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Sansa Stark
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Sansa Stark
A Song of Ice and Fire character
Game of Thrones character
Sophie Turner as Sansa Stark
First appearance
Novel:
A Game of Thrones (1996)
Television:
"Winter Is Coming" (2011)
Created by
George R. R. Martin
Portrayed by
Sophie Turner
(Game of Thrones)
Information
Aliases
Little Bird
Alayne Stone
Jonquil
Gender
Female
Title
Lady of Winterfell (TV series)
Princess
Family
House Stark
House Lannister
House Bolton (TV series)
Spouse(s)
Tyrion Lannister (unconsummated)
Ramsay Bolton (TV series)
Relatives
Ned Stark (father)
Catelyn Tully (mother)
Robb Stark (brother)
Arya Stark (sister)
Bran Stark (brother)
Rickon Stark (brother)
Jon Snow (half-brother; books)
(cousin/adoptive brother; TV series)
Brandon Stark (uncle)
Benjen Stark (uncle)
Lyanna Stark (aunt)
Lysa Tully (aunt)
Edmure Tully (uncle)
Robert/Robin Arryn (cousin)
Kingdom
The North
The Crownlands
Sansa Stark is a fictional character created by American author George R. R. Martin. She is a prominent character in Martin's award-winning A Song of Ice and Fire series.
Introduced in 1996's A Game of Thrones, Sansa is the eldest daughter and second child of Lord Eddard Stark and his wife Lady Catelyn Stark. She subsequently appeared in the following three novels, A Clash of Kings (1998), A Storm of Swords (2000) and A Feast for Crows (2005). While absent from the fifth novel A Dance with Dragons as the books are separated geographically, Sansa is confirmed to return in the forthcoming next book in the series, The Winds of Winter.[1]
In HBO's adaptation of the series, Game of Thrones, Sansa Stark is portrayed by Sophie Turner.[2][3] The character has received critical acclaim, being praised as the 4th greatest character in the series by Rolling Stone.[4] She and the rest of the cast were nominated for Screen Actors Guild Awards for Outstanding Performance by an Ensemble in a Drama Series in 2012, 2014, 2015 and 2016.
Contents
[hide]
1 Character and appearances
2 Storylines
2.1 A Game of Thrones
2.2 A Clash of Kings
2.3 A Storm of Swords
2.4 A Feast for Crows
2.5 Family tree of House Stark
3 TV adaptation
3.1 Storylines
3.1.1 First season
3.1.2 Second season
3.1.3 Third season
3.1.4 Fourth season
3.1.5 Fifth season
3.1.6 Sixth season
3.1.7 Seventh season
3.2 Reception
3.2.1 Controversy
3.3 Recognition and awards
4 References
4.1 Inline citations
4.2 General references
Character and appearances[edit]
Sansa Stark is the second child and elder daughter of Eddard Stark and Catelyn Stark. She was born and raised in Winterfell, until leaving with her father and sister at the beginning of the series. She has a younger sister Arya Stark, two younger brothers Rickon Stark and Bran Stark, as well as an older brother Robb Stark, and an older illegitimate half-brother, Jon Snow [5] who later turned out to be her paternal cousin, but this is only confirmed in the TV show for the time being.
Raised as a lady, Sansa is traditionally feminine. Sansa's interests are music, poetry, and singing. She strives to become like the heroines of romantic tales by attempting to find a prince, knight, or gentleman to fall in love with. For a companion animal, she owned a direwolf named Lady. However, Lady was killed in place of Arya's direwolf, Nymeria, in the first installment. Lady is killed because Nymeria attacked the Crown Prince, Joffrey Baratheon and later fled.
Sansa has been described as tall, slim, womanly, and beautiful, destined to be a lady or a queen. She has blue eyes and thick auburn hair that she inherits from her mother, who came from House Tully in the Riverlands region prior to her marriage to Eddard Stark. She has her hair dyed dark brown later on while in the Vale, disguising as Alayne Stone- the bastard daughter of Petyr Baelish. Sansa is 11 years old in A Game of Thrones and nearly 14 in A Feast for Crows. Arguably the most naive of the Stark children at the start of the series, Sansa often finds herself used as a pawn in the machinations of the other characters. However, as the story progresses, she matures and becomes more of a player of the game rather than a pawn for other characters.[6]
Storylines[edit]
Coat of arms of House Stark
A Game of Thrones[edit]
Sansa Stark begins the novel by being betrothed to Crown Prince Joffrey Baratheon, believing Joffrey to be a gallant prince. While Joffrey and Sansa are walking through the woods, Joffrey notices Arya sparring with the butchers boy, Mycah. A fight breaks out and Joffrey is attacked by Nymeria (Arya's Direwolf) after Joffrey threatens to hurt Arya. Sansa lies to King Robert about the circumstances of the fight in order to protect both Joffrey and her sister Arya. Since Arya ran off with her wolf to save it, Sansa's wolf is killed instead, estranging the Stark daughters.
During the Tourney of the Hand to honour her father Lord Eddard Stark, Sansa Stark is enchanted by the knights performing in the event. At the request of his mother, Queen Cersei Lannister, Joffrey spends a portion of the tourney with Sansa, but near the end he commands his guard Sandor Clegane, better known as The Hound, to take her back to her quarters. The Hound tells Sansa the little known story of his burned face and why he dislikes knights, in turn she comforts him.
After Eddard discovers the truth of Joffrey's paternity, he tells Sansa that they will be heading back to Winterfell. Sansa is devastated and wishes to stay in King's Landing, so she runs off to inform Queen Cersei of her father's plans, unwittingly providing Cersei with the information needed to arrest her father. After Robert dies, Sansa begs Joffrey to show mercy on her father and he agrees to allow Ned to live if Ned will swear an oath of loyalty. After promising Sansa that he will be merciful, Joffrey betrays his word and has her father executed in front of her. Sansa is now effectively a hostage in King's Landing and finally sees Joffrey's true nature after he forces her to look at the tarred head of her now deceased father.
A Clash of Kings[edit]
Sansa is a hostage in King's Landing, and has learned to be outwardly loyal to King Joffrey to avoid severe physical abuse.
At the celebration for Joffrey's name day, she saves the life of Ser Dontos Hollard after he shows up late and heavily inebriated. She begs Joffrey to spare his life and in turn wins Dontos' apparent loyalty. Later Ser Dontos reveals a plan to her to help her escape from King's Landing. Sansa is routinely beaten by Joffrey's guards. After her brother has won a battle against Joffrey's maternal family, she is publicly beaten and has her clothes torn. Tyrion Lannister intervenes on the abuse on her behalf, and Sandor Clegane, gives her his cloak to cover herself. Later, Sandor Clegane saves Sansa from a riot in King's Landing.
During the Battle of Blackwater Bay, all of the highborn ladies in King's Landing stay in the Red Keep with Queen Cersei who drunkenly mocks and berates Sansa. After Cersei learns that they are losing the battle, she flees and Sansa comforts the remaining women before going to her quarters. Once there she finds Sandor Clegane there who offers to take her away with him during the Battle of the Blackwater, although Sansa refuses. Before he vanishes from King's Landing, she gives him a song, and he gives her his cloak a second time. When Sansa awakens, the battle is over. House Lannister has won the battle, her betrothal to Joffrey is called off so he can marry Margaery Tyrell instead. Joffrey informs Sansa that he can still use her when he is married and to expect a nightly visitor for a long while.
A Storm of Swords[edit]
In the third book, Sansa is invited by Margaery to dine with her and her grandmother Olenna Redwyne. The two women seek to learn the true nature of Joffrey Baratheon after he and Margaery have become betrothed. In turn, Olenna suggests that Sansa should marry Willas Tyrell, brother to Margaery and grandson to Olenna. Sansa reveals the marriage plan to Ser Dontos who warns her of the Tyrells, however Sansa develops a close friendship with Margaery and is excited about becoming a part of her family when she marries Willas. However, when Tywin learns of the marriage plot he schemes to have Sansa's brother Robb Stark killed, knowing that would leave Sansa to inherit Winterfell and the North. He then commands his son Tyrion Lannister to marry Sansa. Tyrion is initially opposed to the marriage, but is eventually enticed by the prospect of becoming Lord of Winterfell, and so agrees to marry her.
Sansa is shocked one morning when she is being fitted for a gown that she is to marry Tyrion that day. Joffrey taunts Sansa and acts on behalf of her father to give her away during the ceremony to add further insult. Sansa ignores Tyrion and refuses to bend as he attempts to put his cloak around her, an important marriage custom in Westeros. In turn, Joffrey commands Ser Dontos to act as a stool so that Tyrion can cloak his bride in spite of his short stature. Later Sansa dances with many lords who attempt to offer words of comfort, however when it is her turn to dance with Joffrey, he threatens to rape her after her marriage. Tyrion intervenes and states his desire to castrate Joffrey. After the wedding ceremony, Tyrion chooses not to consummate the marriage due to Sansa's lack of desire in him. It is not long before many in King's Landing come to know that the marriage was never consummated.
It is not long after Sansa's marriage that Joffrey and Margaery are wed and afterwards there is a grand feast. At Joffrey's wedding, Joffrey is poisoned, and Cersei orders both Tyrion and Sansa to be arrested. As Joffrey begins to choke to death, Sansa manages to flee during the chaos. Once in her room, she gathers her belongings and notices that one of the amethysts from her hairnet, a gift from Ser Dontos, is missing. Sansa immediately realizes that the prince had been poisoned and starts to doubt Ser Dontos' rescue plan. Understanding that she will be implicated in the murder of Joffrey, she chooses to flee King's Landing with the knight anyway. Ser Dontos is later killed by Petyr Baelish, who reveals that he is the mastermind behind nearly all of the intrigues in the capital. He reveals that he was the one who sent Dontos to her and that Olenna took the amethyst from her hairnet.
Baelish smuggles Sansa to safety in the Vale of Arryn, where she poses as his bastard daughter Alayne Stone. She is taken to her Aunt Lysa Arryn, now married to Baelish. Lysa declares that Sansa must marry her sickly boy Robert, heir to the Vale. Petyr Baelish and Lysa are wed, however Lysa becomes jealous when she witnesses Littlefinger kissing her niece. Lysa later attempts to murder Sansa, but she is saved once again by Baelish, who kills Lysa.
A Feast for Crows[edit]
After Lysa's death, Sansa becomes mistress of the Eyrie and continues to pretend to be Baelish's illegitimate daughter, Alayne Stone. Baelish successfully pacifies the lords of the Vale, who suspected Baelish's hand in Lysa's death. Afterwards, Baelish reveals to Sansa his plans to eventually marry her to the heir to the Vale, Harrold Hardyng, and his long range plans to reveal her true identity and reclaim the North. Sansa acts as a mother figure to Robert Arryn, caring for him after the death of his mother Lysa, and is shown to have grown in intelligence since the start of the series - she is able to figure out some of Baelish's plans, and does not trust him as she once did with Joffrey.
Family tree of House Stark[edit]
[hide]
v
t
e
Descendants of Rickard Stark
Rickard[a] Lyarra[b]
Brandon[a] Catelyn
Tully[c] Eddard[a] Lyanna[a][d] Benjen[a]
Robb[c] Jeyne
Westerling[e] Sansa[c] Tyrion
Lannister[f] Arya[c] Brandon[c] Rickon[c] Jon
Snow[c][d]
Notes:
^ Jump up to: a b c d e Martin, George R. R. (1996). "Chapter 4: Eddard". A Game of Thrones. pp. 36–45. ISBN 978-0-553-89784-5.
Jump up ^ Martin, George R. R.; García Jr., Elio M.; Antonsson, Linda (2014). "Appendix: Stark Lineage". The World of Ice & Fire. ISBN 978-0-553-80544-4.
^ Jump up to: a b c d e f g Martin. "Appendix: House Stark". A Game of Thrones. pp. 785–786.
^ Jump up to: a b In the TV series Game of Thrones, Jon is the son of Rhaegar Targaryen and Lyanna
Jump up ^ Martin, George R. R. (2000). "Chapter 14: Catelyn". A Storm of Swords. pp. 192–193. ISBN 978-0-553-89787-6.
Jump up ^ Martin, George R. R. (2000). "Chapter 28: Sansa". A Storm of Swords. pp. 382–393. ISBN 978-0-553-89787-6.
TV adaptation[edit]
Storylines[edit]
First season[edit]
Sansa is first seen with Arya at Winterfell during their embroidery lesson with Septa Mordane. Following the arrival of Robert Baratheon and his escort at Winterfell, he insists to Ned that Joffrey and Sansa should be married in order to join their houses. Sansa, who is desperate to leave Winterfell begs Catelyn to make Ned agree to the engagement. Following Sansa, Ned, and Arya's departure from Winterfell, Joffrey is injured by Arya's direwolf Nymeria, after he attacks the butcher's boy (Arya's friend), and Arya. Sansa, who was a witness, claims to Robert and Cersei that she did not know what happened. As retribution for Joffrey's injury, Cersei convinces Robert to have Sansa's direwolf, Lady, slaughtered in place of the missing Nymeria. After arriving at Kings Landing, Sansa attends the Hands Tourney where Petyr 'Littlefinger' Baelish tells Sansa and Arya the story behind how Sandor 'The Hound' Clegane's face was burned. As time passes, Sansa begins to wear her hair like a southerner, and becomes rude towards Mordane, while also expressing fears that she will fail to give Joffrey a male heir. Following Ned's initial resignation as hand of the king, Sansa is devastated to hear she has to return to Winterfell, in which she likens Joffrey to a lion, and that he was nothing like Robert Baratheon. This statement from Sansa inspires Ned to investigate the Baratheon family line, prompting him to realise that Cersei's children were bastards fathered by Jaime Lannister, not Robert Baratheon. Following Robert's death, and Ned's arrest for declaring Joffrey was not the true king, The entire Stark household in Kings Landing, with the exception of Sansa and Arya, are executed. Cersei persuades Sansa to write to Robb and Catelyn Stark imploring them to swear fealty to Joffrey. At court, Sansa pleads to Joffrey to show Ned mercy, in which he agrees on the condition Ned swears loyalty to Joffrey. Sansa is present at the Great Sept of Baelor, where she is initially confident Ned will be saved. However, Sansa is horrified when Joffrey orders Ned's execution, and begs someone to intervene, before fainting as Ned is beheaded. Sansa, grieving the death of her father, is forced by Joffrey to look upon the spiked heads of both Ned and Septa Mordane. Sansa begs Joffrey to let her return home, but he informs Sansa that they are still to be married, and that she will stay and obey. Joffrey also tells Sansa that he will give her Robb's head once he is defeated, in which she retorts that Robb will give her Joffrey's head instead. While on the boardwalk, Sansa moves to push Joffrey to his death, but is stopped by Sandor Clegane, who warns her she will continue to be abused.
Second season[edit]
As the war of the five kings progresses, Sansa's position in Kings Landing becomes more perilous. On Joffrey's name day celebration, Sansa saves an inebriated Ser Dontos Hollard from execution, convincing Joffrey to instead make Dontos his fool. While at the celebration, Tyrion offers his condolences for Ned's death, in which Sansa insists her family are all traitors and that she is loyal to Joffrey. Later on, when her eldest brother Robb wins a battle against the Lannisters, Sansa is publicly beaten and humiliated in front of the court by Joffrey and Ser Meryn (on Joffrey's orders), as payment for her brother's crimes. Tyrion Lannister enters the court and rescues Sansa. Despite being a dwarf, Tyrion takes pity on Sansa's situation, and offers to have the engagement called off. Sansa maintains her facade that she is loyal to Joffrey, which impresses Tyrion to the point of believing Sansa might just survive Kings Landing. Tyrion has his lover, Shae, positioned as Sansa's handmaiden. Sansa and Shae form a friendship, in which Sansa is able to vent about her hatred of the Lannisters without fear of being revealed. Sansa is present when the royal family bids farewell to Joffrey's sister, Myrcella, on her departure to Dorne to form an alliance between the Lannisters and the Martells. While returning to the Red Keep, a riot breaks out in the streets of Kings Landing, amidst which Sansa finds herself caught in the fray. Three peasant men chase Sansa and attempt to rape her, before she is rescued and returned to the castle by Sandor Clegane. The following morning, Sansa has a nightmare of the incident, and wakes up in a bloodstained bed. Sansa had flowered, which meant she could bear Joffrey children. Sansa and Shae attempt to conceal this, which involved Shae threatening to kill a witness handmaiden if she told anyone. However, Sandor Clegane sees the blood, and both Cersei and Joffrey are informed. Cersei invites Sansa to her chambers to share some of her wisdom and experience as a wife and a mother. Cersei reminisces that her husband Robert was not interested in her giving childbirth. Cersei explains to Sansa that while Sansa may never love Joffrey (and vice versa), she will love his children. Cersei warns Sansa that the more people she loves, the weaker she will be. Therefore, Sansa should only love her children, as it is the only love she has no choice in. Before the battle of the Blackwater, Joffrey forces Sansa to kiss the blade of his sword, while bragging he will kill Stannis himself. Sansa implicitly taunts Joffrey by remarking he must be battling in the vanguard (which of course he would not be). Joffrey responds to this by insisting Sansa will kiss the blade again with Stannis' blood on it. During the battle, Sansa takes refuge with Cersei, Shae and the other women and children of Kings Landing. A drunk Cersei openly torments Sansa and the women. She does this by explaining that if the city falls, they will all be raped and have bastards in their bellies come morning. Cersei continues her taunting by also telling Sansa that tears are not the only weapons women have; the greatest weapon they own are between their legs. Following Cersei's departure from the refuge with Tommen, Sansa leaves to hide in her bedchamber, where she finds Sandor Clegane. Sandor, about to leave Kings Landing, offers to take Sansa home. Sansa declines, insisting Stannis would not harm her. After the battle is won by the Lannister-Tyrell forces, Loras Tyrell asks Joffrey to take his sister, Margaery, as his bride. Joffrey accepts the proposal, which annuls his marriage with Sansa. Sansa, while pretending to be devastated, is secretly delighted she no longer has to marry Joffrey. However Petyr Baelish warns that while Sansa is no longer engaged, Joffrey would have greater rein to abuse Sansa, especially now she is a woman. Petyr assures Sansa he will help get her home, in which Sansa once again displays a facade, asserting Kings Landing is her home. Petyr advises Sansa that everyone in Kings Landing is a liar, and that they are much more cunning at it than her.
Third season[edit]
With her engagement to Joffrey annulled, Sansa does not have to worry about spending the rest of her life with him, but is with lesser protection from tormentors. Petyr Baelish, an old friend of her mother's with a reputation for being sadistic and cunning, tells her that he can smuggle her out of the city, but she is reluctant. Sansa finds a friend in Loras Tyrell, who is kind to her and whom she hopes will ask for her hand. His sister, Joffrey's new fiance, Margaery, is also kind to her and takes her to dine with her grandmother, Olenna Tyrell, who asks her for her opinion of Joffrey. Sansa reveals Joffrey's true, cruel personality, but Margaery and Lady Olenna merely pass it by as a trivial matter, saying there is nothing to be done to change a man's character, especially a king's. Sansa's affection for Loras grows, unaware that Loras is gay and, while he likes her and enjoys spending time with her, can never love her. Margaery proposes the idea that Loras will marry Sansa, meaning Sansa can leave King's Landing, which she is overjoyed at. But when this is reported to the Lannisters, they fear that the Tyrells will pose an even greater threat with a member of House Stark as one of their allies, and quickly end the idea of the engagement, betrothing Loras to Cersei and engaging Sansa to Tyrion, which both Sansa and Shae are against. However, the day of the wedding, Tyrion promises not to harm her and, as she prepares to consummate the marriage, Tyrion realizes how unhappy she is and tells her that she doesn't have to consummate it unless she wants to. When Sansa asks Tyrion what would happen if she never wants him in her bed he quips "And so my watch begins." She and Tyrion do form somewhat of a friendly relationship, as he is kind to her and treats her well, and she soon realizes there are worse Lannisters to be wed to. However, their cordial relationship suffers a crushing blow when Sansa receives news of Robb and Catelyn's death at the Red Wedding, an event orchestrated by Tywin Lannister, Tyrion's father.
Fourth season[edit]
Sansa, still distraught over the death of Robb and Catelyn, is approached by Dontos Hollard, a former knight whom Sansa had convinced Joffrey to make his fool instead of executing him. Dontos gives her a necklace, claiming it was his mother's. However, the necklace turns out to be a fake; one of the gems contains poison, which Lady Olenna Tyrell uses to poison Joffrey at his wedding to Margaery Tyrell. In the commotion, Sansa is taken by Dontos, to Baelish's boat in Blackwater Bay. Baelish smuggles Sansa from King's Landing after both revealing the nature of the necklace and having Dontos killed by crossbow.
Lord Baelish, with Sansa posing as his bastard daughter Alayne Stone, pass through the Blood Gates to the Eyrie and to the keep of Lysa Arryn. Lysa initially invites them with open arms, revealing she knows exactly who her niece is, and they are welcome to be housed. It is soon revealed however, Lysa mistrusts the relationship between Sansa and Baelish accusing Baelish of violating Sansa and accusing him of never loving her. Later in the keep, Sansa strikes Lysa's son Robin and Baelish appears. Baelish then proclaims his undying love for her deceased mother, Catelyn and he shares a kiss with a stunned Sansa, with Lysa watching from above. Sansa is immediately summoned to Lysa's throne room, where she believes she had been summoned for striking her son. Lysa reveals she had observed the kiss, and though defending herself and Baelish's actions against her, Lysa holds her to the Moon Door, a trap door that leads hundreds of feet down into the mountains below. Baelish intervenes before she gets the chance to execute Sansa and pushes Lysa to her death instead as he proclaimed his love for her sister. Then Baelish later claimed to the lords of the Vale that she committed suicide. Sansa is called to give testimony, and although she reveals her true identity, she supports Baelish's story. She then joins Baelish and her cousin Robin Arryn on a tour of the Vale.
Fifth season[edit]
Baelish brokers a marriage between Sansa and Ramsay Bolton, now the heir to the North after the death of Robb Stark. Though reluctant to marry Ramsay, as his father Roose had personally murdered Robb, Baelish persuades her by claiming that the marriage will give her the opportunity to avenge her family. On the way to Winterfell, they encounter Brienne of Tarth, who had sworn to Catelyn Stark to take Sansa to safety and tries to convince Sansa to come with her; Baelish has her chased off by his men, but Brienne follows Sansa to Winterfell regardless. Though initially charming, Ramsay's sadistic nature becomes apparent when Sansa discovers that he has captured and enslaved Ned's former ward Theon Greyjoy, who had supposedly killed Sansa's brothers Bran and Rickon, and forced him to assume the identity of his serving man, Reek. After Ramsay rapes Sansa on their wedding night, Sansa asks Reek to signal to Brienne for help. Reek, wishing to spare Sansa Bolton's wrath, instead tells Ramsay, and he proceeds to flay the maid who had told Sansa of the signal and forces Sansa to look at her corpse. Furious, Sansa confronts Reek, who admits that he had failed to capture Bran and Rickon and killed two farm boys in their place. While the Boltons prepare to battle Stannis Baratheon's advancing forces, Sansa signals to Brienne, unaware that she has left to kill Stannis. When help does not come, Sansa attempts to return to her room but is caught by Ramsay's paramour Myranda, who threatens to mutilate Sansa. Finally snapping, Theon throws Myranda to her death, just as the Bolton forces return. Fearful of Ramsay's reaction, the two jump from Winterfell's battlements into the snow.
Sixth season[edit]
Sansa and Theon are captured by Bolton soldiers in the forest outside Winterfell, but Brienne and her squire Podrick Payne arrive in time to rescue them and kill the Bolton soldiers. This time, Sansa accepts Brienne's loyalty. While Theon returns to the Iron Islands, Sansa, Brienne, and Podrick journey on to Castle Black, where her half-brother Jon Snow has just resigned as Lord Commander of the Night's Watch. Sansa tries to persuade Jon to help her drive the Boltons out of Winterfell; although Jon initially refuses, he changes his mind after Ramsay sends a letter to Jon in which he gloats that he holds Rickon Stark captive and threatens to kill the Starks and the Wildlings Jon has let through the Wall if Sansa is not returned. Before Jon and Sansa leave Castle Black, Baelish arranges a meeting with Sansa in Mole's Town. He insists that he was unaware of Ramsay's nature and offers the support of the Knights of the Vale, also mentioning that her great-uncle Brynden "Blackfish" Tully has captured Riverrun from House Frey. Sansa sends Baelish away, declaring that she never wants to see him again, but sends Brienne to the Riverlands to convince the Blackfish to aid the Starks.
Although Jon and Sansa are only able to win over a handful of Northern lords, Jon insists that they must march on Winterfell, despite Sansa's objections. Sansa sends a letter to Baelish asking for his aid, and the Vale forces arrive at Winterfell in time to defeat the Boltons. Ramsay is captured and imprisoned with his hounds, and Sansa watches with satisfaction as they devour him alive. In the aftermath of the battle, she and Jon share a moment where Sansa apologizes for not telling Jon about Baelish and the Knights of the Vale. Jon forgives her but asks that they trust each other completely from now on. Sansa and Jon then share a happy smile when Sansa tells him that Winter is finally here. While in the godswood Baelish confesses his ambition to rule Westeros with Sansa at his side, but Sansa rebuffs his advances. Sansa also ignores Baelish's attempts to drive a wedge between her and Jon, but is surprised when the Northmen and Valemen declare Jon the new King in the North. Despite this she smiles at him happy that he has been praised. But she stops smiling when she notices Littlefinger glaring sinisterly at her and Jon.
Seventh season[edit]
Jon travels to Dragonstone to negotiate with Daenerys Targaryen for her support against the White Walkers, leaving Sansa as regent in his absence. Soon after, Bran and Arya return to Winterfell. Littlefinger seeks to drive a wedge between Sansa and Arya by letting Arya find Sansa's letter to Robb asking him to bend the knee to Joffrey, causing Arya to angrily confront Sansa. Sansa later sneaks into Arya' quarters and comes across the "faces" Arya has taken from the various people she has killed on her travels; Arya catches Sansa and tells Sansa of her ability to assume people's identities with the faces while menacing Sansa with a dagger, before abruptly handing Sansa the dagger and leaving.
Sansa later receives an invitation to King's Landing, where Jon intends to present Cersei (now Queen of the Seven Kingdoms) with proof of the White Walkers' existence. Refusing to return to King's Landing, she sends Brienne as her representative.
Sansa later shows Littlefinger the letter she received from Jon following the meeting in King's Landing, in which Jon states that he had pledged his support to Daenerys Targaryen. Littlefinger continues his manipulation of Sansa by claiming that Jon had betrayed the North and Sansa should seize power from Jon, as well as seemingly convincing her that Arya intends to murder her and take her role as Lady of Winterfell. Sansa summons Arya to the great hall and begins an accusation of treason and murder, but surprisingly directs the accusation towards Littlefinger. With help from their brother Bran (now known as Three-Eyed Raven), Sansa and Arya reveal that they are aware of Baelish's lies and treason and reveal his numerous crimes, including his murder of Lysa Arryn, his orchestrating the murders of both Jon Arryn and Eddard Stark, and his manipulating the Starks and Lannisters to war. Finding himself without support, Baelish tries to plead for his life, but Sansa refuses and allows Arya to slit Baelish's throat with his own Valyrian dagger, ending his manipulation and treachery for good. The Stark sisters later resolve their differences, and acknowledge that the Starks must stand together to survive the winter.
Reception[edit]
Sophie Turner plays the role of Sansa Stark in the television series
As her storyline has progressed, Sansa has received critical acclaim for the development of her character and her emergence from a naive young girl to a strong young woman. Rolling Stone ranked Sansa as No. 4 on a list of the "Top 40 Game of Thrones Characters", saying that Sansa is "often overlooked in favor of her killer kid sister", but that her "quiet, innate political shrewedness and emotional strength have enabled her to survive", and calling her "the show's best-kept secret".[7] In a ranking of the 48 best Game of Thrones characters listed in the main credits in the first five seasons on the website The Wrap, Sansa was ranked at No. 4, ahead of the more popular Daenerys Targaryen, Jon Snow, and Tyrion Lannister, saying that "Sansa has been kind of great in Season 6, turning into the sort of badass we always hoped but never thought she actually could become".[8]
In an article published on Mic.com, Julianne Ross says that "the elder Stark daughter is often cited as one of the most reviled characters on Game of Thrones", while also saying that "not coincidentally, Sansa Stark is also one of the most classically feminine characters on the show." Ross criticized the heavy hatred for Sansa, particularly in contrast to "her universally (and rightly) adored tomboy little sister Arya", stating that Sansa "arguably gets a disproportionate amount of fan hate because she doesn't fit the narrow 'strong female character' mold we're used to rooting for." [9] Blogger Rhiannon Thomas of Feminist Fiction wrote in 2012 that "the focus on this sort of female character - the oft-cited 'strong female character' - seems to suggest that femininity is still bad, and that women can only be strong by adopting stereotypically male roles and attitudes". Thomas went on to say that "in an abusive situation that would break so many people, Sansa survives" and that she has a "woman's courage" that "keeps her alive and in the game where characters like Arya would not last five minutes".[10]
In an article published on MTV.com by Crystal Bell titled "Sansa Stark is the Only Game of Thrones Hero Worth Rooting For",[11] Bell writes: "Sansa is the most relatable character in George R.R. Martin's canon. She's often despised for having no agency, but the way I see it, Sansa is hated for being a woman. Unlike Brienne, Arya, Cersei, and Margaery -- models of the "strong female character" archetype—Sansa's passivity denotes weakness. She doesn't have cool swordplay skills like her sister Arya; she isn’t a smart seductress like Margaery Tyrell or a fierce queen like Cersei. She is the epitome of femininity on Game of Thrones, and therefore, she is dismissed." Bell went on to say: "However, Sansa's greatest strength as a character has been her unwavering resilience. She was tortured and humiliated for seasons by the unhinged man-boys around her. She's been the subject of everyday sexism and misogyny since day one. And yet, she survives, even as armor-clad heroes fall before her. She is the show's survivor. She continuously endures the pain and humiliation of being a woman in Westeros. Just because Sansa doesn't wield a sword as fiercely as Arya and Brienne, or command a horde of dragons like Daenerys Targaryen, doesn't make her any less of a hero."
Sansa received particular acclaim in Season 6 of the show, during which she began her quest to retake her family home and exact revenge on those who wronged her. In an interview with The New York Times, actress Sophie Turner said that "she's [Sansa] no longer a pawn in anyone's game; she's no longer a prisoner...she's the one taking charge and doing her own thing, which is very exciting".[12] Megan Garber of The Atlantic praised the show's decision to have Sansa be the one orchestrating Ramsay's death in Battle of the Bastards, saying that "In the end, it was Sansa and her abuser, alone again in a darkened chamber; in the end though, it was Sansa making the decisions about who would be the victim." [13] On the scene, Turner said: "It's amazing. It's Sansa's first kill and it's such a strong moment for her because all her life she's been affected by these men who have just done such terrible things to her...."[14]
Following the penultimate Season 6 episode, Bennett Madison of Vanity Fair wrote "When Sansa icily reminds her dopey brother that 'No one can protect you', it's because she's always been on her own. As far back as King's Landing, Sansa's between quietly protecting herself, working on her stitchery while taking cool measure of everything going on around her, learning how to game the system, and slithering through situations that would have gotten the best of the show's more flashy or impulsive characters. In 'Battle of the Bastards', she got to show a little flash of her own; by being defiantly, gloriously correct in her convictions, by saving the day with her foresight and savvy, and by feeding Ramsay to the dogs." [15] Turner later told Time magazine about how gratifying it was to watch Sansa's development during Season 6 and defended the show on its cruel treatment of women: "In my opinion, Game of Thrones is not sexist, and its accurate to medieval time. The show puts social boundaries on the women, and they break out of these boundaries."[16]
Controversy[edit]
In the episode "Unbowed, Unbent, Unbroken", Sansa's rape was the main subject of controversy for the season's deviations from the books. The majority of professional criticism concerned the decision to have Ramsay rape Sansa on their wedding night, with most critics describing the scene as gratuitous and artistically unnecessary. "This grim scene was difficult for the show to justify," said Charlotte Runcie of The Daily Telegraph.[17] Joanna Robinson of Vanity Fair added, "this rape scene undercuts all the agency that’s been growing in Sansa since the end of last season. [...] I’d never advocate that Game of Thrones (or any work of fiction) shy away from edgy plots out of fear of pushback or controversy. But edgy plots should always accomplish something above pure titillation or shock value and what, exactly, was accomplished here?"[18] Christopher Orr wrote in The Atlantic, "I continue to be astonished that showrunners Benioff and Weiss still apparently believe that their tendency to ramp up the sex, violence, and—especially—sexual violence of George R.R. Martin’s source material is a strength rather than the defining weakness of their adaptation."[19] Myles McNutt of The A.V. Club wrote, "The issue with the show returning to rape as a trope is not simply because there have been thinkpieces speaking out against it, and is not solely driven by the rational concerns lying at the heart of those thinkpieces. It’s also that the show has lost my faith as a viewer."[20] Writers from Vanity Fair, The Mary Sue and The Daily Beast all disapproved of the decision to use Sansa's victimization as a motivating agent for Theon, saying that the scene undermined Sansa's character development: "Was it really important to make that scene about Theon's pain?" wrote Joanna Robinson of Vanity Fair.[18][21][22]
Other critics responded positively to the scene. Sean T. Collins of Rolling Stone wrote: "[B]y involving a multidimensional main character instead of one introduced primarily to suffer, the series has a chance to grant this story the gravity and seriousness it deserves.[23] Sarah Hughes of The Guardian wrote: "I have repeatedly made clear that I’m not a fan of rape as a plot device – but the story of Ramsay and Sansa’s wedding was more than that. [...] The writers are walking a very fine line here. They handled it well tonight, telling a gothic tale of innocence sacrificed".[24] Alyssa Rosenberg of The Washington Post wrote that the scene "managed to maintain a fine balance, employing a dignity and care for the experiences of victims that Game of Thrones has not always demonstrated."[25]
Some critics questioned why this scene in particular should generate outrage when similar scenes have not. Sara Stewart of the New York Post pointed out that the rape and sexual abuse of both female and male characters is typical for Game of Thrones: "Why are we suddenly so outraged about the rape of Sansa Stark, when this show has served up a steady diet of sexual assault and violence against women since its first season began?"[26] Cathy Young of Reason magazine, writing in Time noted what she calls a lack of complaint in response to the sexual mistreatment of male characters in earlier seasons, specifically the literal emasculation of Theon Greyjoy and the sexual assault of Gendry.[27]
Criticism of the scene has not extended to the quality of the acting. Joanna Robinson of Vanity Fair wrote, "And if we can say one positive thing about that scene it's that Allen nailed his performance. Theon's horror mirrored our own and the camera—focusing on his reaction—let our minds fill in the blanks."[18] Sophie Turner defended the scene as an artistic challenge for herself as an actor, saying, "When I read that scene, I kinda loved it. I love the way Ramsay had Theon watching. It was all so messed up. It's also so daunting for me to do it. [...] I think it's going to be the most challenging season for me so far, just because it's so emotional for her. It's not just crying all the time, like seasons 2 or 3, it's super messed up."[28] Iwan Rheon (Ramsay Bolton) agreed, referring to Turner's performances this season as "absolutely amazing."[29]
Some viewers, including U.S. Senator Claire McCaskill, announced that they would stop watching the show because of this scene.[29][30] According to Business Insider, this scene and increased use of streaming services are likely reasons why ratings dropped from 6.2 million viewers for this episode to 5.4 million for the next episode, "The Gift."[31]
Recognition and awards[edit]
Sophie Turner has received several award nominations for her portrayal of Sansa. For her performance in the series she earned the Glamour Award for Best UK TV Actress in 2016 and 2017,[32][33] and an EWwy Award for Best Supporting Actress in a Drama Series in 2016.[34] Other nominations include the Young Artist Award for Best Performance in a TV Series by a Supporting Young Actress in 2012,[35] and the EWwy Award for Best Supporting Actress in a Drama Series in 2015.[36]
References[edit]
Inline citations[edit]
Jump up ^ "Excerpt from the Winds of Winter - George R.R. Martin". georgerrmartin.com.
Jump up ^ "Game of Thrones: Cast & Crew". HBO. Retrieved May 20, 2014.
Jump up ^ Martin, George R. R. (July 16, 2010). "From HBO". Archived from the original on March 7, 2016. Retrieved May 20, 2014.
Jump up ^ Collins, Sean T. (March 31, 2014). "Top 40 Game of Thrones Characters, Ranked". Rolling Stone. Retrieved September 27, 2015.
Jump up ^ Butler, Leigh (April 8, 2011). "A Read of Ice and Fire: A Game of Thrones, Part 4". Tor. Retrieved May 5, 2016.
Jump up ^ "Sansa Stark - Untold Story- "The Lady of Winterfell" - GOT Untold Stories - The Spoon Boy". www.thespoonboy.com. Retrieved October 17, 2017.
Jump up ^ "Top 40 'Game of Thrones' Characters, Ranked". Rolling Stone. Retrieved July 18, 2016.
Jump up ^ "48 'Game of Thrones' Main Characters, Ranked Worst to Best". June 26, 2016. Retrieved July 18, 2016.
Jump up ^ Mic. "Why Sansa Stark Is the Strongest Character on 'Game of Thrones'". Retrieved July 18, 2016.
Jump up ^ Rhiannon (May 10, 2012). "In Defense of Sansa Stark". Feminist Fiction. Retrieved July 18, 2016.
Jump up ^ "Sansa Stark Is The Only Game Of Thrones Hero Worth Rooting For". Retrieved July 18, 2016.
Jump up ^ Egner, Jeremy (April 25, 2016). "Sophie Turner on 'Game of Thrones,' Sansa's Evolution and Learning From Controversy". The New York Times. ISSN 0362-4331. Retrieved July 18, 2016.
Jump up ^ Garber, Megan. "Justice for Sansa Stark". Retrieved July 18, 2016.
Jump up ^ "Game of Thrones' Sophie Turner Revels in Sansa Stark's Amazing First Kill". Retrieved July 18, 2016.
Jump up ^ Madison, Bennett. "Game of Thrones Episode 609 Recap: It's Finally Sansa's Turn to Be the Best Stark". Retrieved July 18, 2016.
Jump up ^ Dockterman, Eliana. "Sophie Turner Grows Into Her Powers in 'Game of Thrones' and 'X-Men'". TIME.com. Retrieved July 18, 2016.
Jump up ^ Runcie, Charlotte (May 17, 2015). "Game of Thrones: Unbowed, Unbent, Unbroken, season 5 episode 6, review: 'raw emotion'". The Telegraph. Retrieved May 18, 2015.
^ Jump up to: a b c Robinson, Joanna (May 17, 2015). "Game of Thrones Absolutely Did Not Need to Go There with Sansa Stark". Vanity Fair. Retrieved May 18, 2015.
Jump up ^ Kornhaber, Spencer; Orr, Christopher; Sullivan, Amy (May 17, 2015). "Game of Thrones: A Pointless Horror and a Ridiculous Fight". The Atlantic. Retrieved May 18, 2015.
Jump up ^ McNutt, Myles (May 17, 2015). "Game of Thrones (experts): "Unbowed, Unbent, Unbroken"". AV Club. Retrieved May 18, 2015.
Jump up ^ Leon, Melissa (May 19, 2015). "The Rape of Sansa Stark: 'Game of Thrones' Goes Off-book and Enrages Its Female Fans". The Daily Beast. Retrieved May 20, 2015.
Jump up ^ Pantozzi, Jill (May 18, 2015). "We Will No Longer Be Promoting HBO's Game of Thrones". The Mary Sue. Retrieved May 20, 2015.
Jump up ^ Collins, Sean T. (May 17, 2015). "'Game of Thrones' Recap: Stark Reality". Rolling Stone. Retrieved May 23, 2015.
Jump up ^ Hughes, Sarah (May 18, 2015). "Game of Thrones recap: season five, episode six – Unbent, Unbowed, Unbroken". The Guardian. Retrieved May 23, 2015.
Jump up ^ Rosenberg, Alyssa (May 17, 2015). "'Game of Thrones' Season 5, Episode 6 review: "Unbowed, Unbent, Unbroken"". The Washington Post. Retrieved May 23, 2015.
Jump up ^ Stewart, Sara (May 19, 2015). "It's a Stark reality: Outrage over Sansa rape scene misses the point". New York Post. Retrieved May 19, 2015.
Jump up ^ "The Problem with the Backlash to the Game of Thrones Rape Scene". Time. May 21, 2015. Retrieved May 22, 2015.
Jump up ^ Hibberd, James (May 17, 2015). "Game of Thrones: Sophie Turner says she 'loved' that horrifying scene". Entertainment Weekly. Retrieved May 20, 2015.
^ Jump up to: a b "'Gratuitous and disgusting': Senator leads boycott of Game of Thrones over shocking rape scene of Sansa Stark but actress playing her says she 'kinda loved it'". The Daily Mail. May 20, 2015. Retrieved May 20, 2015.
Jump up ^ Tani, Maxwell (May 20, 2015). "A US senator says she's going to stop watching 'Game of Thrones' over 'gratuitous' rape scene". Business Insider. Retrieved May 29, 2015.
Jump up ^ Acuna, Kirsten; Renfro, Kim (May 28, 2015). "'Game of Thrones' ratings are falling: Here are two possible reasons why". Business Insider. Retrieved May 28, 2015.
Jump up ^ "Here's who won what at the GLAMOUR Awards". glamourmagazine. glamourmagazine. 2016. Retrieved June 8, 2016.
Jump up ^ "GLAMOUR Awards 2017: All the talking points". Glamour. June 7, 2017. Retrieved June 9, 2017.
Jump up ^ "Poppy Awards 2016: Meet Your Winners". Entertainment Weekly. September 13, 2016. Retrieved September 15, 2016.
Jump up ^ "34th Annual Young Artist Awards". YoungArtistAwards.org. Archived from the original on April 2, 2013. Retrieved March 31, 2013.
Jump up ^ "EWwy Awards 2015: Meet Your Winners". ew.com. August 11, 2015.
General references[edit]
Martin, George R. R. (September 1996). A Game of Thrones. A Song of Ice and Fire (US hardcover ed.). Bantam Spectra. ISBN 978-0-553-10354-0.
Martin, George R. R. (March 1999). A Clash of Kings. A Song of Ice and Fire (US hardcover ed.). Bantam Spectra. ISBN 978-0-553-10803-3.
Martin, George R. R. (November 2000). A Storm of Swords. A Song of Ice and Fire (US hardcover ed.). Bantam Spectra. ISBN 978-0-553-10663-3.
Martin, George R. R. (November 2005). A Feast for Crows. A Song of Ice and Fire (US hardcover ed.). Bantam Spectra. ISBN 978-0-553-80150-7.
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Constructible polygon
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Construction of a regular pentagon
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are known.
Contents
[hide]
1 Conditions for constructibility
1.1 Detailed results by Gauss's theory
1.2 Connection to Pascal's triangle
2 General theory
3 Compass and straightedge constructions
3.1 Gallery
4 Other constructions
5 See also
6 References
7 External links
Conditions for constructibility[edit]
Number of sides of known constructible polygons having up to 1000 sides (bold) or odd side count (red)
Construction of the regular 17-gon
Some regular polygons are easy to construct with compass and straightedge; others are not. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides,[1]:p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.[1]:pp. 49–50 This led to the question being posed: is it possible to construct all regular polygons with compass and straightedge? If not, which n-gons (that is polygons with n edges) are constructible and which are not?
Carl Friedrich Gauss proved the constructibility of the regular 17-gon in 1796. Five years later, he developed the theory of Gaussian periods in his Disquisitiones Arithmeticae. This theory allowed him to formulate a sufficient condition for the constructibility of regular polygons. Gauss stated without proof that this condition was also necessary, but never published his proof. A full proof of necessity was given by Pierre Wantzel in 1837. The result is known as the Gauss–Wantzel theorem:
A regular n-gon (that is, a polygon with n sides) can be constructed with compass and straightedge if and only if n is the product of a power of 2 and any number of distinct Fermat primes (including none).
(A Fermat prime is a prime number of the form 2 ( 2 m ) + 1. {\displaystyle 2^{(2^{m})}+1.} )
In order to reduce a geometric problem to a problem of pure number theory, the proof uses the fact that a regular n-gon is constructible if and only if the cosine, cos  ( 2 π / n ) {\displaystyle \cos(2\pi /n)} , is a constructible number—that is, can be written in terms of the four basic arithmetic operations and the extraction of square roots. Equivalently, a regular n-gon is constructible if any root of the nth cyclotomic polynomial is constructible.
Detailed results by Gauss's theory[edit]
Restating the Gauss-Wantzel theorem:
A regular n-gon is constructible with straightedge and compass if and only if n = 2kp1p2...pt where k and t are non-negative integers, and the pi's (when t > 0) are distinct Fermat primes.
The five known Fermat primes are:
F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence A019434 in the OEIS).
Since there are 31 combinations of anywhere from one to five Fermat primes, there are 31 known constructible polygons with an odd number of sides.
The next twenty-eight Fermat numbers, F5 through F32, are known to be composite.[2]
Thus a regular n-gon is constructible if
n = 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 272, 320, 340, 384, 408, 480, 510, 512, 514, 544, 640, 680, 768, 771, 816, 960, 1020, 1024, 1028, 1088, 1280, 1285, 1360, 1536, 1542, 1632, 1920, 2040, 2048, ... (sequence A003401 in the OEIS),
while a regular n-gon is not constructible with compass and straightedge if
n = 7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, ... (sequence A004169 in the OEIS).
Connection to Pascal's triangle[edit]
Since there are 5 known Fermat primes, we know of 31 numbers that are multiples of distinct Fermat primes, and hence 31 constructible odd-sided regular polygons. These are 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 65537, 196611, 327685, 983055, 1114129, 3342387, 5570645, 16711935, 16843009, 50529027, 84215045, 252645135, 286331153, 858993459, 1431655765, 4294967295 (sequence A045544 in the OEIS). As John Conway commented in The Book of Numbers, these numbers, when written in binary, are equal to the first 32 rows of the modulo-2 Pascal's triangle, minus the top row, which corresponds to a monogon. (Because of this, the 1s in such a list form an approximation to the Sierpiński triangle.) This pattern breaks down after this, as the next Fermat number is composite (4294967297 = 641 × 6700417), so the following rows do not correspond to constructible polygons. It is unknown whether any more Fermat primes exist, and it is therefore unknown how many odd-sided constructible regular polygons exist. In general, if there are q Fermat primes, then there are 2q−1 odd-sided regular constructible polygons.
General theory[edit]
In the light of later work on Galois theory, the principles of these proofs have been clarified. It is straightforward to show from analytic geometry that constructible lengths must come from base lengths by the solution of some sequence of quadratic equations.[3] In terms of field theory, such lengths must be contained in a field extension generated by a tower of quadratic extensions. It follows that a field generated by constructions will always have degree over the base field that is a power of two.
In the specific case of a regular n-gon, the question reduces to the question of constructing a length
cos(2π/n),
which is a trigonometric number and hence an algebraic number. This number lies in the n-th cyclotomic field — and in fact in its real subfield, which is a totally real field and a rational vector space of dimension
½φ(n),
where φ(n) is Euler's totient function. Wantzel's result comes down to a calculation showing that φ(n) is a power of 2 precisely in the cases specified.
As for the construction of Gauss, when the Galois group is 2-group it follows that it has a sequence of subgroups of orders
1, 2, 4, 8, ...
that are nested, each in the next (a composition series, in group theory terms), something simple to prove by induction in this case of an abelian group. Therefore, there are subfields nested inside the cyclotomic field, each of degree 2 over the one before. Generators for each such field can be written down by Gaussian period theory. For example, for n = 17 there is a period that is a sum of eight roots of unity, one that is a sum of four roots of unity, and one that is the sum of two, which is
cos(2π/17).
Each of those is a root of a quadratic equation in terms of the one before. Moreover, these equations have real rather than complex roots, so in principle can be solved by geometric construction: this is because the work all goes on inside a totally real field.
In this way the result of Gauss can be understood in current terms; for actual calculation of the equations to be solved, the periods can be squared and compared with the 'lower' periods, in a quite feasible algorithm.
Compass and straightedge constructions[edit]
Compass and straightedge constructions are known for all known constructible polygons. If n = p·q with p = 2 or p and q coprime, an n-gon can be constructed from a p-gon and a q-gon.
If p = 2, draw a q-gon and bisect one of its central angles. From this, a 2q-gon can be constructed.
If p > 2, inscribe a p-gon and a q-gon in the same circle in such a way that they share a vertex. Because p and q are relatively prime, there exists integers a,b such that ap + bq = 1. Then 2aπ/q + 2bπ/p = 2π/pq. From this, a p·q-gon can be constructed.
Thus one only has to find a compass and straightedge construction for n-gons where n is a Fermat prime.
The construction for an equilateral triangle is simple and has been known since Antiquity. See equilateral triangle.
Constructions for the regular pentagon were described both by Euclid (Elements, ca 300 BC), and by Ptolemy (Almagest, ca AD 150). See pentagon.
Although Gauss proved that the regular 17-gon is constructible, he did not actually show how to do it. The first construction is due to Erchinger, a few years after Gauss' work. See heptadecagon.
The first explicit constructions of a regular 257-gon were given by Magnus Georg Paucker (1822)[4] and Friedrich Julius Richelot (1832).[5]
A construction for a regular 65537-gon was first given by Johann Gustav Hermes (1894). The construction is very complex; Hermes spent 10 years completing the 200-page manuscript.[6]
Gallery[edit]

From left to right, constructions of a 15-gon, 17-gon, 257-gon and 65537-gon. Only the first stage of the 65537-gon construction is shown; the constructions of the 15-gon, 17-gon, and 257-gon are given complete.
Other constructions[edit]
The concept of constructibility as discussed in this article applies specifically to compass and straightedge construction. More constructions become possible if other tools are allowed. The so-called neusis constructions, for example, make use of a marked ruler. The constructions are a mathematical idealization and are assumed to be done exactly.
A regular polygon with n sides can be constructed with ruler, compass, and angle trisector if and only if n = 2 r 3 s p 1 p 2 ⋯ p k , {\displaystyle n=2^{r}3^{s}p_{1}p_{2}\cdots p_{k},} where r, s, k ≥ 0 and where the pi are distinct Pierpont primes greater than 3 (primes of the form 2 t 3 u + 1 ) . {\displaystyle 2^{t}3^{u}+1).} [7]:Thm. 2
See also[edit]
Polygon
Carlyle circle
References[edit]
^ Jump up to: a b Bold, Benjamin. Famous Problems of Geometry and How to Solve Them, Dover Publications, 1982 (orig. 1969).
Jump up ^ Fermat factoring status Archived 2016-02-10 at the Wayback Machine. by Wilfrid Keller.
Jump up ^ Cox, David A. (2012), "Theorem 10.1.6", Galois Theory, Pure and Applied Mathematics (2nd ed.), John Wiley & Sons, p. 259, doi:10.1002/9781118218457, ISBN 978-1-118-07205-9 .
Jump up ^ Magnus Georg Paucker (1822). "Geometrische Verzeichnung des regelmäßigen Siebzehn-Ecks und Zweyhundersiebenundfünfzig-Ecks in den Kreis". Jahresverhandlungen der Kurländischen Gesellschaft für Literatur und Kunst (in German). 2: 160–219.
Jump up ^ Friedrich Julius Richelot (1832). "De resolutione algebraica aequationis x257 = 1, sive de divisione circuli per bisectionem anguli septies repetitam in partes 257 inter se aequales commentatio coronata". Journal für die reine und angewandte Mathematik (in Latin). 9: 1–26, 146–161, 209–230, 337–358. doi:10.1515/crll.1832.9.337.
Jump up ^ Johann Gustav Hermes (1894). "Über die Teilung des Kreises in 65537 gleiche Teile". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse (in German). Göttingen. 3: 170–186.
Jump up ^ Gleason, Andrew Mattei (March 1988). "Angle trisection, the heptagon, and the triskaidecagon" (PDF). The American Mathematical Monthly. 95 (3): 185–194. doi:10.2307/2323624. Archived from the original (PDF) on 2015-12-19.
External links[edit]
Duane W. DeTemple (1991). "Carlyle Circles and the Lemoine Simplicity of Polygonal Constructions". The American Mathematical Monthly. 98 (2): 97–108. doi:10.2307/2323939. JSTOR 2323939. MR 1089454.
Christian Gottlieb (1999). "The Simple and Straightforward Construction of the Regular 257-gon". Mathematical Intelligencer. 21 (1): 31–37. doi:10.1007/BF03024829. MR 1665155.
Regular Polygon Formulas, Ask Dr. Math FAQ.
Carl Schick: Weiche Primzahlen und das 257-Eck : eine analytische Lösung des 257-Ecks. Zürich : C. Schick, 2008. ISBN 978-3-9522917-1-9.
65537-gon, exact construction for the 1st side, using the Quadratrix of Hippias and GeoGebra as additional aids, with brief description (German)
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