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The Old Man and the Sea
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For other uses, see The Old Man and the Sea (disambiguation).
The Old Man and the Sea
Original book cover
Author
Ernest Hemingway
Country
United States
Language
English
Genre
Literary Fiction
Published
1952 (Charles Scribner's Sons)
Media type
Print (hardback & paperback)
Pages
127
Awards
Pulitzer Prize for fiction (1953)
ISBN
0-684-80122-1
OCLC
19793
Dewey Decimal
813.52
LC Class
PS3515.E37
The Old Man and the Sea is a short novel written by the American author Ernest Hemingway in 1951 in Bimini, Bahamas, and published in 1952.[1] It was the last major work of fiction by Hemingway that was published during his lifetime. One of his most famous works, it tells the story of Santiago, an aging Cuban fisherman who struggles with a giant marlin far out in the Gulf Stream off the coast of Cuba.[2]
In 1953, The Old Man and the Sea was awarded the Pulitzer Prize for Fiction, and it was cited by the Nobel Committee as contributing to their awarding of the Nobel Prize in Literature to Hemingway in 1954.[2]
Contents
[hide]
1 Plot summary
2 Background and publication
3 Literary significance and criticism
4 Legacy
5 References
5.1 Sources
6 Further reading
7 External links
Plot summary[edit]
The Old Man and the Sea tells the story of a battle between an aging, experienced fisherman, Santiago, and a large marlin. The story opens with Santiago having gone 84 days without catching a fish, and now being seen as "salao," the worst form of unluckiness. He is so unlucky that his young apprentice, Manolin, has been forbidden by his parents to sail with him and has been told instead to fish with successful fishermen. The boy visits Santiago's shack each night, hauling his fishing gear, preparing food, talking about American baseball and his favorite player, Joe DiMaggio. Santiago tells Manolin that on the next day, he will venture far out into the Gulf Stream, north of Cuba in the Straits of Florida to fish, confident that his unlucky streak is near its end.
On the eighty-fifth day of his unlucky streak, Santiago takes his skiff into the Gulf Stream, sets his lines and, by noon, has his bait taken by a big fish that he is sure is a marlin. Unable to haul in the great marlin, Santiago is instead pulled by the marlin, and two days and nights pass with Santiago holding onto the line. Though wounded by the struggle and in pain, Santiago expresses a compassionate appreciation for his adversary, often referring to him as a brother. He also determines that, because of the fish's great dignity, no one shall deserve to eat the marlin.
On the third day, the fish begins to circle the skiff. Santiago, worn out and almost delirious, uses all his remaining strength to pull the fish onto its side and stab the marlin with a harpoon. Santiago straps the marlin to the side of his skiff and heads home, thinking about the high price the fish will bring him at the market and how many people he will feed.
On his way in to shore, sharks are attracted to the marlin's blood. Santiago kills a great mako shark with his harpoon, but he loses the weapon. He makes a new harpoon by strapping his knife to the end of an oar to help ward off the next line of sharks; five sharks are slain and many others are driven away. But the sharks keep coming, and by nightfall the sharks have almost devoured the marlin's entire carcass, leaving a skeleton consisting mostly of its backbone, its tail and its head. Santiago knows that he is defeated and tells the sharks of how they have killed his dreams. Upon reaching the shore before dawn on the next day, Santiago struggles to his shack, carrying the heavy mast on his shoulder, leaving the fish head and the bones on the shore. Once home, he slumps onto his bed and falls into a deep sleep.
A group of fishermen gather the next day around the boat where the fish's skeleton is still attached. One of the fishermen measures it to be 18 feet (5.5 m) from nose to tail. Pedrico is given the head of the fish, and the other fishermen tell Manolin to tell the old man how sorry they are. Tourists at the nearby café mistakenly take it for a shark. The boy, worried about the old man, cries upon finding him safe asleep and at his injured hands. Manolin brings him newspapers and coffee. When the old man wakes, they promise to fish together once again. Upon his return to sleep, Santiago dreams of his youth—of lions on an African beach.
Background and publication[edit]
No good book has ever been written that has in it symbols arrived at beforehand and stuck in .... I tried to make a real old man, a real boy, a real sea and a real fish and real sharks. But if I made them good and true enough they would mean many things.
Ernest Hemingway in 1954[3]
Written in 1951, and published in 1952 , The Old Man and the Sea is Hemingway's final full-length work published during his lifetime. The book, dedicated to "Charlie Scribner" and to Hemingway's literary editor "Max Perkins",[4][5] was featured in Life magazine on September 1, 1952, and five million copies of the magazine were sold in two days.[6]
The Old Man and the Sea became a Book of the Month Club selection, and made Hemingway a celebrity.[7] Published in book form on September 1, 1952, the first edition print run was 50,000 copies.[8] The illustrated edition featured black and white pictures by Charles Tunnicliffe and Raymond Sheppard.[9]
In May 1953, the novel received the Pulitzer Prize[9] and was specifically cited when in 1954 he was awarded the Nobel Prize in Literature which he dedicated to the Cuban people.[10][11] The success of The Old Man and the Sea made Hemingway an international celebrity.[7] The Old Man and the Sea is taught at schools around the world and continues to earn foreign royalties.[12]
Literary significance and criticism[edit]
The Old Man and the Sea served to reinvigorate Hemingway's literary reputation and prompted a reexamination of his entire body of work. The novel was initially received with much popularity; it restored many readers' confidence in Hemingway's capability as an author. Its publisher, Scribner's, on an early dust jacket, called the novel a "new classic," and many critics favorably compared it with such works as William Faulkner's short story The Bear and Herman Melville's novel Moby-Dick.
Ernest Hemingway and Henry ("Mike") Strater with the remaining 500 lbs of an estimated 1000 lb marlin that was half-eaten by sharks before it could be landed in the Bahamas in 1935. See Pilar for details of this episode.
Gregorio Fuentes, who many critics believe was an inspiration for Santiago, was a blue-eyed man born on Lanzarote in the Canary Islands. After going to sea at age ten on ships that called in African ports, he migrated permanently to Cuba when he was 22. After 82 years in Cuba, Fuentes attempted to reclaim his Spanish citizenship in 2001.[13] Critics have noted that Santiago was also at least 22 when he immigrated from Spain to Cuba, and thus old enough to be considered an immigrant—and a foreigner—in Cuba.[14]
Hemingway at first planned to use Santiago's story, which became The Old Man and the Sea, as part of an intimacy between mother and son. Relationships in the book relate to the Bible, which he referred to as "The Sea Book". Some aspects of it did appear in the posthumously published Islands in the Stream. Hemingway mentions the real life experience of an old fisherman almost identical to that of Santiago and his marlin in On the Blue Water: A Gulf Stream Letter (Esquire, April 1936).[15][16]
Joseph Waldmeir's essay "Confiteor Hominem: Ernest Hemingway's Religion of Man" is a favorable critical reading of the novel—and one which has defined analytical considerations since. Perhaps the most memorable claim is Waldmeir's answer to the question—What is the book's message?
The answer assumes a third level on which The Old Man and the Sea must be read—as a sort of allegorical commentary on all his previous work, by means of which it may be established that the religious overtones of The Old Man and the Sea are not peculiar to that book among Hemingway's works, and that Hemingway has finally taken the decisive step in elevating what might be called his philosophy of Manhood to the level of a religion.[17]
Waldmeir considered the function of the novel's Christian imagery, made most evident through Hemingway's obvious reference to the crucifixion of Christ following Santiago's sighting of the sharks that reads:
"Ay," he said aloud. There is no translation for this word and perhaps it is just a noise such as a man might make, involuntarily, feeling the nail go through his hands and into the wood.[18]
One of the most outspoken critics of The Old Man and the Sea is Robert P. Weeks. His 1962 piece "Fakery in The Old Man and the Sea" presents his claim that the novel is a weak and unexpected divergence from the typical, realistic Hemingway (referring to the rest of Hemingway's body of work as "earlier glories").[19] In juxtaposing this novel against Hemingway's previous works, Weeks contends:
The difference, however, in the effectiveness with which Hemingway employs this characteristic device in his best work and in The Old Man and the Sea is illuminating. The work of fiction in which Hemingway devoted the most attention to natural objects, The Old Man and the Sea, is pieced out with an extraordinary quantity of fakery, extraordinary because one would expect to find no inexactness, no romanticizing of natural objects in a writer who loathed W.H. Hudson, could not read Thoreau, deplored Melville's rhetoric in Moby Dick, and who was himself criticized by other writers, notably Faulkner, for his devotion to the facts and his unwillingness to 'invent.'[19]
Some critics suggest Hemingway wrote The Old Man and the Sea in reaction against the overtly negative criticism he received for Across the River and into the Trees.
Legacy[edit]
In 1954 Hemingway donated his Nobel prize gold medal in Literature to the venerated Marian image of Our Lady of Charity. The Swedish medal was stolen in 1986, but was returned later upon the threat of Raul Castro.[20]
The Old Man and the Sea has been adapted for the screen three times: a 1958 film starring Spencer Tracy, a 1990 miniseries starring Anthony Quinn, and a 1999 animated short film. It is often taught in high schools as a part of the American Literature curriculum.
In 2003 the book was listed at number 173 on the BBC's The Big Read poll of the UK's 200 "best-loved novels."[21] The book is featured in a 2007 episode of American animated comedy series South Park.
The plot is recounted in the style of Wade Wilson (Ryan Reynolds) in a text crawl at the end of the teaser trailer for Deadpool 2 that played before the movie Logan.
References[edit]
Jump up ^ The Editors (25 August 1952). "From Ernest Hemingway to the Editors of Life". Life. Time Inc. 33 (8): 124. ISSN 0024-3019. Hemingway's work is a 27,000-word novel called The Old Man and the Sea. CS1 maint: Extra text: authors list (link)
^ Jump up to: a b "The Nobel Prize in Literature 1954". The Nobel Foundation. Retrieved January 31, 2005.
Jump up ^ "Books: An American Storyteller". TIME. December 13, 1954. Retrieved February 1, 2011.
Jump up ^ Hemingway. The Old Man and the Sea. p. 5
Jump up ^ Perkins, Maxwell (2004). Bruccoli, Matthew J.; Baughman, Judith, eds. The sons of Maxwell Perkins: letters of F. Scott Fitzgerald, Ernest Hemingway, Thomas Wolfe, and their editor. University of South Carolina Press. p. xxvii. ISBN 1-57003-548-2.
Jump up ^ "A Hemingway timeline Any man's life, told truly, is a novel". The Kansas City Star. KansasCity.com. June 27, 1999. Archived from the original on October 12, 2008. Retrieved 2009-08-29.
^ Jump up to: a b Desnoyers, p. 13
Jump up ^ Oliver 1999, p. 247
^ Jump up to: a b Meyers 1985, p. 489
Jump up ^ "Heroes:Life with Papa". TIME. November 8, 1954. Retrieved 2009-12-12.
Jump up ^ "The Nobel Prize in Literature 1954". Nobelprize.org. Retrieved October 4, 2009.
Jump up ^ Meyers 1985, p. 485
Jump up ^ "El pescador que inspiró a Hemingway 'El viejo y el mar' recupera la nacionalidad española". Retrieved June 7, 2013.
Jump up ^ Herlihy, Jeffrey. "Eyes the same color as the sea: Santiago's Expatriation from Spain and Ethnic Otherness and in Hemingway's the Old Man and the Sea" (PDF). Hemingway Review. Retrieved 2015-04-17.
Jump up ^ Old Man and the Sea. Introduction: The Ripening of a Masterpiece. Simon and Schuster. Retrieved September 29, 2012.
Jump up ^ Hemingway, Ernest (edited by William White) (1967). By-Line: Ernest Hemingway. Selected articles and dispatches of four decades. New York: Scribner's.
Jump up ^ Joseph Waldmeir (1957). "Confiteor Hominem: Ernest Hemingway's Religion of Man". Papers of the Michigan Academy of Sciences, Arts, and Letters. XLII: 349–356.
Jump up ^ Hemingway. The Old Man and the Sea. p. 118
^ Jump up to: a b Robert P. Weeks, Robert P. (1962). "Fakery in The Old Man and the Sea". College English. XXIV (3): 188–192. doi:10.2307/373283. JSTOR 373283.
Jump up ^ "Huffington Post". The Huffington Post. March 27, 2012. Retrieved October 7, 2014.
Jump up ^ "BBC – The Big Read". BBC. April 2003, Retrieved August 23, 2017
Sources[edit]
Desnoyers, Megan Floyd. "Ernest Hemingway: A Storyteller's Legacy". John F. Kennedy Presidential Library Online Resources. John F. Kennedy Presidential Library and Museum. Retrieved December 9, 2011.
Meyers, Jeffrey (1985). Hemingway: A Biography. London: Macmillan. ISBN 0-333-42126-4.
Oliver, Charles M. (1999). Ernest Hemingway A to Z: The Essential Reference to the Life and Work. New York: Checkmark. ISBN 0-8160-3467-2.
Further reading[edit]
Baker, Carlos (1972). Hemingway: The Writer as Artist (4th ed.). Princeton University Press. ISBN 0-691-01305-5.
Jobes, Katharine T., ed. (1968). Twentieth Century Interpretations of The Old Man and the Sea. Englewood Cliffs, New Jersey: Prentice Hall. ISBN 0-13-633917-4.
Mellow, James R. (1992). Hemingway: A Life Without Consequences. New York: Houghton Mifflin. ISBN 0-395-37777-3.
Young, Philip (1952). Ernest Hemingway. New York: Holt, Rinehart, & Winston. ISBN 0-8166-0191-7.
External links[edit]
The Old Man and the Sea at Faded Page (Canada)
Rare, Unseen: Hemingway in Cuba—slideshow by Life magazine
"Michael Palin's Hemingway Adventure: Cuba". PBS. Retrieved January 21, 2006.
Awards and achievements
Preceded by
Winston Churchill
1953 Nobel Prize in Literature
1954 Succeeded by
Halldór Laxness
1955
[show]
v
t
e
Pulitzer Prize for Fiction
1918–1925
His Family by Ernest Poole (1918)
The Magnificent Ambersons by Booth Tarkington (1919)
The Age of Innocence by Edith Wharton (1921)
Alice Adams by Booth Tarkington (1922)
One of Ours by Willa Cather (1923)
The Able McLaughlins by Margaret Wilson (1924)
So Big by Edna Ferber (1925)
1926–1950
Arrowsmith by Sinclair Lewis (declined) (1926)
Early Autumn by Louis Bromfield (1927)
The Bridge of San Luis Rey by Thornton Wilder (1928)
Scarlet Sister Mary by Julia Peterkin (1929)
Laughing Boy by Oliver La Farge (1930)
Years of Grace by Margaret Ayer Barnes (1931)
The Good Earth by Pearl S. Buck (1932)
The Store by Thomas Sigismund Stribling (1933)
Lamb in His Bosom by Caroline Pafford Miller (1934)
Now in November by Josephine Winslow Johnson (1935)
Honey in the Horn by Harold L. Davis (1936)
Gone with the Wind by Margaret Mitchell (1937)
The Late George Apley by John Phillips Marquand (1938)
The Yearling by Marjorie Kinnan Rawlings (1939)
The Grapes of Wrath by John Steinbeck (1940)
In This Our Life by Ellen Glasgow (1942)
Dragon's Teeth by Upton Sinclair (1943)
Journey in the Dark by Martin Flavin (1944)
A Bell for Adano by John Hersey (1945)
All the King's Men by Robert Penn Warren (1947)
Tales of the South Pacific by James A. Michener (1948)
Guard of Honor by James Gould Cozzens (1949)
The Way West by A. B. Guthrie Jr. (1950)
1951–1975
The Town by Conrad Richter (1951)
The Caine Mutiny by Herman Wouk (1952)
The Old Man and the Sea by Ernest Hemingway (1953)
A Fable by William Faulkner (1955)
Andersonville by MacKinlay Kantor (1956)
A Death in the Family by James Agee (1958)
The Travels of Jaimie McPheeters by Robert Lewis Taylor (1959)
Advise and Consent by Allen Drury (1960)
To Kill a Mockingbird by Harper Lee (1961)
The Edge of Sadness by Edwin O'Connor (1962)
The Reivers by William Faulkner (1963)
The Keepers of the House by Shirley Ann Grau (1965)
The Collected Stories of Katherine Anne Porter by Katherine Anne Porter (1966)
The Fixer by Bernard Malamud (1967)
The Confessions of Nat Turner by William Styron (1968)
House Made of Dawn by N. Scott Momaday (1969)
The Collected Stories of Jean Stafford by Jean Stafford (1970)
Angle of Repose by Wallace Stegner (1972)
The Optimist's Daughter by Eudora Welty (1973)
The Killer Angels by Michael Shaara (1975)
1976–2000
Humboldt's Gift by Saul Bellow (1976)
Elbow Room by James Alan McPherson (1978)
The Stories of John Cheever by John Cheever (1979)
The Executioner's Song by Norman Mailer (1980)
A Confederacy of Dunces by John Kennedy Toole (1981)
Rabbit Is Rich by John Updike (1982)
The Color Purple by Alice Walker (1983)
Ironweed by William Kennedy (1984)
Foreign Affairs by Alison Lurie (1985)
Lonesome Dove by Larry McMurtry (1986)
A Summons to Memphis by Peter Taylor (1987)
Beloved by Toni Morrison (1988)
Breathing Lessons by Anne Tyler (1989)
The Mambo Kings Play Songs of Love by Oscar Hijuelos (1990)
Rabbit at Rest by John Updike (1991)
A Thousand Acres by Jane Smiley (1992)
A Good Scent from a Strange Mountain by Robert Olen Butler (1993)
The Shipping News by E. Annie Proulx (1994)
The Stone Diaries by Carol Shields (1995)
Independence Day by Richard Ford (1996)
Martin Dressler: The Tale of an American Dreamer by Steven Millhauser (1997)
American Pastoral by Philip Roth (1998)
The Hours by Michael Cunningham (1999)
Interpreter of Maladies by Jhumpa Lahiri (2000)
2001–present
The Amazing Adventures of Kavalier & Clay by Michael Chabon (2001)
Empire Falls by Richard Russo (2002)
Middlesex by Jeffrey Eugenides (2003)
The Known World by Edward P. Jones (2004)
Gilead by Marilynne Robinson (2005)
March by Geraldine Brooks (2006)
The Road by Cormac McCarthy (2007)
The Brief Wondrous Life of Oscar Wao by Junot Díaz (2008)
Olive Kitteridge by Elizabeth Strout (2009)
Tinkers by Paul Harding (2010)
A Visit from the Goon Squad by Jennifer Egan (2011)
No award given (2012)
The Orphan Master's Son by Adam Johnson (2013)
The Goldfinch by Donna Tartt (2014)
All the Light We Cannot See by Anthony Doerr (2015)
The Sympathizer by Viet Thanh Nguyen (2016)
The Underground Railroad by Colson Whitehead (2017)
[show]
v
t
e
Ernest Hemingway
Bibliography
Novels
The Torrents of Spring (1926)
The Sun Also Rises (1926)
A Farewell to Arms (1929)
To Have and Have Not (1937)
For Whom the Bell Tolls (1940)
Across the River and into the Trees (1950)
The Old Man and the Sea (1952)
Non-fiction
Death in the Afternoon (1932)
Green Hills of Africa (1935)
Posthumous
A Moveable Feast (1964)
Islands in the Stream (1970)
The Dangerous Summer (1985)
The Garden of Eden (1986)
True at First Light (1999)
Under Kilimanjaro (2005)
Short stories
"Indian Camp" (1925)
"The Doctor and the Doctor's Wife" (1925)
"The End of Something" (1925)
"The Three-Day Blow" (1925)
"The Battler" (1925)
"A Very Short Story" (1925)
"Soldier's Home" (1925)
"The Revolutionist" (1925)
"Mr. and Mrs. Elliot" (1925)
"Cat in the Rain" (1925)
"Out of Season" (1925)
"Cross Country Snow" (1925)
"My Old Man" (1925)
"Big Two-Hearted River" (1925)
"A Clean, Well-Lighted Place" (1926)
"A Canary for One" (1926)
"Fifty Grand" (1927)
"Hills Like White Elephants" (1927)
"The Killers" (1927)
"The Undefeated" (1927)
"Che Ti Dice La Patria?" (1927)
"In Another Country" (1927)
"On the Quai at Smyrna" (1930)
"Fathers and Sons" (1932)
"A Day's Wait" (1933)
"The Gambler, the Nun, and the Radio" (1933)
"A Way You'll Never Be" (1933)
"The Snows of Kilimanjaro" (1936)
"The Capital of the World" (1936)
"The Short Happy Life of Francis Macomber" (1936)
Short story
collections
Three Stories and Ten Poems (1923)
In Our Time (1925)
Men Without Women (1927)
Winner Take Nothing (1933)
The Fifth Column and the First Forty-Nine Stories (1938)
The Snows of Kilimanjaro (1961)
The Fifth Column and Four Stories of the Spanish Civil War (1969)
The Nick Adams Stories (1972)
The Complete Short Stories of Ernest Hemingway (1987)
Ernest Hemingway: The Collected Stories (1995)
Story fragments
"On Writing"
Poetry
88 Poems (1979)
Complete Poems
Letters and
journalism
Ernest Hemingway Selected Letters 1917–1961 (1981)
Dateline: Toronto (1985)
The Cambridge Edition of the Letters of Ernest Hemingway (2011)
Adaptations
The Sun Also Rises
1957 film
1984 film
Opera
The Select (The Sun Also Rises)
Ballet
"The Killers"
1946 film
1956 film
1964 film
Bukowski short story
A Farewell to Arms
1932 film
1957 film
1966 TV series
To Have and Have Not
1944 film
The Breaking Point (1950)
The Gun Runners (1958)
Captain Khorshid (1987)
For Whom the Bell Tolls
1943 film
1965 TV series
Metallica song
The Old Man and the Sea
1958 film
1990 miniseries
1999 film
Other film adaptations
The Macomber Affair (1947)
The Snows of Kilimanjaro (1952)
Hemingway's Adventures of a Young Man (1962)
Islands in the Stream (1977)
See also
Nick Adams
Michigan cottage
Idaho house
Key West home
Hotel Ambos Mundos, Havana home
Finca Vigía, Cuba home
Pilar (boat)
The Spanish Earth (1937 film)
Bacall to Arms (1946 cartoon)
Hello Hemingway (1990 film)
In Love and War (1996 film)
Hemingway & Gellhorn (2012 film)
Cooper & Hemingway: The True Gen (2013 documentary)
Papa: Hemingway in Cuba (2015 film)
Hemingway Foundation/PEN Award
Kennedy Library Hemingway collection
Family
Elizabeth Hadley Richardson (first wife)
Jack Hemingway (son)
Pauline Pfeiffer (second wife)
Patrick Hemingway (son)
Gregory Hemingway (son)
Martha Gellhorn (third wife)
Mary Welsh Hemingway (fourth wife)
Grace Hall Hemingway (mother)
Leicester Hemingway (brother)
Authority control
GND: 4099230-5
BNF: cb122159627 (data)
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A Clash of Kings
From Wikipedia, the free encyclopedia
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This article is about the George R. R. Martin novel. For the video game, see Clash of Kings.
A Clash of Kings
US hardcover edition
Author
George R. R. Martin
Audio read by
Roy Dotrice
Cover artist
Steve Youll
Country
United States
Language
English
Series
A Song of Ice and Fire
Genre
Fantasy
Published
1998 (Voyager Books/UK)
1999 (Bantam Spectra/US)
Pages
768
Award
Locus Award for Best Fantasy Novel (1999)
ISBN
0-00-224585-X (UK Hardback)
ISBN 0-553-10803-4 (US Hardback)
OCLC
59667381
Dewey Decimal
813/.54
LC Class
PS3563.A7239 C58 1999
Preceded by
A Game of Thrones
Followed by
A Storm of Swords
A Clash of Kings is the second novel in A Song of Ice and Fire, an epic fantasy series by American author George R. R. Martin expected to consist of seven volumes. It was first published on 16 November 1998 in the United Kingdom, although the first United States edition did not follow until March[citation needed] 1999. Like its predecessor, A Game of Thrones, it won the Locus Award (in 1999) for Best Novel and was nominated for the Nebula Award (also in 1999) for best novel. In May 2005 Meisha Merlin released a limited edition of the novel, fully illustrated by John Howe.
The novel has been adapted for television by HBO as the second season of the TV series Game of Thrones.
A Clash of Kings is also the name of the first expansion to the Game of Thrones board game.
Contents
[hide]
1 Plot summary
1.1 In the Seven Kingdoms
1.2 Beyond the Wall
1.3 Across the Narrow Sea
2 Characters
3 Editions
4 Television adaptation
5 Reception
6 Awards and nominations
7 References
8 External links
Plot summary[edit]
A Clash of Kings depicts the Seven Kingdoms of Westeros in civil war, while the Night's Watch mounts a reconnaissance to investigate the mysterious people known as wildlings. Meanwhile, Daenerys Targaryen continues her plan to reconquer the Seven Kingdoms.
In the Seven Kingdoms[edit]
With King Robert Baratheon dead, his alleged son Joffrey and brothers Renly and Stannis all claim the throne of Westeros. Robb Stark is declared 'King in the North' while Balon Greyjoy declares himself king of the Iron Islands and attacks the western coast of the North. Robb's younger brother Bran Stark finds new friends in Jojen and Meera Reed.
Stannis Baratheon, as Robert's eldest brother, declares himself King of Westeros, encouraged by Melisandre of Asshai, a priestess who believes Stannis the reincarnation of Azor Ahai, a messianic figure of her faith. The war is dubbed the War of the Five Kings. Catelyn Stark, under orders from her son King Robb Stark, meets Renly and Stannis to discuss alliance against the Lannisters; but despite Stannis offering to make Renly his heir over his daughter Shireen the ensuing parley ends in acrimony and Renly resolves to destroy his brother with his larger army. Renly has married the daughter of the greedy and arrogant Lord Mace Tyrell, who is therefore supporting his attempt to usurp the throne. However, without warning a mysterious shadow comes to life in Renly's own tent and kills him. Shocked, Catelyn and the only other witness, the warrior-maid Brienne of Tarth, flee the scene. Having lost Renly, the storm lords have no choice but to declare for Stannis. Storm's End itself only falls, however, when Stannis's loyal Ser Davos, a former smuggler, sneaks Melisandre below the castle in a small boat. To his horror, Melisandre gives birth to a shadow which enters Storm's End and slays its stubborn castellan Ser Cortnay Penrose.
Tyrion Lannister arrives at King's Landing as acting Hand of the King, the closest adviser to the monarch Joffrey. Whilst intriguing against Joffrey's mother, the Queen Regent Cersei, Tyrion improves the defenses of the city. Learning of Renly's death, Tyrion resolves on two courses of action. Knowing that the Tyrells will not be happy following Stannis, he decides to make them a better offer. He also resolves to bring the Martells of Dorne into the war on his side. He sends Littlefinger to treat with the Tyrells and sends other messengers to Dorne. The negotiations are solidified by marriage arrangements. Mace Tyrell agrees to wed his daughter Margaery to King Joffrey I, whilst Prince Doran Martell agrees to marry his youngest son Trystane to Joffrey's sister Myrcella.
To conquer the North and to impress his father Balon, Theon Greyjoy captures Winterfell, taking Bran and Rickon captive; but Bran and Rickon disappear in the night. Rather than admit his failure, Theon murders two anonymous peasant boys similar in size to Bran and Rickon and mutilates their faces to enhance the resemblance. Believing this ruse, Stark supporters besiege the castle, joined by a force from House Bolton. Theon having conspired with Bolton's bastard son, Ramsay Snow, the Bolton soldiers turn on the besiegers and Theon opens the gates to the victorious Boltons, whereupon they destroy Winterfell, slaughter its inhabitants and take Theon prisoner. Osha, a captured wildling turned castle servant, takes Rickon to safety while Bran, accompanied by Meera, Jojen, and his simpleton manservant Hodor, travels north. Robb Stark wins several victories against the Lannisters, and Tywin Lannister advances against him, but receiving news that King's Landing is threatened, withdraws.
Arya Stark, posing as an orphan boy named Arry, is taken north by Yoren as a new recruit for the Night's Watch. However, they are attacked by Lannister freeriders led by Ser Amory Lorch and Yoren is killed at a town on the shores of Gods Eye. The survivors are taken to Harrenhal and put to work as servants in the undermanned castle. For saving his life during the attack, a man named Jaqen H'ghar promises to repay Arya by killing three men of her choice. For her three choices, Arya selects Chiswyck, a soldier in Gregor Clegane's forces, Weese, her servant overseer, and Jaqen H'ghar himself. The first two murders he carries out without question; in lieu of the third choice, Arya leverages H'ghar to help her slay the Lannister soldiers guarding Robett Glover, who had been taken prisoner by the Brave Companions. After Glover is freed, the Brave Companions turn their cloaks and join with the North. H'ghar gives Arya a mysterious iron coin and tells her to find him in Braavos if she should ever desire to learn his secrets. He then adopts a new identity and leaves. Control of Harrenhal is ceded to Roose Bolton, whom Arya serves as cupbearer, but soon escapes.
In the Battle of Blackwater Bay, Stannis Baratheon's army reaches King's Landing and launches assaults by both land and sea. The Baratheon forces vastly outnumber the Lannister defenders but under Tyrion's command, the Lannister forces use "wildfire" (similar to Greek fire) to ignite the bay, and raise a massive chain across its mouth to prevent Stannis's fleet from retreating. Stannis's attack fails when Tywin Lannister leads his army (and the remaining forces under Mace Tyrell) to King's Landing. During the defense of the castle, Tyrion is attacked by one of Joffrey's Kingsguard, and rescued by his squire, Podrick Payne, killing the Kingsguard. Stannis's fate is left uncertain.
Beyond the Wall[edit]
A scouting party from the Night's Watch learns that the wildlings are uniting under 'King-beyond-the-Wall' Mance Rayder. The Watch then continue to an ancient hill-top fortress known as the Fist of the First Men, whence Jeor Mormont sends Jon Snow and Qhorin Halfhand with others to the Skirling Pass, where they are hunted by wildling warriors. Facing certain defeat, Halfhand commands Snow to infiltrate the wildlings and learn their plans. They are captured by wildlings who demand Jon fight Qhorin to join them. Jon kills Qhorin with the aid of his direwolf, Ghost, and Jon learns that Mance Rayder is advancing on the Wall with thirty-thousand wildlings, giants, and mammoths.
Across the Narrow Sea[edit]
Daenerys Targaryen travels east, accompanied by the knight Jorah Mormont, her remaining followers, and three newly hatched dragons. Scouts find a safe route to the city of Qarth, where her dragons make Daenerys notorious. Xaro Xhoan Daxos, the leader of the Thirteen, a prominent group of traders in Qarth, initially befriends the outsiders; but Daenerys cannot secure aid in claiming the throne of Westeros, because she refuses to give away any of her dragons. As a last resort, Daenerys seeks counsel from the warlocks of Qarth, who show Daenerys many confusing visions and threaten her life, whereupon one of Daenerys's dragons, Drogon, burns down the warlocks' "House of the Undying". An attempt to assassinate Daenerys is thwarted by a fat warrior named Strong Belwas and his squire Arstan Whitebeard: agents of Daenerys's ally Illyrio Mopatis, who have come to escort her back to Pentos.
Characters[edit]
The tale is told through the eyes of 9 recurring POV characters plus one prologue POV character:
Prologue: Maester Cressen, maester at Dragonstone
Tyrion Lannister, youngest son of Lord Tywin Lannister, a dwarf and a brother to Queen Cersei, and the acting Hand of the King
Lady Catelyn Stark, of House Tully, widow of Eddard Stark, Lord of Winterfell
Ser Davos Seaworth, a smuggler turned knight in the service of King Stannis Baratheon, often called the Onion Knight
Sansa Stark, eldest daughter of Eddard Stark and Catelyn Stark, held captive by Queen Cersei at King's Landing
Arya Stark, youngest daughter of Eddard Stark and Catelyn Stark, missing and presumed dead
Bran Stark, second son of Eddard Stark and Catelyn Stark and heir to Winterfell and the King in the North
Jon Snow, bastard son of Eddard Stark, and a man of the Night's Watch
Theon Greyjoy, heir to the Seastone Chair and former ward of Lord Eddard Stark
Queen Daenerys Targaryen, the Unburnt and Mother of Dragons, of the Targaryen dynasty
Editions[edit]
Foreign language editions
Arabic: "اغنية الثلج والنار: صراع الملوك" ("A Song of Ice and Fire : Clash of kings")
Bulgarian: Бард :"Сблъсък на Крале"
Catalan: Alfaguara :"Xoc de reis" ("Clash of kings")
Croatian: Algoritam: "Sraz kraljeva"
Chinese: "列王的纷争", 重庆出版社(2006) ("Conflict of Kings").
Czech: Talpress: "Střet králů" ("Clash of Kings")
Danish: Gyldendal :"Kongernes Kamp" ("The Battle of Kings")
Dutch: One volume, Luithing Fantasy (1999): hardcover : De Strijd der Koningen ("The Clash of Kings")
Estonian: Two volumes, hardcover : Varrak (2008, 2009), "Kuningate heitlus I & II" ("A Clash of Kings")
Finnish: Kirjava: "Kuninkaiden koitos"
French: Three volumes (Hardcover: Pygmalion (2000); paperback: J'ai Lu (2002)): "La bataille des rois", "L'ombre maléfique", "L'invincible forteresse" ("The Battle of Kings", "The Evil Shadow", "The Invincible Fortress").
German: Single volume, Fantasy Productions (2004): "Königsfehde" ("King's Feud"). Two volumes, Blanvalet (2000): "Der Thron der Sieben Königreiche", "Die Saat des goldenen Löwen" ("The Throne of the Seven Kingdoms", "The Seed of the Golden Lion").
Georgian: Paperback, Arete (2014): "მეფეთა ჯახი" I/II ("Clash of Kings" I/II)
Greek: Anubis: "Σύγκρουση Βασιλέων" ("Clash of Kings")
Hebrew: "I/II עימות המלכים" ("Clash of Kings")
Hungarian: Alexandra Könyvkiadó : "Királyok csatája" ("Battle of Kings")
Icelandic: UGL: "Konungar kljást" ("Kings Clash")
Indonesian: Fantasious: "Pertempuran Raja-raja" ("Battle of Kings")
Italian: Two volumes, Arnoldo Mondadori Editore (2001, 2002): "Il regno dei lupi", "La regina dei draghi" ("The Kingdom of Wolves", "The Queen of Dragons").
Japanese: Two volumes, hardcover : Hayakawa (2004), paperback : Hayakawa (2007): "王狼たちの戦旗" ("Banner of the Wolf Kings")
Korean: Eun Haeng Namu Publishing Co. :"왕들의 전쟁" ("War of Kings")
Latvian: Whitebook: "Karaļu cīņa" ("War of Kings")
Lithuanian: Alma Littera "Karalių kova" ("A Battle of Kings")
Norwegian: Two volumes (2012) 'Bok II Del I: Kongenes kamp' (Book II Part I: The Battle of Kings) and 'Bok II Del II: Dragenes dronning' (Book II Part II: The Queen of Dragons)
Polish: Zysk i s-ka: "Starcie królów"
Brazilian Portuguese: Leya: "A Fúria dos Reis" ("Wrath of the Kings")
European Portuguese: Two Volumes, Saída de Emergência : "A Fúria dos Reis", "O Despertar da Magia"
Romanian: Nemira: "Încleștarea regilor"
Russian: Single volume, AST (2004, 2005, 2006): "Битва королей" ("The Battle of Kings"). Two volumes, AST (2000): "Битва королей. Книга 1", "Битва королей. Книга 2" ("The Battle of Kings: Book 1", "The Battle of Kings: Book 2).
Serbian: Лагуна : "Судар краљева"
Slovenian: "Spopad kraljev" ("Clash of Kings")
Spanish: Gigamesh (2003): "Choque de reyes" ("Clash of Kings").
Swedish: Forum bokförlag :"Kungarnas krig" ("War of the Kings")
Turkish: Two volumes, Epsilon Yayınevi: "Buz ve Ateşin Şarkısı II: Kralların Çarpışması - Kısım I & Kralların Çarpışması - Kısım II" ("A Clash of Kings")
Ukrainian: One volume, KM Publishing (2014): "Битва Королів" ("A Clash of Kings")
Vietnamese: Two volumes: "Trò Chơi Vương Quyền 2A: Hậu Duệ Của Sư Tử Vàng", "Trò Chơi Vương Quyền 2B: Bảy Phụ Quốc". ("Game of Thrones 2A: Descendants of the Golden Lion", "Game of Thrones 2B: Seven Kingdoms")
Television adaptation[edit]
A Clash of Kings has been adapted for television by HBO as the second season of its successful adaptation of A Song of Ice and Fire.[1] Filming began July 2011, and the first episode of season 2 of Game of Thrones aired on April 1, 2012.[2]
Reception[edit]
As with its predecessor, A Clash of Kings was positively received by critics. Dorman Shindler of The Dallas Morning News described it as "one of the best [works] in this particular subgenre", praising "the richness of this invented world and its cultures ... [that] lends Mr. Martin's novels the feeling of medieval history rather than fiction."[3] Writing in The San Diego Union-Tribune, Jim Hopper called A Clash of Kings "High Fantasy with a vengeance" and commented: "I'll admit to staying up too late one night last week to finish off this big book, and I hope it's not too terribly long until the next one comes out."[4] Danielle Pilon wrote in the Winnipeg Free Press that the book "shows no signs of the usual 'middle book' aimlessness". Although she found the constantly switching viewpoints "momentarily confusing", she felt that it "draws the reader deep into the labyrinthine political and military intrigues and evokes sympathy for characters on all sides of the conflict."[5] Bradley H. Sinor of the Tulsa World praised Martin for "keep[ing] readers balanced on a sword's edge" and managing to do "three important things" with A Clash of Kings: "It grips the reader whether or not they read the earlier book, tells a satisfying story and leaves the reader wanting the next book as soon as possible."[6] The Oregonian's Steve Perry called the book "easily as good as the first novel" and commented that the Song of Ice and Fire books were "so complex, fascinating and well-rendered that readers will almost certainly be hooked into the whole series." However, he cautioned that "if it were a movie, it would be rated "R" for sex and violence, so don't pick the book up for your 10-year-old nephew who likes Conan."[7]
Awards and nominations[edit]
Locus Award – Best Novel (Fantasy) (Won) – (1999)[1]
Nebula Award – Best Novel (Nominated) – (1999)[1]
Ignotus Award – Best Novel (Foreign) (Won) – (2004)
References[edit]
^ Jump up to: a b c "1999 Award Winners & Nominees". Worlds Without End. Retrieved 2009-07-25.
Jump up ^ Crider, Michael. "'Game Of Thrones' Season 2 Starts Filming In July; Producers Talk Cast & Story". Archived from the original on 21 June 2011. Retrieved July 15, 2011.
Jump up ^ Shindler, Dorman (February 21, 1999). "In Martin's 'Clash of Kings,' the delight is in the details". The Dallas Morning News.
Jump up ^ Hopper, Jim (March 19, 1999). "They're wiping out intelligent races -- What? Me worry?". The San Diego Union-Tribune.
Jump up ^ Pilon, Danielle (March 28, 1999). "Second book in Martin series shines amid dull tomes". Winnipeg Free Press.
Jump up ^ Sinor, Bradley H. (April 25, 1999). "All the king's horses ...". Tulsa World.
Jump up ^ Perry, Steve (June 27, 1999). "Adventure drives medieval-style fantasy". The Oregonian.
External links[edit]
A Clash of Kings title listing at the Internet Speculative Fiction Database
A Clash of Kings at the Internet Book List
[show]
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George R. R. Martin's A Song of Ice and Fire
A Game of Thrones (1996)
A Clash of Kings (1998)
A Storm of Swords (2000)
A Feast for Crows (2005)
A Dance with Dragons (2011)
The Winds of Winter (TBA)
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Daario Naharis
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[show]
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Locus Award for Best Fantasy Novel
1978–1990
The Silmarillion by J. R. R. Tolkien (1978)
Harpist in the Wind by Patricia A. McKillip (1980)
Lord Valentine's Castle by Robert Silverberg (1981)
The Claw of the Conciliator by Gene Wolfe (1982)
The Sword of the Lictor by Gene Wolfe (1983)
The Mists of Avalon by Marion Zimmer Bradley (1984)
Job: A Comedy of Justice by Robert A. Heinlein (1985)
Trumps of Doom by Roger Zelazny (1986)
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Seventh Son by Orson Scott Card (1988)
Red Prophet by Orson Scott Card (1989)
Prentice Alvin by Orson Scott Card (1990)
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Brittle Innings by Michael Bishop (1995)
Alvin Journeyman by Orson Scott Card (1996)
A Game of Thrones by George R. R. Martin (1997)
Earthquake Weather by Tim Powers (1998)
A Clash of Kings by George R. R. Martin (1999)
Harry Potter and the Prisoner of Azkaban by J. K. Rowling (2000)
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A Storm of Swords by George R. R. Martin (2001)
American Gods by Neil Gaiman (2002)
The Scar by China Miéville (2003)
Paladin of Souls by Lois McMaster Bujold (2004)
Iron Council by China Miéville (2005)
Anansi Boys by Neil Gaiman (2006)
The Privilege of the Sword by Ellen Kushner (2007)
Making Money by Terry Pratchett (2008)
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Kraken by China Miéville (2011)
A Dance with Dragons by George R. R. Martin (2012)
The Apocalypse Codex by Charles Stross (2013)
The Ocean at the End of the Lane by Neil Gaiman (2014)
The Goblin Emperor by Katherine Addison (2015)
Uprooted by Naomi Novik (2016)
All the Birds in the Sky by Charlie Jane Anders (2017)
Best Novel (1971–1981)
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Cavalieri's principle
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Not to be confused with Cavalieri's quadrature formula.
Two stacks of British coins with the same volume, illustrating Cavalieri's principle in three dimensions
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:[1]
2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas.
3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
Today Cavalieri's principle is seen as an early step towards integral calculus, and while it is used in some forms, such as its generalization in Fubini's theorem, results using Cavalieri's principle can often be shown more directly via integration. In the other direction, Cavalieri's principle grew out of the ancient Greek method of exhaustion, which used limits but did not use infinitesimals.
Contents
[hide]
1 History
2 Examples
2.1 Spheres
2.2 Cones and pyramids
2.3 The napkin ring problem
2.4 Cycloids
3 See also
4 References
5 External links
History[edit]
Bonaventura Cavalieri, the mathematician the principle is named after.
Cavalieri's principle was originally called the method of indivisibles, the name it was known by in Renaissance Europe. Cavalieri developed a complete theory of indivisibles, elaborated in his Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, advanced in a new way by the indivisibles of the continua, 1635) and his Exercitationes geometricae sex (Six geometrical exercises, 1647).[2]
In the 3rd century BC, Archimedes, using a method resembling Cavalieri's principle,[3] was able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the 5th century AD, Zu Chongzhi and his son Zu Gengzhi established a similar method to find a sphere's volume.[4] The transition from Cavalieri's indivisibles to Evangelista Torricelli's and John Wallis's infinitesimals was a major advance in the history of the calculus. The indivisibles were entities of codimension 1, so that a plane figure was thought as made out of an infinity of 1-dimensional lines. Meanwhile, infinitesimals were entities of the same dimension as the figure they make up; thus, a plane figure would be made out of "parallelograms" of infinitesimal width. Applying the formula for the sum of an arithmetic progression, Wallis computed the area of a triangle by partitioning it into infinitesimal parallelograms of width 1/∞.
Examples[edit]
Spheres[edit]
The disk-shaped cross-section of the sphere has the same area as the ring-shaped cross-section of that part of the cylinder that lies outside the cone.
If one knows that the volume of a cone is 1 3 ( base × height ) {\displaystyle {\frac {1}{3}}\left({\text{base}}\times {\text{height}}\right)} , then one can use Cavalieri's principle to derive the fact that the volume of a sphere is 4 3 π r 3 {\displaystyle {\frac {4}{3}}\pi r^{3}} , where r {\displaystyle r} is the radius.
That is done as follows: Consider a sphere of radius r {\displaystyle r} and a cylinder of radius r {\displaystyle r} and height r {\displaystyle r} . Within the cylinder is the cone whose apex is at the center of one base of the cylinder and whose base is the other base of the cylinder. By the Pythagorean theorem, the plane located y {\displaystyle y} units above the "equator" intersects the sphere in a circle of area π ( r 2 − y 2 ) {\displaystyle \pi \left(r^{2}-y^{2}\right)} . The area of the plane's intersection with the part of the cylinder that is outside of the cone is also π ( r 2 − y 2 ) {\displaystyle \pi \left(r^{2}-y^{2}\right)} . As we can see, the area of every intersection of the circle with the horizontal plane located at any height y {\displaystyle y} equals to the area of the intersection of the plane with the part of the cylinder that is "outside" of the cone; thus, applying Cavalieri's principle, we could say that the volume of the half sphere equals to the volume of the part of the cylinder that is "outside" the cone. The aforementioned volume of the cone is 1 3 {\displaystyle {\frac {1}{3}}} of the volume of the cylinder, thus the volume outside of the cone is 2 3 {\displaystyle {\frac {2}{3}}} the volume of the cylinder. Therefore the volume of the upper half of the sphere is 2 3 {\displaystyle {\frac {2}{3}}} of the volume of the cylinder. The volume of the cylinder is
base × height = π r 2 ⋅ r = π r 3 {\displaystyle {\text{base}}\times {\text{height}}=\pi r^{2}\cdot r=\pi r^{3}}
("Base" is in units of area; "height" is in units of distance. Area × distance = volume.)
Therefore the volume of the upper half-sphere is ( 2 3 ) π r 3 {\displaystyle \left({\frac {2}{3}}\right)\pi r^{3}} and that of the whole sphere is ( 4 3 ) π r 3 {\displaystyle \left({\frac {4}{3}}\right)\pi r^{3}} .
Cones and pyramids[edit]
The fact that the volume of any pyramid, regardless of the shape of the base, whether circular as in the case of a cone, or square as in the case of the Egyptian pyramids, or any other shape, is (1/3) × base × height, can be established by Cavalieri's principle if one knows only that it is true in one case. One may initially establish it in a single case by partitioning the interior of a triangular prism into three pyramidal components of equal volumes. One may show the equality of those three volumes by means of Cavalieri's principle.
In fact, Cavalieri's principle or similar infinitesimal argument is necessary to compute the volume of cones and even pyramids, which is essentially the content of Hilbert's third problem – polyhedral pyramids and cones cannot be cut and rearranged into a standard shape, and instead must be compared by infinite (infinitesimal) means. The ancient Greeks used various precursor techniques such as Archimedes's mechanical arguments or method of exhaustion to compute these volumes.
The napkin ring problem[edit]
Main article: Napkin ring problem
If a hole of height h is drilled straight through the center of a sphere, the volume of the remaining band does not depend on the size of the sphere. For a larger sphere, the band will be thinner but longer.
In what is called the napkin ring problem, one shows by Cavalieri's principle that when a hole is drilled straight through the centre of a sphere where the remaining band has height h, the volume of the remaining material surprisingly does not depend on the size of the sphere. The cross-section of the remaining ring is a plane annulus, whose area is the difference between the areas of two circles. By the Pythagorean theorem, the area of one of the two circles is π times r 2 − y 2, where r is the sphere's radius and y is the distance from the plane of the equator to the cutting plane, and that of the other is π times r 2 − (h/2) 2. When these are subtracted, the r 2 cancels; hence the lack of dependence of the bottom-line answer upon r.
Cycloids[edit]
The horizontal cross-section of the region bounded by two cycloidal arcs traced by a point on the same circle rolling in one case clockwise on the line below it, and in the other counterclockwise on the line above it, has the same length as the corresponding horizontal cross-section of the circle.
N. Reed has shown[5] how to find the area bounded by a cycloid by using Cavalieri's principle. A circle of radius r can roll in a clockwise direction upon a line below it, or in a counterclockwise direction upon a line above it. A point on the circle thereby traces out two cycloids. When the circle has rolled any particular distance, the angle through which it would have turned clockwise and that through which it would have turned counterclockwise are the same. The two points tracing the cycloids are therefore at equal heights. The line through them is therefore horizontal (i.e. parallel to the two lines on which the circle rolls). Consequently each horizontal cross-section of the circle has the same length as the corresponding horizontal cross-section of the region bounded by the two arcs of cyloids. By Cavalieri's principle, the circle therefore has the same area as that region.
Consider the rectangle bounding a single cycloid arch. From the definition of a cycloid, it has width 2πr and height 2r, so its area is four times the area of the circle. Calculate the area within this rectangle that lies above the cycloid arch by bisecting the rectangle at the midpoint where the arch meets the rectangle, rotate one piece by 180° and overlay the other half of the rectangle with it. The new rectangle, of area twice that of the circle, consists of the "lens" region between two cycloids, whose area was calculated above to be the same as that of the circle, and the two regions that formed the region above the cycloid arch in the original rectangle. Thus, the area bounded by a rectangle above a single complete arch of the cycloid has area equal to the area of the circle, and so, the area bounded by the arch is three times the area of the circle.
See also[edit]
Fubini's theorem (Cavalieri's principle is a particular case of Fubini's theorem)
References[edit]
Jump up ^ Howard Eves, "Two Surprising Theorems on Cavalieri Congruence", The College Mathematics Journal, volume 22, number 2, March, 1991), pages 118–124
Jump up ^ Katz, Victor J. (1998), A History of Mathematics: An Introduction (2nd ed.), Addison-Wesley, p. 477.
Jump up ^ "Archimedes' Lost Method"
Jump up ^ Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009). Calculus: Early Transcendentals (3 ed.). Jones & Bartlett Learning. p. xxvii. ISBN 0-7637-5995-3. Extract of page 27
Jump up ^ N. Reed, "Elementary proof of the area under a cycloid", Mathematical Gazette, volume 70, number 454, December, 1986, pages 290–291
External links[edit]
Weisstein, Eric W. "Cavalieri's Principle". MathWorld.
(in German) Prinzip von Cavalieri
Cavalieri Integration
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List of medical abbreviations: U
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p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-List_of_medical_abbreviations_U rootpage-List_of_medical_abbreviations_U skin-vector action-view