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You'll Never Walk Alone
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For other uses, see You'll Never Walk Alone (disambiguation).
"You'll Never Walk Alone"
Song
Published
1945
Genre
Show tune
Composer(s)
Richard Rodgers
Lyricist(s)
Oscar Hammerstein II
"You'll Never Walk Alone" is a show tune from the 1945 Rodgers and Hammerstein musical Carousel. In the second act of the musical, Nettie Fowler, the cousin of the protagonist Julie Jordan, sings "You'll Never Walk Alone" to comfort and encourage Julie when her husband, Billy Bigelow, the male lead, falls on his knife and dies after a failed robbery attempt. It is reprised in the final scene to encourage a graduation class of which Louise (Billy and Julie's daughter) is a member. The now invisible Billy, who has been granted the chance to return to Earth for one day in order to redeem himself, watches the ceremony and is able to silently motivate the unhappy Louise to join in the song.
The song is also sung at association football clubs around the world, where it is performed by a massed chorus of supporters on matchday; this tradition began at Liverpool F.C. after the chart success of the 1963 single of the song by the local Liverpool group Gerry and the Pacemakers.[1]
Contents
1 Background
2 Subsequent history
3 Sporting anthem
4 Recorded versions
5 References
6 External links
Background[edit]
Christine Johnson, who created the role of Nettie Fowler, introduced the song in the original Broadway production.[2] Later in the show Jan Clayton, as Julie Jordan, reprised it, with the chorus joining in.
In the film, it is first sung by Claramae Turner as Nettie. The weeping Julie Jordan (Shirley Jones) tries to sing it but cannot; it is later reprised by Julie and those attending the graduation.
Subsequent history[edit]
Besides the recordings of the song on the Carousel cast albums and the film soundtrack, the song has been recorded by many artists, with notable hit versions made by Roy Hamilton,[3] Frank Sinatra, Roy Orbison, Billy Eckstine, Gerry and the Pacemakers, Judy Garland, Elvis Presley, Johnny Cash, Andy Williams, Johnny Maestro and The Brooklyn Bridge, Olivia Newton-John and Doris Day. Progressive rock group Pink Floyd took a recording by the Liverpool Kop choir, and "interpolated" it into their own song, "Fearless", on their 1971 album Meddle.
From 1964 through 2010, Jerry Lewis concluded the annual Jerry Lewis Labor Day MDA Telethon by singing the song.[4] After the end of a concert by the rock band Queen, the audience spontaneously sang this song, according to lead guitarist Brian May,[5] and this helped to inspire the creation of their songs "We Are the Champions" and "We Will Rock You". Italian-American tenor Sergio Franchi sang a notable version accompanied by the Welsh Men's Choir on the 9 June 1968 telecast of The Ed Sullivan Show.[6] He also covered this song in his 1964 RCA Victor album The Exciting Voice of Sergio Franchi.[7] American singer and songwriter Barbra Streisand sang this song in a surprise appearance at the close of the 2001 Emmy Awards, in honor of the victims of the 11 September 2001 attacks.[8]
In 1990 at the Nelson Mandela: An International Tribute for a Free South Africa concert at Wembley Stadium London, the audience spontaneously broke out into a mass rendition. Mandela turned to Adelaide Tambo who accompanied him onto the stage and asked what the song was. She replied, "A football song".
Renée Fleming sang the song at the Concert for America, which marked the first anniversary of 9/11 (11/9),[9][10][better source needed] and for the Inauguration of Barack Obama on January 20, 2009.[11]
In 2010, this was sung during the festivities of the Last Night of the Proms, with the choir at the Royal Albert Hall joined by crowds of the public from Hillsborough Castle, Northern Ireland; Caird Hall, Dundee; Hyde Park, London; Salford, Greater Manchester; and Wales, to mark the fiftieth anniversary of the death of Oscar Hammerstein II.[citation needed]
In the second season of American Horror Story, this song was recited as a poem.
It has been the song of the Madison Scouts Drum and Bugle Corps song since 1954, where they first performed it as a part of their first field show in 1954. Challenged by the Rosemont Cavaliers singing "Over the Rainbow" in 1957, the corps responded with "You'll Never Walk Alone", and it has been the official corps song ever since.
Punk band Dropkick Murphys covered the song for their 2017 album 11 Short Stories of Pain & Glory. Vocalist/bassist Ken Casey said in a December 2016 interview discussing the reason behind their version. "As you may know, opiate overdoses are an epidemic in America now particularly in (the Boston) area. I've been to thirty wakes in two years, three this week, one being my cousin, Al's lost a brother in law. It's hit home close to us. I was leaving one of the wakes and this song came on and as I was listening to the lyrics it summed up exactly how I was feeling. Sad, but knowing there is hope. You never have to be alone. I hope you like our version".
Sporting anthem[edit]
"You'll Never Walk Alone"
Single by Gerry and the Pacemakers
from the album How Do You Like It
B-side
"It's All Right"
Released
October 1963
Format
7"
Recorded
2 July 1963
Studio
EMI Studios, London[12]
Genre
Merseybeat, baroque pop
Length
2:40
Label
Columbia (EMI) (UK), Laurie Records (US)
Composer(s)
Richard Rodgers
Lyricist(s)
Oscar Hammerstein II
Producer(s)
George Martin
In the UK, the song's most successful cover was released in 1963 by the Liverpudlian Merseybeat group Gerry and the Pacemakers, peaking at number one on the UK singles chart for four consecutive weeks. Sung by Liverpool fans in 1963, the song quickly became the anthem of Liverpool F.C. and is sung by its supporters moments before the start of each home game with the Gerry and the Pacemakers version played over the public address system.[1][13][14]
According to former player Tommy Smith, lead vocalist Gerry Marsden presented Liverpool manager Bill Shankly with a recording of his forthcoming cover single during a pre-season coach trip in the summer of 1963. "Shanks was in awe of what he heard. ... Football writers from the local newspapers were travelling with our party and, thirsty for a story of any kind between games, filed copy back to their editors to the effect that we had adopted Gerry Marsden's forthcoming single as the club song."[15] The squad was subsequently invited to perform the track with the band on The Ed Sullivan Show[1] with Marsden stating, "Bill came up to me. He said, 'Gerry my son, I have given you a football team and you have given us a song'."[1]
The 'Shankly Gates' entrance to Liverpool's home stadium Anfield
Shankly picked the song as his eighth and final selection for the BBC's Desert Island Discs on the eve of the 1965 FA Cup Final.[16] As Liverpool fans sang "You'll Never Walk Alone" at Wembley during the 1965 FA Cup Final win over Leeds, commentator Kenneth Wolstenholme referred to it as "Liverpool's signature tune".[17] Marsden told BBC Radio how, in the 1960s, the disc jockey at Anfield would play the top ten commercial records in descending order, with the number one single played last, shortly before kickoff. Liverpool fans on the Kop would sing along, but unlike with other hit singles, once "You'll Never Walk Alone" dropped out of the top ten, instead of disregarding the song, supporters continued to sing it.[18][19]
The song was adopted by Scottish team Celtic after a 1966 Cup Winners Cup semi-final against Liverpool at Anfield.[1][17] It is now sung by Celtic fans prior to every home European tie.[1][17][20] The song has also been adopted by Dutch team Feyenoord, SC Cambuur,[21] Germany's Borussia Dortmund,[17] 1. FSV Mainz 05, TSV 1860 Munich,[22] Japan's F.C. Tokyo,[23] Spain's CD Lugo.[24] the Marist St. Pats MSP 80/80 Blues, and Bali United.[25] In ice hockey, the song has been adopted by German Deutsche Eishockey Liga side Krefeld Pinguine and Croatian Medveščak Zagreb.
A special recording of the song was made in solidarity with Bradford City following the Valley Parade fire in 1985, when 56 spectators died and many more were seriously injured. The song was performed by The Crowd, which was a supergroup featuring Gerry Marsden, Paul McCartney and others, and spent two weeks at number one in the UK.
Some years later, after witnessing a rendition of "You'll Never Walk Alone" at Anfield in 2007, the President of the Spanish Olympic Committee, Alejandro Blanco, said he felt inspired to seek lyrics to his country's wordless national anthem, the Marcha Real, ahead of Madrid's bid to host the 2016 Olympic Games.[26][27]
During the 2014 Hong Kong protests, legislator Tam Yiu Chung quoted the song during a Legislative Council of Hong Kong meeting, to salute the Hong Kong Police,[28] who had received widespread criticism for using excessive force against pro-democracy protesters. More than 2,000 Liverpool Football Club fans in Hong Kong condemned his inappropriate use of the song, comparing his support of the police action to the police actions in the 1989 Hillsborough disaster, where South Yorkshire Police were found to have distorted facts relating to the unlawful killing by negligence of 96 Liverpool supporters.[29][30][31]
On 13 March 2016, after Borussia Dortmund's 2-0 win against 1. FSV Mainz 05 in the German Bundesliga, supporters of both teams performed the song to commemorate a Dortmund fan who died from a cardiac arrest in the stands during the game.[32]
Recorded versions[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2017) (Learn how and when to remove this template message)
The Adicts[33]
Alfie Boe ("Onward") (2007)
Alicia Keys (Hurricane Katrina disaster relief, 2005)
André Rieu (2009 Maastricht concert)
Andy Williams (with orchestra conducted by Archie Bleyer)
Aretha Franklin (1972, on the live album Amazing Grace)
Barry Manilow & Cilla Black (1993)[34]
Bela B. & the Tikiwolves feat. Gary'o'Wolf[22] (official FC St. Pauli Stadionhymn, 1992)
Bernadette Peters
Billy Eckstine (1960): Live album No Cover, No Minimum, recorded in Las Vegas. Production was by Teddy Reig. The album was originally released by Roulette Records, but is also available on the Blue Note label.
Bryn Terfel (1996) – Something Wonderful: Bryn Terfel Sings Rodgers and Hammerstein
Charice (2008)
Celtic Woman (Believe 2011)
Chris de Burgh (2008)
Christy Gibson (Thai Language Version) (2001) – Soo Yod Kao
Christine Johnson on the Carousel Original Cast Album (1945)
Claramae Turner on the Carousel film soundtrack (1956)
The Crowd (1985)
The Crusaders (1966)
David Campbell (2010)
David Phelps on the album Classic (2012)
Die Toten Hosen (2000, Bayern ep)
Dionne Warwick (1967, On Stage and in the Movies album track)
Doris Akers (1963)
Doris Day (on the You'll Never Walk Alone album) (1962)
Dropkick Murphys (appears on their album 11 Short Stories of Pain & Glory) (2017)
Dudu Fisher (2006)
Elha Mae Nympha (2015, performed on the Live Semi-finals on the second season of The Voice Kids, and was moved to the grand finals)
Elvis Presley (1968 single release)
Engelbert Humperdinck (1972 album "Live at the Riviera", in Las Vegas)
Frank Sinatra (1945) (1963)
Frankie Vaughan (1979)
Gene Vincent (1958) (Gene Vincent Rocks and the Blue Caps Roll album track)
Gerry & The Pacemakers (1963)
Glen Campbell (1970)
Hayley Westenra (2001)
Il Divo (A Musical Affair, 2013)
Jackie Wilson (1965)
Jerry Reed (1971) (Ko-Ko Joe album track)
Jo Stafford and Gordon MacRae (1963)
John Barrowman (2010) (John Barrowman album track)
John Farnham (1998) - The Spirit of Christmas (compilation album)
Johnny Cash (2003)
Johnny Preston (1960)[35]
Johnny Maestro & the Brooklyn Bridge (1969)
Joseph Calleja (Last Night of the Proms, 2012)[36]
Josh Groban (2015)[37]
Joyce DiDonato (2012)[38]
Juan Diego Flórez (Live 8 – Berlin) (2005)
Judy Garland (1960)[39]
Katherine Jenkins (2005)
Kevin Rowland (1999)
Kiri Te Kanawa with the Mormon Tabernacle Choir (1990) – Songs of Inspiration
The Knickerbockers (1966)
Lee Greenwood
Lee Towers (1976)[40]
The Lettermen (1964)[41]
Tammy Wynette (1969 Inspiration)
Liverpool F.C. (1977) (FA Cup single: A-side - "We Can Do It" / "Liverpool Lou" B-side - "We Shall Not Be Moved" / "You'll Never Walk Alone")
Los Fastidios
Louis Armstrong (1954) in a medley with Tenderly
Mahalia Jackson
Malena Ernman (2013)
Malcolm Vaughan (1959)
Mark Vincent (2010)
Mario Lanza (1952 and 1956)
Maureen Forrester on the Carousel MCA Classics album (1987)
Melanie Chisholm (2012)
Michael Crawford (1987)
Mormon Tabernacle Choir (1971)
Nina Simone (1960, At Newport)
Olivia Newton-John (1989) – Warm and Tender
Patricia Neway in the soundtrack of the 1967 television adaptation of Carousel (1967)
Patti Labelle & The Blue Belles (1964)
Patti LaBelle (1980's)
Pink Floyd (1971) – "Fearless"
Pips, Chips & Videoclips (Dernjava album, 1995)
The Priests (2009)
Perry Como (1951) (with Mitchell Ayres Orchestra)
Ray Charles (Ingredients in a Recipe for Soul album track, July 1963)
Regine Velasquez (1992)
Renée Fleming (2003)
The Righteous Brothers (1965)
Riverdale Cast featuring main vocals of Madelaine Petsch (2018), appeared on Riverdale [42]
Robin S (appears on the 1998 movie soundtrack, Welcome to Woop Woop)
Robson & Jerome (1996)
Roy Hamilton (1954)[3]
Roy Orbison (1969) recorded (2015) [Released]]
Samuel Ramey (1989)
Sergio Franchi recorded on 1964 RCA album, The Exciting Voice of Sergio Franchi
The Shadows (Reflection album track, 1990)
Shirley Bassey (1962, single B-side to "Ave Maria")[43]
Shirley Jones recorded it on the original movie soundtrack of Carousel and again on her 1989 album Silent Strength
Sissel Kyrkjebø (2004)
Smoking Popes
The Soldiers (2011)
Steven Houghton (1997) – Steven Houghton
Susan Boyle (Standing Ovation: The Greatest Songs from the Stage, 2012)
The Three Tenors (The Three Tenors: Paris 1998, 1998)
Tokyo Ska Paradise Orchestra (2009) – Paradise Blue
Tom Jones (1969)
Trisha Yearwood (2016) - The Passion
Vocal Majority (1997) – How Sweet the Sound
Wayne Hussey and Julianne Regan (as Hussey-Regan) (2011) (in support of Liverpool F.C.'s disability charity, Respect 4 All)[44]
Keith Jack (2008)
References[edit]
^ Jump up to: a b c d e f Hart, Simon (25 October 2013). "Anfield's 50 years of never walking alone". The Independent. Retrieved 6 April 2015.
Jump up ^ "You'll Never Walk Alone (original version 1945)". Youtube. Retrieved April 20, 2011.
^ Jump up to: a b Gilliland, John (1969). "Show 3 - The Tribal Drum: The rise of rhythm and blues. [Part 1]" (audio). Pop Chronicles. University of North Texas Libraries.
Jump up ^ "Milestones: Retiring: Jerry Lewis", Time magazine, May 30, 2011, p. 17
Jump up ^ Interview with Tom Browne for BBC Radio One, broadcast Christmas Eve and Boxing Day 1977
Jump up ^ "SOFA Entertainment - Ed Sullivan Show". www.edsullivan.com.
Jump up ^ "Discogs - Database and Marketplace for Music on Vinyl, CD, Cassette a…". July 13, 2014. Archived from the original on July 13, 2014.
Jump up ^ Streisand's stage fright spiked with thought of terror, By Edna Gundersen, USA Today, December 12, 2001
Jump up ^ Scott Simon (April 28, 2018). "'Carousel' Returns To Broadway". Weekend Edition Saturday. NPR. Retrieved April 30, 2018. : "SIMON: ... 'You'll Never Walk Alone' - you sang this at the Obama inauguration too, didn't you? FLEMING: Yes, and also the 9/11 memorial a year after the attacks."
Jump up ^ Video on YouTube
Jump up ^ Gallo, Phil (January 18, 2009). "We Are One: The Obama Inaugural Celebration". Variety. RBI. Retrieved February 8, 2009.
Jump up ^ "Gerry's Datebook". www.britbands.bravepages.com.
Jump up ^ Nik Brumsack. The story of 'You'll Never Walk Alone', independent.co.uk, April 14, 2014.
Jump up ^ Liverpool vs. Leeds United on YouTube, F.A. Cup Final, BBC, 1965. "The song was covered by Liverpool group Gerry & The Pacemakers in 1963. At this time, supporters standing on the Spion Kop terrace at Anfield began singing popular chart songs of the day. The mood was captured on camera by a BBC Panorama camera crew in 1964. One year later, when Liverpool faced Leeds in the cup final, the travelling Kop sang the same song and match commentator Kenneth Wolstenholme commended the 'Liverpool signature tune'." Paul Coslett, You'll Never Walk Alone BBC Online. June 9, 2008.
Jump up ^ Smith, Tommy. Anfield Iron, Bantam Press, p. 68-69
Jump up ^ Bill Shankly, Desert island Discs BBC, Mon April 26, 1965.
^ Jump up to: a b c d Why Liverpool fans sing 'You'll Never Walk Alone'. FourFourTwo. Retrieved 10 October 2016
Jump up ^ Cavanagh, John. "The History of You'll Never Walk Alone", BBC Songlines, 2006.
Jump up ^ Morgan, John. "The Other Mersey Sound", BBC Panorama, 1964.
Jump up ^ Aldred, Jessica. Liverpool or Celtic: who Walked Alone first? The Guardian. March 12, 2003.
Jump up ^ Whyatt, Chris. McClaren's new charges BBC. August 13, 2008.
^ Jump up to: a b Bela B. & The Tikiwolves feat. Gary 'O' Wolf: You'll Never Walk Alone (FC St. Pauli hymn) at Discogs (list of releases)
Jump up ^ Nagatomo tells Japan "You'll never walk alone", The mainichi Daily News. March 2011.
Jump up ^ anfieldcarro (June 30, 2011). ""You´ll never walk alone" polo Anfield Carro PUNTO PELOTA" – via YouTube.
Jump up ^ Chants, North Side Boys 12. "Bali United YNWA". Youtube. Youtube. Retrieved 1 May 2018.
Jump up ^ Liverpool fans inspire Spain to write words to anthem, Reuters. June 5, 2005
Jump up ^ Spain to add lyrics to wordless national anthem, MSNBC. June 26, 2007.
Jump up ^ Legistrative Council Record.
Jump up ^ 香港特別行政區立法會 (October 16, 2014). "立法會會議 (2014/10/16) - IV. 立法會休會待續議案 - 根據《議事規則》第16(2)條動議的立法會休會待續議案 (第五部分)" – via YouTube.
Jump up ^ "利迷聯署強烈譴責：譚耀宗勿侮辱YNWA - Yahoo奇摩新聞".
Jump up ^ Hong Kong Legislative Council Record 08:07:18 - 08:07:35
Jump up ^ Whaling, James (13 March 2016). "Borussia Dortmund fan dies from heart attack during Bundesliga match against Mainz". Daily Mirror. Retrieved 14 August 2016.
Jump up ^ John The Punk. "Welcome to The Adicts Official Website!". Adicts.us. Archived from the original on May 4, 2011. Retrieved April 20, 2011.
Jump up ^ "Cilla Black Discography: You'll Never Walk Alone (duet with Barry Manilow) – Single". Retrieved May 21, 2009.
Jump up ^ Johnny Preston, Running Bear Retrieved September 10, 2015
Jump up ^ "Richard Rogers: You'll Never Walk Alone - Last Night of the BBC Proms 2012". BBC YouTube channel. September 8, 2012. Retrieved October 5, 2012.
Jump up ^ "Stages — Josh Groban". iTunes Store. Apple Inc. Retrieved March 10, 2015.
Jump up ^ "Joyce contributes to highly anticipated new recording: Rogers & Hammerstein at the Movies". .joycedidonato.com. August 22, 2012. Retrieved October 5, 2012.
Jump up ^ Recorded for Capitol Records Archived April 30, 2008, at the Wayback Machine. Judy Garland with Orchestra conducted, by Norrie Paramor, August 3, 1960.
Jump up ^ It's Raining In My Heart[permanent dead link] (LP/MC) (Goud & Platina) 1976
Jump up ^ "You'll Never Walk Alone". Thelettermen.com. Archived from the original on July 17, 2011. Retrieved April 20, 2011.
Jump up ^ https://genius.com/Riverdale-cast-youll-never-walk-alone-lyrics
Jump up ^ Columbia Catalog Number DB4816"
Jump up ^ "You'll Never Walk Alone". Youtube.com (Liverpool FC's Channel). Retrieved December 27, 2011.
External links[edit]
Lyrics of this song at MetroLyrics
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text:
Octagon
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other uses, see Octagon (disambiguation).
"Octagonal" redirects here. For other uses, see Octagonal (disambiguation).
Regular octagon
A regular octagon
Type
Regular polygon
Edges and vertices
8
Schläfli symbol
{8}, t{4}
Coxeter diagram

Symmetry group
Dihedral (D8), order 2×8
Internal angle (degrees)
135°
Dual polygon
Self
Properties
Convex, cyclic, equilateral, isogonal, isotoxal
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
A regular octagon has Schläfli symbol {8} [1] and can also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges. A truncated octagon, t{8} is a hexadecagon, t{16}.
Contents
[hide]
1 Properties of the general octagon
2 Regular octagon
2.1 Area
2.2 Circumradius and inradius
2.3 Diagonals
2.4 Construction and elementary properties
2.5 Standard coordinates
2.6 Dissection
3 Skew octagon
3.1 Petrie polygons
4 Symmetry
5 Uses of octagons
5.1 Other uses
6 Derived figures
6.1 Related polytopes
7 See also
8 References
9 External links
Properties of the general octagon[edit]
The diagonals of the green quadrilateral are equal in length and at right angles to each other
The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°.
If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other).[2]:Prop. 9
The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on the sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square.[2]:Prop. 10
Regular octagon[edit]
A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° ( 3 π 4 {\displaystyle \scriptstyle {\frac {3\pi }{4}}} radians). The central angle is 45° ( π 4 {\displaystyle \scriptstyle {\frac {\pi }{4}}} radians).
Area[edit]
The area of a regular octagon of side length a is given by
A = 2 cot  π 8 a 2 = 2 ( 1 + 2 ) a 2 ≃ 4.828 a 2 . {\displaystyle A=2\cot {\frac {\pi }{8}}a^{2}=2(1+{\sqrt {2}})a^{2}\simeq 4.828\,a^{2}.}
In terms of the circumradius R, the area is
A = 4 sin  π 4 R 2 = 2 2 R 2 ≃ 2.828 R 2 . {\displaystyle A=4\sin {\frac {\pi }{4}}R^{2}=2{\sqrt {2}}R^{2}\simeq 2.828\,R^{2}.}
In terms of the apothem r (see also inscribed figure), the area is
A = 8 tan  π 8 r 2 = 8 ( 2 − 1 ) r 2 ≃ 3.314 r 2 . {\displaystyle A=8\tan {\frac {\pi }{8}}r^{2}=8({\sqrt {2}}-1)r^{2}\simeq 3.314\,r^{2}.}
These last two coefficients bracket the value of pi, the area of the unit circle.
The area of a regular octagon can be computed as a truncated square.
The area can also be expressed as
A = S 2 − a 2 , {\displaystyle \,\!A=S^{2}-a^{2},}
where S is the span of the octagon, or the second-shortest diagonal; and a is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of the eight sides overlap with the four sides of the square) and then takes the corner triangles (these are 45–45–90 triangles) and places them with right angles pointed inward, forming a square. The edges of this square are each the length of the base.
Given the length of a side a, the span S is
S = a 2 + a + a 2 = ( 1 + 2 ) a ≈ 2.414 a . {\displaystyle S={\frac {a}{\sqrt {2}}}+a+{\frac {a}{\sqrt {2}}}=(1+{\sqrt {2}})a\approx 2.414a.}
The area is then as above:
A = ( ( 1 + 2 ) a ) 2 − a 2 = 2 ( 1 + 2 ) a 2 ≈ 4.828 a 2 . {\displaystyle A=((1+{\sqrt {2}})a)^{2}-a^{2}=2(1+{\sqrt {2}})a^{2}\approx 4.828a^{2}.}
Expressed in terms of the span, the area is
A = 2 ( 2 − 1 ) S 2 ≈ 0.828 S 2 . {\displaystyle A=2({\sqrt {2}}-1)S^{2}\approx 0.828S^{2}.}
Another simple formula for the area is
A = 2 a S . {\displaystyle \ A=2aS.}
More often the span S is known, and the length of the sides, a, is to be determined, as when cutting a square piece of material into a regular octagon. From the above,
a ≈ S / 2.414. {\displaystyle a\approx S/2.414.}
The two end lengths e on each side (the leg lengths of the triangles (green in the image) truncated from the square), as well as being e = a / 2 , {\displaystyle e=a/{\sqrt {2}},} may be calculated as
e = ( S − a ) / 2. {\displaystyle \,\!e=(S-a)/2.}
Circumradius and inradius[edit]
The circumradius of the regular octagon in terms of the side length a is[3]
R = ( 4 + 2 2 2 ) a , {\displaystyle R=\left({\frac {\sqrt {4+2{\sqrt {2}}}}{2}}\right)a,}
and the inradius is
r = ( 1 + 2 2 ) a . {\displaystyle r=\left({\frac {1+{\sqrt {2}}}{2}}\right)a.}
Diagonals[edit]
The regular octagon, in terms of the side length a, has three different types of diagonals:
Short diagonal;
Medium diagonal (also called span or height), which is twice the length of the inradius;
Long diagonal, which is twice the length of the circumradius.
The formula for each of them follows from the basic principles of geometry. Here are the formulas for their length:[citation needed]
Short diagonal: a 2 + 2 {\displaystyle a{\sqrt {2+{\sqrt {2}}}}} ;
Medium diagonal: ( 1 + 2 ) a {\displaystyle (1+{\sqrt {2}})a} ;
Long diagonal: a 4 + 2 2 {\displaystyle a{\sqrt {4+2{\sqrt {2}}}}} .
Construction and elementary properties[edit]
building a regular octagon by folding a sheet of paper
A regular octagon at a given circumcircle may be constructed as follows:
Draw a circle and a diameter AOE, where O is the center and A, E are points on the circumcircle.
Draw another diameter GOC, perpendicular to AOE.
(Note in passing that A,C,E,G are vertices of a square).
Draw the bisectors of the right angles GOA and EOG, making two more diameters HOD and FOB.
A,B,C,D,E,F,G,H are the vertices of the octagon.
Octagon at a given circumcircle
Octagon at a given side length, animation
(The construction is very similar to that of hexadecagon at a given side length.)
A regular octagon can be constructed using a straightedge and a compass, as 8 = 23, a power of two:
Each side of a regular octagon subtends half a right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of 8 isosceles triangles, leading to the result:
Area = 2 a 2 ( 2 + 1 ) {\displaystyle {\text{Area}}=2a^{2}({\sqrt {2}}+1)}
for an octagon of side a.
Standard coordinates[edit]
The coordinates for the vertices of a regular octagon centered at the origin and with side length 2 are:
(±1, ±(1+√2))
(±(1+√2), ±1).
Dissection[edit]
8-cube projection
24 rhomb dissection

Regular
Isotoxal
Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.[4] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular octagon, m=4, and it can be divided into 6 rhombs, with one example shown below. This decomposition can be seen as 6 of 24 faces in a Petrie polygon projection plane of the tesseract. The list (sequence A006245 in the OEIS) defines the number of solutions as 8, by the 8 orientations of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings.
Regular octagon dissected

Tesseract
4 rhombs and 2 square
Skew octagon[edit]
A regular skew octagon seen as edges of a square antiprism, symmetry D4d, [2+,8], (2*4), order 16.
A skew octagon is a skew polygon with 8 vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A skew zig-zag octagon has vertices alternating between two parallel planes.
A regular skew octagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew octagon and can be seen in the vertices and side edges of a square antiprism with the same D4d, [2+,8] symmetry, order 16.
Petrie polygons[edit]
The regular skew octagon is the Petrie polygon for these higher-dimensional regular and uniform polytopes, shown in these skew orthogonal projections of in A7, B4, and D5 Coxeter planes.
A7
D5
B4

7-simplex
5-demicube
16-cell
Tesseract
Symmetry[edit]
Symmetry
The 11 symmetries of a regular octagon. Lines of reflections are blue through vertices, purple through edges, and gyration orders are given in the center. Vertices are colored by their symmetry position.
The regular octagon has Dih8 symmetry, order 16. There are 3 dihedral subgroups: Dih4, Dih2, and Dih1, and 4 cyclic subgroups: Z8, Z4, Z2, and Z1, the last implying no symmetry.
Example octagons by symmetry

r16

d8

g8

p8

d4

g4

p4

d2

g2

p2

a1
On the regular octagon, there are 11 distinct symmetries. John Conway labels full symmetry as r16.[5] The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars) Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the regular form is r16 and no symmetry is labeled a1.
The most common high symmetry octagons are p8, a isogonal octagon constructed by four mirrors can alternate long and short edges, and d8, an isotoxal octagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular octagon.
Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g8 subgroup has no degrees of freedom but can seen as directed edges.
Uses of octagons[edit]
The octagonal floor plan, Dome of the Rock.
The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa, Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery, Zum Friedefürsten church (Germany) and a number of octagonal churches in Norway. The central space in the Aachen Cathedral, the Carolingian Palatine Chapel, has a regular octagonal floorplan. Uses of octagons in churches also include lesser design elements, such as the octagonal apse of Nidaros Cathedral.
Architects such as John Andrews have used octagonal floor layouts in buildings for functionally separating office areas from building services, notably the Intelsat Headquarters in Washington D.C., Callam Offices in Canberra, and Octagon Offices in Parramatta, Australia.
Other uses[edit]
Umbrellas often have an octagonal outline.
The famous Bukhara rug design incorporates an octagonal "elephant's foot" motif.
The street & block layout of Barcelona's Eixample district is based on non-regular octagons
Janggi uses octagonal pieces.
Japanese lottery machines often have octagonal shape.
Stop sign used in English-speaking countries, as well as in most European countries
An icon of a stop sign with a hand at the middle.
The trigrams of the Taoist bagua are often arranged octagonally
Famous octagonal gold cup from the Belitung shipwreck
Classes at Shimer College are traditionally held around octagonal tables
The Labyrinth of the Reims Cathedral with a quasi-octagonal shape.
Derived figures[edit]
The truncated square tiling has 2 octagons around every vertex.
An octagonal prism contains two octagonal faces.
An octagonal antiprism contains two octagonal faces.
The truncated cuboctahedron contains 6 octagonal faces.
The omnitruncated cubic honeycomb
Related polytopes[edit]
The octagon, as a truncated square, is first in a sequence of truncated hypercubes:
Truncated hypercubes
...
Octagon Truncated cube Truncated tesseract Truncated 5-cube Truncated 6-cube Truncated 7-cube Truncated 8-cube
As an expanded square, it is also first in a sequence of expanded hypercubes:
Expanded hypercubes
...
Octagon Rhombicuboctahedron Runcinated tesseract Stericated 5-cube Pentellated 6-cube Hexicated 7-cube Heptellated 8-cube
See also[edit]
Bumper pool
Octagon house
Octagonal number
Octagram
Oktogon, a major intersection in Budapest, Hungary
Rub el Hizb (also known as Al Quds Star and as Octa Star)
Smoothed octagon
References[edit]
Jump up ^ Wenninger, Magnus J. (1974), Polyhedron Models, Cambridge University Press, p. 9, ISBN 9780521098595 .
^ Jump up to: a b Dao Thanh Oai (2015), "Equilateral triangles and Kiepert perspectors in complex numbers", Forum Geometricorum 15, 105--114. http://forumgeom.fau.edu/FG2015volume15/FG201509index.html
Jump up ^ Weisstein, Eric. "Octagon." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Octagon.html
Jump up ^ Coxeter, Mathematical recreations and Essays, Thirteenth edition, p.141
Jump up ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)
External links[edit]
Octagon Calculator
Definition and properties of an octagon With interactive animation
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text:
List of Prime Ministers of India
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
India
This article is part of a series on the
politics and government of
India
Constitution and law[show]
Constitutional amendment
Basic structure doctrine
Fundamental rights
Human rights
———————
Code of Civil Procedure, 1908
Uniform civil code
Code of Criminal Procedure, 1973
Indian Penal Code
Law enforcement
Government of India[show]
President (Head of state) (List)
Vice president (List)
———————
Executive:
Prime minister (Head of government) (List)
Union Council of Ministers
Cabinet secretary
Secretaries:
(Defence • Finance • Foreign • Home)
Civil services
All India Services (IAS • IFoS • IPS)
Central Civil Services (IRS • IFS • IA&AS • IPoS • IRAS • IRTS • IRPS • ICAS • IDAS • IDES • ICLS • IIS • ITrS • IP&TAFS • IOFS)
———————
Legislature:
Parliament
Rajya Sabha (Chairman)
Lok Sabha (Speaker)
Judiciary:
Supreme court (Chief justice)
High courts (Chief justices)
District courts
Elections[show]
Election commission:
Chief Election Commissioner (Election commissioners)
Recent general elections: 2009
2014
2019
Recent state elections: 2017
2018
2019
———————
Political parties
National parties
State parties
National coalitions:
National Democratic Alliance (NDA)
United Progressive Alliance (UPA)
Federalism[show]
Administrative divisions
———————
State governments
Governors (List)
Chief ministers (List)
Chief secretary (Principal secretaries)
Field-level officers
Divisional commissioners
District magistrates
Sub-divisional magistrates
Legislatures:
Vidhan Sabha
Vidhan Parishad
———————
Local governments: Rural bodies:
District councils
Block panchayats
Gram Panchayats
Urban bodies:
Municipal corporations
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Other countries
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v
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The Prime Minister of India is the chief executive of the Government of India. In India's parliamentary system, the Constitution names the President as head of state de jure, but his or her de facto executive powers are vested in the Prime Minister and his Council of Ministers. Appointed and sworn-in by the President, the Prime Minister is usually the leader of the party or alliance that has a majority in the Lok Sabha, the lower house of India's Parliament.[1]
Since 1947, India has had fourteen Prime Ministers, fifteen including Gulzarilal Nanda who twice acted in the role. The first was Jawaharlal Nehru of the Indian National Congress party,[2] who was sworn-in on 15 August 1947, when India gained independence from the British. Serving until his death in May 1964, Nehru remains India's longest-serving prime minister. He was succeeded by fellow Congressman Lal Bahadur Shastri, whose 19-month term also ended in death. Indira Gandhi, Nehru's daughter, succeeded Shastri in 1966 to become the country's first woman premier. Eleven years later, she was voted out of power in favour of the Janata Party, whose leader Morarji Desai became the first non-Congress prime minister. After he resigned in 1979, his former deputy Charan Singh briefly held office until Indira Gandhi was voted back six months later. Indira Gandhi's second stint as Prime Minister ended five years later on the morning of 31 October 1984, when she was gunned down by her own bodyguards. That evening, her son Rajiv Gandhi was sworn-in as India's youngest premier, and the third from his family. Thus far, members of Nehru-Gandhi family have been Prime Minister for a total of 37 years and 303 days.[3]
Rajiv's five-year term ended with his former cabinet colleague, V. P. Singh of the Janata Dal, forming the year-long National Front coalition government in 1989. A seven-month interlude under Prime Minister Chandra Shekhar followed, after which the Congress party returned to power, forming the government under P. V. Narasimha Rao in June 1991. Rao's five-year term was succeeded by four short-lived governments—the Bharatiya Janata Party's Atal Bihari Vajpayee for 13 days in 1996, a year each under United Front prime ministers H. D. Deve Gowda and I. K. Gujral, and Vajpayee again for 19 months in 1998–99. After Vajpayee was sworn-in for the third time, in 1999, he managed to lead his National Democratic Alliance (NDA) government to a full five-year term, the first non-Congressman to do so. Vajpayee was succeeded by Congressman Manmohan Singh, the first Sikh premier, whose United Progressive Alliance government was in office for 10 years between 2004 and 2014. The incumbent Prime Minister of India is Narendra Modi who has headed the BJP-led NDA government since 26 May 2014 which is India's first non-Congress single party majority government.[4]
Contents
1 Key
2 Prime Ministers of India
3 See also
4 References
4.1 General
4.2 Specific
Key
Colour key for party of the prime ministers
Bharatiya Janata Party
Indian National Congress
designated Indian National Congress (I) 1977–1996[5]
Janata Dal
Janata Party
Janata Party (Secular)
Samajwadi Janata Party
Other key
№: Incumbent number
† Assassinated or died in office
§ Returned to office after a previous term
RES Resigned
NC Resigned following a no-confidence motion
Prime Ministers of India
№
Name
(birth–death)
Portrait
Prior Office
Party
(Alliance)
Elected constituency
Term of office[6]
Appointed by
Lok Sabha[a]
1
Jawaharlal Nehru
(1889–1964) Vice President of Executive Council Indian National Congress Phulpur, Uttar Pradesh 15 August 1947 15 April
1952
16 years, 286 days Lord Mountbatten Constituent Assembly[b]
15 April 1952 17 April 1957 Rajendra Prasad 1st
17 April 1957 2 April 1962 2nd
2 April 1962 27 May
1964[†] 3rd
–
Gulzarilal Nanda (acting)
(1898–1998) Minister of Labour and Employment Indian National Congress Sabarkantha, Gujarat 27 May
1964 9 June
1964 13 days Sarvepalli Radhakrishnan
2
Lal Bahadur Shastri
(1904–1966) Minister of Home Affairs Indian National Congress Allahabad, Uttar Pradesh 9 June
1964 11 January
1966[†] 1 year, 216 days
–
Gulzarilal Nanda (acting)
(1898–1998) Minister of Home Affairs Indian National Congress Sabarkantha, Gujarat 11 January
1966 24 January
1966 13 days
3
Indira Gandhi
(1917–1984) Minister of Information and Broadcasting
Prime Minister (Re-elected)
Indian National Congress Rajya Sabha MP for Uttar Pradesh
Amethi, Uttar Pradesh
24 January
1966 4 March 1967 11 years, 59 days
4 March 1967 15 March 1971 V. V. Giri 4th
15 March 1971 24 March
1977 5th
4
Morarji Desai
(1896–1995) Minister of Finance and Deputy Prime Minister of India before he resigned in 1969 Janata Party Surat, Gujarat 24 March
1977 28 July
1979[RES] 2 years, 126 days B. D. Jatti
(acting President)
6th
5
Charan Singh
(1902–1987) Minister of Finance Janata Party (Secular)
with INC Baghpat, Uttar Pradesh 28 July
1979 14 January
1980[RES] 170 days Neelam Sanjiva Reddy
(3)
Indira Gandhi
(1917–1984) Former Prime Minister Indian National Congress (I) Medak, Andhra Pradesh 14 January
1980[§] 31 October
1984[†] 4 years, 291 days 7th
6
Rajiv Gandhi
(1944–1991) MP for Amethi Indian National Congress (I) Amethi, Uttar Pradesh 31 October
1984 31 December 1984 5 years, 32 days Zail Singh
31 December 1984 2 December
1989 8th
7
Vishwanath Pratap Singh
(1931–2008) Minister of Defence Janata Dal
(National Front) Fatehpur, Uttar Pradesh 2 December
1989 10 November
1990[NC] 343 days R. Venkataraman 9th
8
Chandra Shekhar
(1927–2007) MP for Ballia Samajwadi Janata Party
with INC Ballia, Uttar Pradesh 10 November
1990 21 June
1991[c] 223 days
9
Pamulaparti Venkata Narasimha Rao
(1921–2004) Minister of External Affairs Indian National Congress (I) Nandyal, Andhra Pradesh 21 June
1991 16 May
1996 4 years, 330 days 10th
10
Atal Bihari Vajpayee
(1924–2018) Minister of External Affairs Bharatiya Janata Party Lucknow, Uttar Pradesh 16 May
1996 1 June
1996[RES] 16 days Shankar Dayal Sharma 11th
11
Haradanahalli Doddegowda Deve Gowda
(born 1933) Chief Minister of Karnataka Janata Dal
(United Front) Rajya Sabha MP for Karnataka 1 June
1996 21 April
1997[RES] 324 days
12
Inder Kumar Gujral
(1919–2012) Minister of External Affairs Janata Dal
(United Front) Rajya Sabha MP for Bihar 21 April
1997 19 March
1998 332 days
(10)
Atal Bihari Vajpayee
(1924–2018) Former Prime Minister Bharatiya Janata Party
(NDA) Lucknow, Uttar Pradesh 19 March
1998[§] 10 October 1999 6 years, 64 days K. R. Narayanan 12th
10 October 1999 22 May
2004 13th
13
Manmohan Singh
(born 1932) Minister of Finance Indian National Congress
(UPA) Rajya Sabha MP for Assam 22 May
2004 22 May 2009 10 years, 4 days A. P. J. Abdul Kalam 14th
22 May 2009 26 May
2014 Pratibha Patil 15th
14
Narendra Modi
(born 1950) Chief Minister of Gujarat Bharatiya Janata Party
(NDA) Varanasi, Uttar Pradesh 26 May
2014[7] Incumbent 4 years, 156 days Pranab Mukherjee 16th
Jump up ^ Although the Prime Minister can be a member of either house of the Parliament, they have to command the confidence of the Lok Sabha. Upon dissolution of the Lok Sabha, the outgoing PM remains in office until their successor is sworn-in.
Jump up ^ The Constituent Assembly of India consisted of 389 members elected in 1946 by the provincial assemblies by a single, transferable-vote system of proportional representation. The Assembly was replaced by the Provisional Parliament of India after adoption of the Constitution on 26 January 1950 until the first general elections.
Jump up ^ Chandra Shekhar officially resigned as Prime Minister on 13 March 1991, but he and his ministers continued in office until Rao succeeded him.
See also
Government of India portal
India portal
Prime Minister's Office
List of Prime Ministers of India by longevity
List of Presidents of India
References
General
"Former Prime Minister's of India". Prime Minister's Office (PMO). Retrieved 22 November 2017.
"Gallery of Prime Ministers". Press Information Burea. Retrieved 22 November 2017.
Guha, Ramachandra (2011). India After Gandhi: The History of the World's Largest Democracy. Pan Macmillan. ISBN 9780330540209.
Brass, Paul R. (1994). The Politics of India Since Independence. Cambridge University Press. ISBN 9780521459709.
Specific
Jump up ^ Constitutional Government in India. S. Chand Publishing. 2003. ISBN 9788121922036.
Jump up ^ "Former Prime Ministers | Prime Minister of India". www.pmindia.gov.in. Retrieved 2018-01-03.
Jump up ^ "In India, next generation of Gandhi dynasty". Washington Post. Retrieved 2016-12-27.
Jump up ^ Diplomat, Ankit Panda, The. "BJP, Modi Win Landslide Victory in Indian Elections". The Diplomat. Retrieved 2016-12-27.
Jump up ^ "Indian National Congress". Encyclopædia Britannica. Retrieved 21 May 2014.
Jump up ^ "Former Prime Ministers". PM India. Archived from the original on 9 October 2014. Retrieved 2 January 2015.
Jump up ^ "Narendra Modi appointed Prime Minister, swearing in on May 26". The Times of India. 20 May 2014. Retrieved 22 January 2015.
show
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Prime Minister of India
Jawaharlal Nehru
Gulzarilal Nanda (acting)
Lal Bahadur Shastri
Gulzarilal Nanda (acting)
Indira Gandhi
Morarji Desai
Charan Singh
Rajiv Gandhi
V. P. Singh
Chandra Shekhar
P. V. Narasimha Rao
Atal Bihari Vajpayee
H. D. Deve Gowda
I. K. Gujral
Manmohan Singh
Narendra Modi
List
List by longevity
Official residence
PM's Office
show
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Indian union ministries
Interim
Nehru I
Nehru II
Nehru III
Nehru IV
Shastri
I. Gandhi I
I. Gandhi II
Desai
C. Singh
I. Gandhi III
R. Gandhi
V. P. Singh
Chandra Shekhar
Rao
Vajpayee I
Deve Gowda
Gujral
Vajpayee II
Vajpayee III
M. Singh I
M. Singh II
Modi
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