Tower Bridge Approach and Tower Bridge Road
County Hall, London
County Hall is a building in London that was the headquarters of London County Council and the Greater London Council. The building is on the South Bank of the River Thames, with Westminster Bridge being next to it and it faces west toward the City of Westminster and is close to the Palace of Westminster. The nearest London Underground stations are Waterloo and Westminster, County Hall is the site of businesses and attractions, including the London Sea Life Aquarium, London Dungeon and a Namco Station amusement arcade. The London Eye is next to County Hall, and its centre is inside the building. There is a suite of rooms which was home to the Saatchi Gallery from 2003 to 2006. Other parts of the house two hotels, several restaurants, and some flats. Various spaces are available for hire for functions, including the chamber at the heart of the building. Until January 2010 the Dali Universe was in the building but this has now closed, confirmed in early 2014, the building will become the home of the new Merlin Entertainments attraction and was opening in July 2015.
The area is home to three other Merlin Entertainments attractions. In 2016 London event venue company etc. venues announced plans to open a conference, based on the 4th floor overlooking the Thames, which opened in January 2017. The main six storey building was designed by Ralph Knott and it is faced in Portland stone in an Edwardian Baroque style. The construction, which was undertaken by Holland, Hannen & Cubitts, started in 1911, the North and South blocks, which were built by Higgs and Hill, were added between 1936 and 1939. The Island block was not completed until 1974, for 64 years County Hall served as the headquarters of local government for London. During the 1980s the powerful Labour-controlled GLC led by Ken Livingstone was locked in conflict with the Conservative government of Margaret Thatcher. Since the Parliament buildings were just across the river from County Hall, when the government of Margaret Thatcher abolished the GLC in 1986, County Hall lost its role as the seat of Londons government.
Today, the majority of the building, including the fourth and fifth floors. Another small section of the building is occupied as a Premier Inn, the County Hall Island Block, an annex of the main building, was demolished in 2006 to make way for a hotel, the Park Plaza Westminster Bridge. The building, known as No 1 Westminster Bridge Road, had been disused since 1986 and had become a derelict eyesore, a blue plaque commemorates the LCC, GLC and the Inner London Education Authority at County Hall
Norman Foster, Baron Foster of Thames Bank
Norman Robert Foster, Baron Foster of Thames Bank, OM, HonFREng is a British architect whose company, Foster + Partners, maintains an international design practice famous for high-tech architecture. He is one of Britains most prolific architects of his generation, in 1999, he was awarded the Pritzker Architecture Prize, often referred to as the Nobel Prize of architecture. In 2009, Foster was awarded the Prince of Asturias Award in the Arts category, in 1994, he received the AIA Gold Medal. Foster was born to Robert Foster and Lilian Smith in 1935 in Reddish and they moved, soon after his birth, two miles to 4 Crescent Grove in Levenshulme, which they rented for fourteen shillings a week, Foster has no recollection of Reddish. He attended Burnage Grammar School for Boys in Burnage, in a Guardian interview in 1999, Foster said he always felt different at school and was bullied and he retired into the world of books. He considered himself quiet and awkward in his early years often making faux pas and he was fascinated with engineering and the process of designing.
He says that caused him to pursue a career designing buildings, specific interests included aircraft, a hobby he maintains today, and trains, generated by viewing passing trains on the railway outside his terraced home during his childhood. Fosters father convinced him to take the exam for Manchester Town Halls trainee scheme which he passed in 1951. A colleague, Mr Cobbs son, was studying architecture and his interest led to Foster considering a career in architecture. After working in the Manchester City Treasurers office, Foster completed his National Service in 1953 serving in the Royal Air Force, Foster returned to Manchester, not wanting to return to the town hall as his parents wished and unsure of which path to follow. Foster was searching for an away from his working-class roots which led to the alienation of his parents. Foster took a job as assistant to a manager with John Bearshaw and Partners. The staff advised him, that if he wished to become an architect, he should prepare a portfolio of drawings using the perspective, Bearshaw was so impressed with the drawings that he promoted the young Foster to the drawing department of the practice.
In 1956 Foster won a place at the University of Manchester School of Architecture and he combined these with self-tuition via visits to the local library in Levenshulme. Foster took a keen interest in the works of Frank Lloyd Wright, Ludwig Mies van der Rohe, Le Corbusier and Oscar Niemeyer, Foster won the Henry Fellowship to the Yale School of Architecture, where he met future business partner Richard Rogers and earned his masters degree. Vincent Scully encouraged Foster and Rogers to travel in America for a year, after returning to the UK in 1963 he set up an architectural practice as Team 4 with Rogers and the sisters Georgie and Wendy Cheesman. Georgie was the one of the team that had passed her RIBA exams allowing them to set up in practice on their own. Team 4 quickly earned a reputation for industrial design
Canary Wharf is a major business district located in Tower Hamlets, East London. Canary Wharf contains around 16,000,000 square feet of office and retail space, Morgan, KPMG, MetLife, Morgan Stanley, RBC, S&P Global, State Street, and Thomson Reuters. Canary Wharf is located on the West India Docks on the Isle of Dogs, from 1802 to 1939, the area was one of the busiest docks in the world. After the 1960s, the industry began to decline, leading to all the docks being closed by 1980. Canary Wharf itself takes its name from No.32 berth of the West Wood Quay of the Import Dock and this was built in 1936 for Fruit Lines Ltd, a subsidiary of Fred Olsen Lines for the Mediterranean and Canary Islands fruit trade. The Canary islands were so named after the dogs found there by the Spanish and as it is located on the Isle of Dogs. The Canary Wharf of today began when Michael von Clemm, former chairman of Credit Suisse First Boston, further discussions with G Ware Travelstead led to proposals for a new business district.
The first buildings were completed in 1991, including One Canada Square, which became the UKs tallest building at the time, by the time it opened, the London commercial property market had collapsed, and Olympia and York Canary Wharf Limited filed for bankruptcy in May 1992. Initially, the City of London saw Canary Wharf as an existential threat and it modified its planning laws to expand the provision of new offices in the City of London, for example, creating offices above railway stations and roads. The resulting oversupply of office space contributed to the failure of the No 1 Canada Square project, in 1997, some residents living on the Isle of Dogs launched a lawsuit against Canary Wharf Ltd for private nuisance because the tower interfered with television signals. In December 1995 an international consortium, backed by the owners of Olympia & York and other investors. The new company was called Canary Wharf Limited, and became Canary Wharf Group, recovery in the property market generally, coupled with continuing demand for large floorplate Grade A office space, slowly improved the level of interest.
A critical event in the recovery was the start of work on the Jubilee Line Extension. At the peak of property prices in 2007, the HSBC building sold for a record £1.1 billion, in March 2014 planning permission was granted for the second residential building on the Canary Wharf estate, a 58-storey tower including 566 apartments plus shops and a health club. In July 2014 Canary Wharf Group was granted planning permission for a major expansion of the Canary Wharf estate. The plans include the construction of 30 buildings comprising a total of 4.9 million square feet, construction is planned to commence in autumn 2014 with the first buildings to be occupied at the end of 2018. In 2014, Singapore listed Oxley Holdings, together with developer Ballymore UK, have a joint venture to set up a new waterfront township of Royal Wharf with 3385 new homes housing over 10,000 people. This table lists completed buildings in Canary Wharf that are over 60 metres tall, the Canary Wharf developers played a pro-active role in improving transport links, which they recognised as essential to the success of the project
The Round Table is King Arthurs famed table in the Arthurian legend, around which he and his Knights congregate. As its name suggests, it has no head, implying that everyone who sits there has equal status, the table was first described in 1155 by Wace, who relied on previous depictions of Arthurs fabulous retinue. The symbolism of the Round Table developed over time, by the close of the 12th century it had come to represent the order associated with Arthurs court. The Round Table first appears in Waces Roman de Brut, a Norman language adaptation of Geoffrey of Monmouths Historia Regum Britanniae finished in 1155, Wace says Arthur created the Round Table to prevent quarrels among his barons, none of whom would accept a lower place than the others. Layamon added to the story when he adapted Waces work into the Middle English Brut in the early 13th century, in response a Cornish carpenter built an enormous but easily transportable Round Table to prevent further dispute. Wace claims he was not the source of the Round Table, some scholars have doubted this claim, while others believe it may be true.
Though the Round Table itself is not mentioned until Wace, the concept of Arthur having a court made up of many prominent warriors is much older. Geoffrey of Monmouth says that after establishing peace throughout Britain, Arthur increased his personal entourage by inviting very distinguished men from far-distant kingdoms to join it, though no Round Table appears in the early Welsh texts, Arthur is associated with various items of household furniture. A henge at Eamont Bridge near Penrith, Cumbria is known as King Arthurs Round Table, the still-visible Roman amphitheatre at Caerleon has been associated with the Round Table. and has been suggested as a possible source for the legend. The Round Table takes on new dimensions in the romances of the late 12th and early 13th century, where it becomes a symbol of the famed order of chivalry which flourishes under Arthur. In Robert de Borons Merlin, written around the 1190s, the wizard Merlin creates the Round Table in imitation of the table of the Last Supper and of Joseph of Arimatheas Holy Grail table.
This table, here made for Arthurs father Uther Pendragon rather than Arthur himself, has twelve seats and this seat must remain empty until the coming of the knight who will achieve the Grail. The Didot Perceval, a continuation of Roberts work, takes up the story. The prose cycles of the 13th century, the Lancelot-Grail cycle, here it is the perfect knight Galahad, rather than Percival, who assumes the empty seat, now called the Siege Perilous. Galahads arrival marks the start of the Grail quest as well as the end of the Arthurian era, in these works the Round Table is kept by King Leodegrance of Cameliard after Uthers death, Arthur inherits it when he marries Leodegrances daughter Guinevere. Other versions treat the Round Table differently, for instance Italian Arthurian works often distinguish between the Old Table of Uthers time and Arthurs New Table, during the Middle Ages, festivals called Round Tables were celebrated throughout Europe in imitation of Arthurs court. These events featured jousting and feasting, and in some cases attending knights assumed the identities of Arthurs entourage, the earliest of these was held in Cyprus in 1223 to celebrate a knighting.
Round Tables were popular in various European countries through the rest of the Middle Ages and were at times very elaborate, René of Anjou even erected an Arthurian castle for his 1446 Round Table
A helix is a type of smooth space curve, i. e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a line called the axis. Examples of helices are coil springs and the handrails of spiral staircases, a filled-in helix – for example, a spiral ramp – is called a helicoid. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices, the word helix comes from the Greek word ἕλιξ, curved. Helices can be either right-handed or left-handed, handedness is a property of the helix, not of the perspective, a right-handed helix cannot be turned to look like a left-handed one unless it is viewed in a mirror, and vice versa. Most hardware screw threads are right-handed helices, the alpha helix in biology as well as the A and B forms of DNA are right-handed helices. The Z form of DNA is left-handed, the pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two helices with the axis, differing by a translation along the axis.
A conic helix may be defined as a spiral on a conic surface, an example is the Corkscrew roller coaster at Cedar Point amusement park. A circular helix, has constant band curvature and constant torsion, a curve is called a general helix or cylindrical helix if its tangent makes a constant angle with a fixed line in space. A curve is a general helix if and only if the ratio of curvature to torsion is constant, a curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space. It can be constructed by applying a transformation to the frame of a general helix. Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions, in mathematics, a helix is a curve in 3-dimensional space. The following parametrisation in Cartesian coordinates defines a particular helix, Probably the simplest equations for one is x = cos , y = sin , z = t. As the parameter t increases, the point traces a right-handed helix of pitch 2θ and radius 1 about the z-axis, in cylindrical coordinates, the same helix is parametrised by, r =1, θ = t, h = t. A circular helix of radius a and slope b/a is described by the following parametrisation, another way of mathematically constructing a helix is to plot the complex-valued function exi as a function of the real number x.
The value of x and the real and imaginary parts of the function value give this plot three real dimensions, except for rotations and changes of scale, all right-handed helices are equivalent to the helix defined above. The equivalent left-handed helix can be constructed in a number of ways, in music, pitch space is often modeled with helices or double helices, most often extending out of a circle such as the circle of fifths, so as to represent octave equivalency