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The Rise and Fall of the Third Reich
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The Rise and Fall of the Third Reich
Cover of the first edition
Author
William L. Shirer
Country
United States
Language
English
Subject
Nazi Germany
Publisher
Simon & Schuster
Publication date
1960
Media type
Print (hardcover and paperback)
Pages
1,245
ISBN
0-671-72868-7 (1990 paperback)
OCLC
22888118
The Rise and Fall of the Third Reich: A History of Nazi Germany is a book by William L. Shirer chronicling the rise and fall of Nazi Germany from the birth of Adolf Hitler in 1889 to the end of World War II in 1945. It was first published in 1960, by Simon & Schuster in the United States, where it won a National Book Award.[1] It was a bestseller in both the United States and Europe, and a critical success outside Germany; in Germany, criticism of the book stimulated sales. The book was feted by journalists, as reflected by its receipt of the National Book Award for non-fiction. But the reception from academic historians was mixed.
Rise and Fall is based upon captured Nazi documents, the available diaries of propaganda minister Joseph Goebbels, General Franz Halder, and of the Italian Foreign Minister Galeazzo Ciano, evidence and testimony from the Nuremberg trials, British Foreign Office reports, and the author's recollection of six years reporting on Nazi Germany for newspapers, the United Press International (UPI), and CBS Radio—terminated by Nazi Party censorship in 1940.[2] The work was written and initially published in four parts, but a larger one-volume edition has become more common.
Contents
[hide]
1 Content and themes
2 Development history
3 Success and acclaim
4 Criticism
5 Publication and adaptation
6 See also
7 References
8 External links
Content and themes[edit]
The Rise and Fall of the Third Reich is a comprehensive historical interpretation of the Nazi era, positing that German history logically proceeded from Martin Luther to Adolf Hitler;[3][a][page needed] that Hitler’s ascension to power was an expression of German national character, not of totalitarianism as an ideology that was internationally fashionable in the 1930s.[4][5][6] Author William L. Shirer summarised his perspective: "[T]he course of German history ... made blind obedience to temporal rulers the highest virtue of Germanic man, and put a premium on servility."[7] This reportorial perspective[clarification needed], the Sonderweg interpretation of German history (special path or unique course), was then common in American scholarship. Yet, despite extensive footnotes and references, some academic critics consider its interpretation of Nazism to be flawed.[8] The book also includes (identified) speculation, such as the theory that SS Chief Heinrich Müller afterward joined the NKVD of the USSR.
Development history[edit]
The editor for the book was Joseph Barnes, a foreign editor of the New York Herald Tribune, a former editor of PM, another New York newspaper, and a former speechwriter for Wendell Willkie. Barnes was an old friend of Shirer. The manuscript was very late and Simon & Schuster threatened to cancel the contract several times; each time Barnes would win a reprieve for Shirer. The original title of the book was Hitler's Nightmare Empire with The Rise and Fall of the Third Reich as the sub-title. The title and cover had already been sent out in catalogs when Robert Gottlieb decided that both title and cover had to go. Nina Bourne decided that they should use the sub-title as the title and art director Frank Metz designed the black jacket bearing the swastika. Initially bookstores across the country protested displaying the swastika and threatened not to stock the book. The controversy soon blew over and the cover shipped with the symbol.[9]
Success and acclaim[edit]
In the U.S., where it was published on October 17, 1960, The Rise and Fall of the Third Reich sold more than one million hardcover copies, two-thirds via the Book of the Month Club, and more than one million paperback copies. It won the 1961 National Book Award for Nonfiction[1] and the Carey–Thomas Award for non-fiction.[10] In 1962, the Reader's Digest magazine serialization reached some 12 million additional readers.[11][12] In a New York Times Book Review, Hugh Trevor-Roper praised it as "a splendid work of scholarship, objective in method, sound in judgment, inescapable in its conclusions."[13] The book sold well in Britain, France, Italy,[14] and in West Germany, because of its international recognition, bolstered by German editorial attacks.[15]
Both its recognition by journalists as a great history book and its popular success surprised Shirer[16] as the publisher commissioned a first printing of merely 12,500 copies. More than fifteen years after the end of the Second World War, neither Shirer nor the publisher anticipated much popular interest in Adolf Hitler (1889–1945) or Nazi Germany (1933–45).
Criticism[edit]
Whereas nearly all American journalists praised the book, scholars were split. Some acknowledged Shirer's achievement but some condemned it.[10] The harshest criticism came from those who disagreed with the Sonderweg or "Luther to Hitler" thesis. In West Germany, the Sonderweg interpretation was almost universally rejected in favor of the view that Nazism was simply one instance of totalitarianism that arose in various countries. Gavriel Rosenfeld asserted in 1994 that Rise and Fall had been unanimously condemned by German historians in the 1960s, and considered dangerous to relations between America and West Germany, as it might inflame anti-German sentiments in the United States.[17]
Klaus Epstein listed what he contended were "four major failings": a crude understanding of German history; a lack of balance, leaving important gaps; no understanding of a modern totalitarian regime; and ignorance of current scholarship of the Nazi period.[16]
Elizabeth Wiskemann concluded in a review that the book was "not sufficiently scholarly nor sufficiently well written to satisfy more academic demands... It is too long and cumbersome... Mr Shirer, has, however compiled a manual... which will certainly prove useful."[18]
LGBT activist Peter Tatchell criticized Shirer's attitude toward homosexuality, which he repeatedly describes as a perversion, and called for revisions to be made to the book's language and for mention to be made of the persecution of homosexuals in Nazi Germany and the Holocaust.[19] In Jon Stewart's anthology The Hegel Myths and Legends (1996), The Rise and Fall of the Third Reich is listed as a work that has propagated "myths" about the philosopher Georg Wilhelm Friedrich Hegel.[20]
The historian Richard J. Evans, author of The Third Reich Trilogy (2003 to 2008), conceded that Rise and Fall is a "readable general history of Nazi Germany" and that "there are good reasons for [its] success." Evans contended that Shirer worked outside of the academic mainstream and that Shirer's account was not informed by the historical scholarship of the time (1960).[21]
Publication and adaptation[edit]
Swedish two versions of William L Shirer's The Rise and Fall of the Third Reich, in four separate parts to the right
A film adaptation was broadcast by the U.S. ABC television network in 1968, one hour a night over three nights.
The Rise and Fall of the Third Reich
Directed by
Jack Kaufman
Narrated by
Richard Basehart
Theme music composer
Lalo Schifrin
Production
Producer(s)
Mel Stuart (executive producer)
Editor(s)
John Soh
Running time
180 minutes (counting the commercials)
Release
Original release
1968
The book has been reprinted many times (but not updated) since it was published in 1960. Current[when?] in-print editions are:
ISBN 0-671-72868-7 (Simon & Schuster, US, 1990 paperback)
ISBN 0-09-942176-3 (Arrow Books, UK, 1990 paperback)
Folio Society edition (2004 hardback)
ISBN 84-7069-368-9 (Grupo Océano, 1987 SP, hardcover)
There is also an audiobook version, released in 2010 by Blackstone Audio and read by Grover Gardner.
See also[edit]
Berlin Diary
List of books by or about Adolf Hitler
The Collapse of the Third Republic, also by Shirer
List of Holocaust films
References[edit]
Explanatory notes
Jump up ^ "The notion that 'rectitude and authenticity [were] integrally German attributes, in contrast to Roman or Latin influences which were degrading' held to have originated with Luther developed with German Romanticism in the 19th Century, and culminated with National Socialism." Johnson 2001.[page needed]
Citations
^ Jump up to: a b "National Book Awards – 1961". National Book Foundation. Retrieved 2012-02-20.
Jump up ^ Evans 2004, p. xvi.
Jump up ^ Rosenfeld 1994, p. 102.
Jump up ^ Shirer p. 236.
Jump up ^ Rosenfeld 1994, pp. 101–02.
Jump up ^ Evans 2004, p. xxiv.
Jump up ^ Shirer, p. 1080.
Jump up ^ Rosenfeld 1994, p. 106.
Jump up ^ Korda, Michael (1999). Another Life : A Memoir of Other People (1st ed.). New York: Random House. ISBN 0679456597.
^ Jump up to: a b Rosenfeld 1994, p. 101.
Jump up ^ Cedar Rapids Gazette, 9 October 1960, p. 47.
Jump up ^ Rosenfeld 1994, pp. 100–01.
Jump up ^ William L. Shirer (1990). The Rise and Fall of the Third Reich (3rd ed.). New York: Simon & Schuster. p. 1146.
Jump up ^ Shirer, p. 1145.
Jump up ^ Rosenfeld 1994, p. 96.
^ Jump up to: a b Epstein 1961, p. 230.
Jump up ^ Rosenfeld 1994, pp. 95–96, 98.
Jump up ^ Wiskemann 1961, pp. 234–35.
Jump up ^ Peter Tatchell: No place in History for Gay Victims of Nazism, The Independent, July 2, 1995
Jump up ^ Stewart, Jon, ed. (1996). The Hegel Myths and Legends. Evanston, Illinois: Northwestern University Press. p. 383. ISBN 0-8101-1301-5.
Jump up ^ Evans 2004, pp. xvi–xvii.
Bibliography
Epstein, Klaus. The Review of Politics, Vol. 23, No. 2 (April 1961). "Shirer's History of Nazi Germany."
Evans, Richard J. The Coming of the Third Reich (2004) Penguin Press HC. ISBN 1-59420-004-1
Johnson, Lonnie Rf. Central Europe: Enemies, Neighbors and Friends (2001) Oxford University Press, USA. ISBN 0-19-514826-6
Rosenfeld, Gavriel D. (1995). "The Reception of William L. Shirer's the Rise and Fall of the Third Reich in the United States and West Germany, 1960–62" (PDF). Journal of Contemporary History. 29 (1): 95–128. doi:10.1177/002200949402900104.
Shanahan, William O. ([https://query.nytimes.com/gst/fullpage.html?res=9C0CEEDB1730F932A25751C1A966958260 Obituary) The American Historical Review, Vol. 68, No. 1. (October 1962).
Siemon Netto, Uwe. The Fabricated Luther: Refuting Nazi Connections and Other Modern Myths (2007) Concordia Publishing House. ISBN 0-7586-0855-1
Wiskemann, Elizabeth. International Affairs, Vol. 37, No. 2. (April 1961)
External links[edit]
Wikiquote has quotations related to: The Rise and Fall of the Third Reich
Digitalized version of the 1960 edition at the University of Michigan Digital General Collection
Review of the book by Bryan Hiatt
Online WWII references Online collection of many original World War II documents, including some of Shirer's sources (e.g. British/French "Color" books, captured German Foreign Office docs, various Nuremberg and NCA documents).
Third Reich in Ruins Geoff Walden's then/now photo-essay collection of many sites mentioned in Shirer's book, early Hitler locations featured.
Rosenfeld, Gavriel D (January 1994), "The reception of William L. Shirer's 'The Rise and Fall of the Third Reich' in the United States and West Germany, 1960–62", Journal of Contemporary History, 29 (1), JStor, pp. 95–128 (paywall).
Documentary
The Rise and Fall of the Third Reich on IMDb
The Rise and Fall of the Third Reich at AllMovie
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Works of William L. Shirer
Non-fiction
Berlin Diary
The Rise and Fall of the Third Reich
The Collapse of the Third Republic
The Nightmare Years
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text:
Fictional universe of Avatar
From Wikipedia, the free encyclopedia
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In the 2009 science fiction film Avatar, director James Cameron conceived a fictional universe in which humans seek to mine unobtanium on the fictional exoplanetary moon, Pandora. The Earth-like moon is inhabited by a sapient indigenous humanoid species called the Na'vi, and varied fauna and flora. Resources Development Administration (RDA) scientists, administrators, recruits, support, and security personnel travel to Pandora in the 22nd century to discover this lush world, which is inhabited by many lifeforms including the human-like Na'vi. The clan with which the humans have contact in the film "[lives] in a giant tree that sits on a vast store of a mineral called unobtanium, which humans want as an energy supply."[1]
The Pandoran biosphere teems with a biodiversity of bioluminescent species ranging from six-legged animals to other types of exotic fauna and flora. The Pandoran ecology forms a vast neural network spanning the entire lunar surface into which the Na'vi and other creatures can connect. The strength of this collective consciousness is powerfully illustrated when the human invaders are defeated in battle by the Pandoran ecology, after the resolute Na'vi were nearly defeated. Cameron used a team of expert advisors in order to make the various examples of fauna and flora as scientifically feasible as possible.[2]
Contents
1 Astronomy and geology
2 Pandoran biosphere
3 Human interest
3.1 Technology
4 Reception
5 Notes
6 References
7 External links
Astronomy and geology[edit]
Artist's interpretation of Polyphemus and Pandora
In the film, Pandora is depicted as being located in the Alpha Centauri A system, about 4.37 light-years (276,000 AU) from Earth. It is one of the many natural satellites orbiting the gas giant Polyphemus,[3] named for the Polyphemus of Greek mythology. Pandora's atmosphere is a mix of nitrogen, oxygen, carbon dioxide, xenon, ammonia, methane, and hydrogen sulfide. Humans cannot breathe this, so they wear Exo-Packs when outside their buildings or vehicles.
Leri Greer, a designer at Weta Workshop, explained the unusual day/night cycle experienced by the Na'vi, who inhabit a moon orbiting a planet, that in turn orbits around a star.
I actually wrote about how it causes a particular sky coloration across the visible spectrum at moments of pure dusk. And the Na'vi, depending on what elevation they live at (sea level versus higher altitudes), perceive a distinct color in narrow band at the horizon at that moment. They identify themselves, and signify in their markings, with this color. Which helps other Na'vi quickly discern at a distance what/where they are from, or what they are likely to be like (fishermen, high plains, skyriders, etc.). That pure dusk "color," combined with their other predominant color markings lets you also know how they relate to Eywa as a "religion" versus Eywa as a physical reality. And during ceremonial gatherings you can "read" a Na'vi by how they mark themselves with dyes, muds, and paints. And the environment and day/night cycle is directly responsible for the development of this social expression behavior. Again, this was an internal idea to help us design things at Weta Workshop, it's hard to say how much filtered upward to the larger production.[4]
Pandora has lush, tropical rainforests that cover much of its continents. Pandora also possesses a lesser gravitational force than Earth does. The geology of Pandora is strongly affected by the presence of unobtanium, a mineral whose superconductive properties allow it to float in magnetic fields. This property makes it highly valued by humans, who mine it for transport back to Earth. Pandora's levitating Hallelujah Mountains contain significant quantities of unobtanium, which allows them to ride the strong magnetic fields in their region.
Cameron hopes to explore the other moons in future sequels, books, and spin-offs.[1][5][6][7]
Pandoran biosphere[edit]
Main article: Pandoran biosphere
The Pandoran biosphere teems with a biodiversity of bioluminescent species ranging from hexapodal animals to other types of exotic fauna and flora. The Pandoran ecology forms a vast neural network spanning the entire lunar surface into which the Na'vi and other creatures can connect. The strength of this collective consciousness is powerfully illustrated when the human invaders are defeated in battle by the Pandoran ecology, after the Na'vi were nearly defeated. Cameron hired a team of expert advisors to make the various examples of fauna and flora as scientifically feasible as possible.
Human interest[edit]
Of interest to the humans is Pandora's reserves of unobtanium, a valuable room-temperature superconductor mineral valued at "20 million a kilo". The name is a reference to mythical materials used in engineering which have better properties than real materials.
In the Avatar universe (set in the year 2154), humans have achieved a technologically advanced, post-industrial society dominated by powerful corporations and industries. One of Earth's most powerful corporations is the globally integrated Resources Development Administration (RDA), a quasi-governmental organization that owns all resources off Earth. The Interplanetary Commerce Administration granted these sole rights to the RDA under the stipulation that the use of weapons of mass destruction is prohibited.[8] Known RDA personnel on Pandora include head administrator Parker Selfridge, Colonel Miles Quaritch, Private Sean Fike, Corporal Lyle Wainfleet, Dr. Max Patel, Dr. Grace Augustine, Dr. Norm Spellman, and Samson 16 pilot Trudy Chacon.
Although Earth is never seen in the film, other than in the extended collectors edition, Cameron developed the future Earth of Avatar as a dystopian, overpopulated, overpolluted, global urban slum wrecked by corrupt, nature-destroying industrialism; the movie's background cyberpunk theme is a regular feature of his work. According to Jake, the Earth is a "dying world" where humans have "killed their mother", suggesting that there is very little, if any, functioning natural ecosystem left. By the film's 22nd century timeframe, Earth faces a worldwide economic/energy crisis due to the depletion of natural resources. Earth is also apparently so politically unstable that the services of private security contractors and the militaries of Earth's nations are in high demand; Colonel Quaritch boasts about serving three combat tours of duty in Nigeria before coming to Pandora and notes that Jake is a veteran of a military operation in Venezuela. The planet has also suffered serious natural and man-made disasters, such as an intra-continental conflict and tsunamis hitting the east and west coasts of the United States.
Technology[edit]
One of the futuristic computer screens, used for the AVATAR program, which employ 3D graphics and touchscreen interface.
Technologically, humans have achieved monumental advancements by 2154: interplanetary and interstellar space travel and colonization; virtual 3D printing and holography mapping; and advanced methods of cryonics and psionics (via synthetic telepathy interface) are employed. Using their capability of advanced genetic engineering, humans develop "Avatar" hybrid bodies from genetically distinct modified-human DNA and Na'vi alien genetic material. Through psionics, genetically matched humans are then mind-linked to these "Avatars" for remote control operation. In the area of medicine, humans have developed advanced stem cell neuroregeneration technology that can cure Jake's paralysis. However, in 2154, it is still extremely expensive and is not covered by Veterans Affairs benefits. Thus, RDA is initially able to use Jake's desire to regain the use of his legs as leverage against him.
As with many science fiction films, many space vehicles, aircraft, ground vehicles, weapons and technologies were created to fit the story. Many were patterned after historical or contemporary technologies to give the film a sense of futuristic realism.[9] Concept artist Ryan Church based many drawings on aerodynamic research from previously classified NASA and DARPA technical papers. Unlike the movie Aliens which employed one drop ship from de-orbit to ground combat, several vehicles cover specific roles of utility transport, gunship, and base resupply. This is similar to the specialization of aircraft and helicopters in the United States military since the Vietnam war.
Amplified Mobility Platform is an MK-6 vehicle redesigned for Pandora's hostile environment that is worn and controlled as a large "mech" motorized suit. They are 16-foot-tall (4.9 m) exoskeletons powered by ceramic turbines. Soldiers at Hell's Gate use these for patrol and for battle. AMP suits are controlled via a semi-master-slave system – with the AMP's arm motion slaved to the pilot's arm motion. Motion-sensing gloves worn by the pilot are used to control the AMP arms – the result being that the AMP's arm movements exactly match the pilot's movement. In their military role, AMP's are usually armed with 30mm GAU-90 autocannons, (occasionally equipped with a blade below the barrel, allowing the AMP to cut its way through denser foliage without putting the weapon aside) which the suit deploys as a soldier or Marine would hold and use a rifle. There is an ammo belt that extends into the gun, into an ammo canister on the shoulder, over the arm, into a socket at the back. The GAU-90 fires 350 rounds per minute. The AMP suit has GPS, thermal imaging display, FLIR, and radar. Stan Winston Studios animator and Avatar Design Supervisor John Rosengrant described the AMP suit as "An Apache helicopter with legs". It also has a ceramic knife that is three feet long. Quaritch owns an AMP suit and has named it "Beyond Glory". Its GAU-90 has a dragon painted on the ammo tube.
SA-2 Samson is a twin-ducted fan VTOL utility aircraft, similar in role and appearance to the real-world UH-60 Black Hawk, Mi-8 or UH-1 Huey utility helicopters. It is armed with two door mounted machine guns and two pylons near the cockpit with missile pods mounted on them. The pair of ducted-fan assemblies, each with two coaxial propellers, enable the Samson of 6,000 kilograms lifting capability by manufacturers specifications, but lifting performance is rated at 150% of that on Pandora due to the thicker atmosphere. Both ducted-fan assemblies are capable of changing blade pitch independently. From the pilot perspective, forward and aft, lift, yaw and roll authority are accomplished by similar sets of controls found in conventional helicopters. Propulsion is twin Goetz-Korman turbine generators.[10]
AT-99 Scorpion Gunship is the heavily armed gunship counterpart to Samson and is similar in role and appearance to the AH-64 Apache, Mi-28 or AH-1 Cobra gunships. Dual co-axial ducted-fan rotor systems with a total of four prop-rotors each with three blades lead as the aircraft's primary proplusion. It drives on redundant fuel cells. Twin turbine generators driving counter-rotating annular ceramic motors. It is equipped with radar and sonar generators. It is armed with hex-cluster pylon-mounted .50 caliber rotary chain gun systems that can rotate a full 360 degrees with 700 rounds per minute cyclic rate of fire as close range primary weapons. The Scorpion has two pair of stub-wing pylons to carry its armament. Scorpions carry 190 TK-411 WAFAR (Wrap-Around Fin Aerial Rocket) rockets in ten 19-tube rocket launchers. The use of the rocket varies according to the warhead that can range from tactical applications to impact-based sensor systems. Eight Hawkeye NPB-9 Hellfire (Helicopter Launched Fire-and-forget) missiles are used to engage air-to-air targets in conjunction with the nose-mounted sensor suite. The tail doubles as a rear stabilizer.
C-21 Dragon Assault Ship is a large four-post ducted-fan VTOL heavily armed transport and gunship which can deliver AMP suits through drop doors. Quaritch led RDA forces with one of these. Its myriad arsenal of heavy machine guns, dozens upon dozens of rocket and missile pods, and door-gunners makes it the RDA's largest ship so far, with the Valkyrie shuttle being the only larger vehicle designed for extended use in the atmosphere of Pandora. Quad turbine generators drive the four-posted ceramic propellers. The Dragon is heavily armed with multiple weapons systems included grenades, rockets, missiles and point-defense Gatling cannons. Ability to deploy many troops and AMP suits, variety of medium automatic guns, ATG and ATA missiles, incendiary rockets, grenades, door gunners, plus dual and quad Gatling gun systems. All gun and missile systems are constrained by friendly fire avoidance codes (IFF Lockout). It has twin cockpits. Its propellers counter-rotate to navigate, plus the nose-mounted radar suite. There are eight fifty-millimeter sentry guns mounted below the right cockpit.
GAV Swan is a six-wheeled terrain assault vehicle. Its full name is the Ground Assault Vehicle JL-723. It has a gyrostabilized platform so when it travels over rough terrain, the gunner platform is stabilized. The extended gunner's chair can rise up 3.6 meters above the vehicle to see over obstructions between the gun and the target, like the long neck of a swan, hence the name. This 6x6 is built for all terrain, and its permalloy armor and four turret-mounted sixty-millimeter rotary autocannons provide protection from the Pandoran environment. The wheels have little armor and are designed with a thick polymer alloy. Swans have a gyrostabilized system that rotates a full 360 degrees. Swans also have a roll bar and four rear headlights. Swans have redundant fuel cells in the rear. When the chair extends, the ammunition storage canister is located at the back.
Hell's Gate is a secure forward operating base with airfield, resembling a "modern day Khe Sanh". Slightly more than a third of the site is taken up by the shuttle runway, VTOL pads, hangars, equipment storage areas, and garage structures. The armor bay is where vehicles come to get stored, repaired or refitted. This building is the main storage area of all AMP suits. There is also a small weight room inside a weapons locker that Quaritch uses. Designed for security and rapid force deployment, the Armor Bay is the core of Hell’s Gate’s defenses. Housed inside its fortified hangar and at the ready are Dragon Assault Ships configured for forward strike operations, Scorpion Gunships, Samson Helicopters, Model 10 Slash-Cutters, an array of AMP Suits, and other attack craft including support vehicles and assorted battle-ready machinery.
ISV Venture Star or Interstellar Vehicle Venture Star is an interstellar bulk carrier starship that uses antimatter propulsion systems to enable interstellar travel. It transports supplies, equipment, humans in cryonic hibernation, refined ore, and data between Earth and Pandora, taking around six years to travel from one to the other. The Venture Star does not land on the planetary surface, but stations itself in orbit and rendezvous with operations on Earth and Pandora via Valkyrie shuttlecraft that dock with it. The Venture Star is one of twelve RDA ISV mineral carriers, continuously traveling between the Sol and Alpha Centauri A systems. According to film designer Ben Proctor:
The huge glowing radiators mounted to the engines dissipate their heat, and the enormously long central truss, with its own protective coolers and reflectors, protects the cargo and crew modules from the engines' heat and radiation using the simple rule of r-squared attenuation rather than heavy shielding. (Yes, [James Cameron] really thinks about this kind of stuff and explains it very clearly in text and in person.) The ship has a pair of centrifugal-gravity-gen modules for the crew who remain awake for the duration, which has become a pretty typical feature of quasi-realistic ship designs in movies. But one unique feature it has which directly relates to the sub-light realistic travel is a cascade-style shield stack to protect the speeding craft from interstellar debris. Jim's [brief] completely explains this technology, apparently based on current NASA research, and how it obliterates potentially catastrophic particles by letting them slam through a series of thin, light shield surfaces.[4]
The ship was based on designs by scientist and author Charles Pellegrino, who served as science advisor on the film,[11] and deceased scientist and author Robert L. Forward. It also resembles the spaceship Discovery One from the movie 2001: A Space Odyssey.
Valkyrie TAV is a delta-wing space vehicle/aircraft used to transport equipment and personnel between ISV Venture Star and Hell's Gate on Pandora and its chief purpose is to bring Unobtanium to the spacecraft. The Valkyrie's official name is SSTO-TAV-37 B-class shuttlecraft. The Valkyrie has a payload of up to 60 armed troops, 25 AMP suits, 25 tons of refined Unobtanium and/or supplies. Two Valkyries carried by the ISV Venture Star are used for transfer of personnel and cargo between the orbiting ISV and the surface of Pandora. It has VTOL capability by rotating its fusion engines, and like the C-130 Hercules was adapted as a bomber to drop daisy cutter bombs out of the rear cargo ramp. It can also be fixed with machine gun nests on the wings and cargo ramp.
Reception[edit]
Owen Gleiberman of Entertainment Weekly writes, "Cameron turns Pandora into a vertiginously suspended forest landscape...Jake and the sexy tribal princess Neytiri (Zoë Saldana) wow us with their fluid, prancing movements, but there's no subtext to their smoothly virtual faces."[12] Carol Kaesuk Yoon of the New York Times wrote that Avatar "has recreated what is the heart of biology: the naked, heart-stopping wonder of really seeing the living world".[13]
CNN reported that the film's universe has had a profound effect on the audience over their perception of Earth, and life on it, in reality. Avatar Forums posted a topic thread entitled "Ways to cope with the depression of the dream of Pandora being intangible" which received "1,000 posts from people experiencing depression and fans trying to help them cope" (a second thread was posted for more room). Philippe Baghdassarian, the site administrator, commented that, "I wasn't depressed myself. In fact the movie made me happy, but I can understand why it made people depressed. The movie was so beautiful and it showed something we don't have here on Earth. I think people saw we could be living in a completely different world and that caused them to be depressed." Many have confessed to falling to depression and harbouring suicidal thoughts, while others have expressed disgust towards humanity and "disengagement with reality." Psychiatrist Dr. Stephan Quentzel added that "Virtual life is not real life and it never will be, but this is the pinnacle of what we can build in a virtual presentation so far."[14]
In February 2010, CNN published an article exploring the "Avatar science" (the technology linking the human mind to a remotely controlled body). Elizabeth Landau wrote, "Scientists say we are many decades, even centuries, away from making this kind of sophisticated interaction possible, if it can be done at all." A neuroscientist at the University of Pittsburgh, Andrew Schwartz, further commented that it "shouldn't be taken as anything but fantasy."[15]
Notes[edit]
^ Jump up to: a b Rottenberg, Josh (December 18, 2009). "James Cameron Talks Avatar: Brave Blue World". Entertainment Weekly (1081). p. 51.
Jump up ^ Kozlowski, Lori (January 2, 2010). "Inventing the plants of "Avatar"". Los Angeles Times. Retrieved January 3, 2010.
Jump up ^ Although not mentioned in the movie, Polyphemus was discussed in the book James Cameron's Avatar: An Activist Survival Guide by Maria Wilhelm & Dirk Mathison. ISBN 978-0-06-189675-0.
^ Jump up to: a b Anders, Charlie Jane (February 4, 2010). "27 Avatar Questions, Answered By The Movie's Designers". io9.com. Retrieved February 8, 2010.
Jump up ^ Carroll, Larry (June 29, 2006). "'Titanic' Mastermind James Cameron's King-Size Comeback: Two Sci-Fi Trilogies". MTV. Retrieved October 18, 2006.
Jump up ^ Murphy, Mekado (December 21, 2009). "A Few Questions for James Cameron". The New York Times.
Jump up ^ Eric Ditzian (December 21, 2009). "James Cameron Talks 'Avatar' Sequel Plans". MTV. Retrieved January 2, 2010.
Jump up ^ Wilhelm, Maria; Dirk Mathison (November 2009). James Cameron's Avatar: A Confidential Report on the Biological and Social History of Pandora. HarperCollins. p. 147. ISBN 0-06-189675-6.
Jump up ^ "Avatar's hardware was all based on real-life stuff". io9.
Jump up ^ "SA-2 Samson". Archived from the original on 6 October 2014. Retrieved 5 October 2014.
Jump up ^ "Charles Pellegrino Web Site". Retrieved 5 October 2014.
Jump up ^ Gleiberman, Owen (December 25, 2009). "But What About Avatar? James Cameron's 3-D epic didn't make our top 10 lists. But critic Owen Gleiberman praises its visual artistry". Entertainment Weekly (1082/1083): 84.
Jump up ^ Kaesuk Yoon, Carol (January 19, 2010). "Luminous 3-D Jungle Is a Biologist's Dream". The New York Times. p. D-1.
Jump up ^ Piazza, Jo (January 11, 2010). "Audiences experience 'Avatar' blues". cnn.com. Retrieved February 19, 2010.
Jump up ^ landau, Elizabeth (February 3, 2010). "Is the 'Avatar' concept really possible?". CNN.com. Retrieved February 9, 2010.
References[edit]
Fitzgerald, Lisa (2009). The Art of Avatar: James Cameron's Epic Adventure. Abrams. ISBN 0-8109-8286-2.
Wilhelm, Maria; Mathison, Dirk (2009). Avatar: A Confidential Report on the Biological and Social History of Pandora. It Books. ISBN 0-06-189675-6.
Wilhelm, Maria; Mathison, Dirk (2009). James Cameron's Avatar: The Movie Scrapbook. HarperFestival. ISBN 0-06-180124-0.
External links[edit]
Wikinews has related news: Elvish, Klingon and Na'vi: Constructed languages gain foothold in film
"The Tet Zoo guide to the creatures of Avatar" at Tetrapod Zoology
"The Complete History Of Pandora, According To Avatar's Designers" at io9.com
Is the 'Avatar' Concept Really Possible? by CNN
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Grande Prairie Roman Catholic Separate School District No. 28
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Grande Prairie Roman Catholic Separate School District No. 28
Location
9902 101 ST
Grande Prairie, Alberta, Canada[1]
Canada
Other information
Website
gpcsd.ca
Grande Prairie Roman Catholic Separate School District No. 28 or Grande Prairie and District Catholic Schools is a separate school authority within the Canadian province of Alberta operated out of Grande Prairie.[1]
See also[edit]
List of school authorities in Alberta
References[edit]
^ Jump up to: a b "Authority Information Report" (XLSX). Alberta Education. August 2, 2014. Retrieved August 3, 2014.
External links[edit]
Official website
Retrieved from "https://en.wikipedia.org/w/index.php?title=Grande_Prairie_Roman_Catholic_Separate_School_District_No._28&oldid=673946548"
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Mozart in the Jungle
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Mozart in the Jungle
Genre
Comedy-drama
Based on
Mozart in the Jungle: Sex, Drugs, and Classical Music
by Blair Tindall
Developed by
Roman Coppola
Jason Schwartzman
Alex Timbers
Paul Weitz
Starring
Lola Kirke
Gael García Bernal
Saffron Burrows
Bernadette Peters
Peter Vack
Hannah Dunne
Malcolm McDowell
Theme music composer
Roger Neill
Opening theme
"Lisztomania" by Phoenix
Country of origin
United States
Original language(s)
English
No. of seasons
4
No. of episodes
40 (list of episodes)
Production
Executive producer(s)
Roman Coppola
Jason Schwartzman
Paul Weitz
Location(s)
New York City
Venice, Italy
Camera setup
Single camera
Running time
26–30 minutes
Production company(s)
American Zoetrope
Depth of Field
Picrow
Amazon Studios
Distributor
Amazon.com
Release
Original network
Amazon Video
Original release
February 6, 2014 (2014-02-06) – present
External links
Website
Mozart in the Jungle is a comedy-drama web television series produced by Picrow for Amazon Studios.[1] It was created by Roman Coppola, Jason Schwartzman, Alex Timbers, and directed by Paul Weitz. The show received a production order in March 2014.
The story was inspired by Mozart in the Jungle: Sex, Drugs, and Classical Music, oboist Blair Tindall's 2005 memoir of her professional career in New York, playing various high-profile gigs with ensembles including the New York Philharmonic and the orchestras of numerous Broadway shows.[2] The series stars Gael García Bernal as Rodrigo, a character based on conductor Gustavo Dudamel,[3] alongside Lola Kirke, Malcolm McDowell, Saffron Burrows, Hannah Dunne, Peter Vack, and Bernadette Peters.
The first season premiered in full on December 23, 2014.[4] The show's renewal for a second season was announced by Amazon on February 18, 2015.[5] All episodes of the second season were made available online on December 30, 2015. On February 9, 2016 a third season was announced.[6] All episodes of the third season were made available online on December 9, 2016.[7] On January 30, 2017, Amazon announced that the series had been renewed for a fourth season,[8] which was released on February 16, 2018.[9]
Contents
[hide]
1 Cast and characters
1.1 Main cast
1.2 Recurring cast
2 Episodes
3 Production
4 Reception
4.1 Accolades
5 References
6 External links
Cast and characters[edit]
Main cast[edit]
Lola Kirke as Hailey Rutledge, an oboist with a yearning ambition to play with the New York Symphony. She develops a strong bond with Rodrigo as the series progresses.
Gael García Bernal as Rodrigo De Souza, the new conductor of the New York Symphony
Bernadette Peters as Gloria Windsor, the president of the New York Symphony (recurring, season 1; season 2–present)
Malcolm McDowell as Thomas Pembridge, the conductor emeritus of the New York Symphony
Saffron Burrows as Cynthia Taylor, a philandering cellist with the New York Symphony
Hannah Dunne as Elizabeth "Lizzie" Campbell, Hailey's roommate and best friend
Peter Vack as Alex Merriweather, Hailey's dancer boyfriend (seasons 1 & 2)
Recurring cast[edit]
Debra Monk as Betty Cragdale, the long-time oboist for the New York Symphony who instantly despises Hailey
Mark Blum as Union Bob, a piccolo player for the symphony and known for bringing up the union rules
Jennifer Kim as Sharon, Rodrigo's assistant
Joel Bernstein as Warren Boyd, the concertmaster for the symphony
Nora Arnezeder as Ana Maria, Rodrigo's estranged violinist wife
John Miller as Dee Dee, the drug-dealing percussionist of the New York Symphony
Rubio Qian as Triangle Tanya, the triangle player of the New York Symphony.
Brennan Brown as Edward Biben, an orchestra board member
Gretchen Mol as Nina, the New York Symphony's lawyer who falls for Cynthia
Makenzie Leigh as Addison, Alex's dancing partner and roommate
Margaret Ladd as Claire, Thomas' ex-wife who dies after hearing his completed symphony.
Jason Schwartzman as Bradford Sharpe, a classical music enthusiast and host of his own podcast, "B-Sharpe"
John Hodgman as Marlin Guggenheim, a purported billionaire infatuated with Hailey
Wallace Shawn as Winslow Eliot, a neurotic concert pianist.
Tenoch Huerta Mejía as Manuel, Rodrigo's childhood friend
Dermot Mulroney as Andrew Walsh, a cello soloist who fraternizes with Hailey.
Monica Bellucci as Alessandra, a reclusive Italian soprano living in Venice, Italy, also known as "La fiamma".
Ana María Martínez provides Alessandra's singing voice.
Sandro Isaack as Pavel, the orchestra's stagehand who becomes friendly with Gloria
Philip Jackson Smith as Mike, a friend of Hailey's whom she recruits to work for the orchestra
Episodes[edit]
Main article: List of Mozart in the Jungle episodes
Season
Episodes
Originally aired
First aired
Last aired
1 10 February 6, 2014 (2014-02-06) December 23, 2014 (2014-12-23)
2 10 December 30, 2015 (2015-12-30) December 30, 2015 (2015-12-30)
3 10 December 9, 2016 (2016-12-09) December 9, 2016 (2016-12-09)
4 10 February 16, 2018 (2018-02-16) February 16, 2018 (2018-02-16)
Production[edit]
The many oboe solos played by the protagonist and other characters throughout the series are performed by Lelie Resnick, principal oboist of the Hollywood Bowl Orchestra, while the character of Rodrigo is loosely based on Gustavo Dudamel, the Venezuelan music director of the Los Angeles Philharmonic.[10] Dudamel coached García Bernal before the latter conducted, in the character of Rodrigo, for a real performance of the Los Angeles Philharmonic at the Hollywood Bowl, scenes of which were used for the second season opener.[11] Dudamel has a cameo in that episode, acting as a stagehand trying to convince Rodrigo to move to Los Angeles. Other musicians that have cameos in the series are violinist Joshua Bell, pianists Emanuel Ax and Lang Lang, composers Anton Coppola and Nico Muhly, Broadway star Brian d'Arcy James and conductors Alan Gilbert and Bernard Uzan. Blair Tindall, oboist and writer of the book on which the series is based, also appears in a cameo.[12] Interior shots of the home concert hall were filmed at the Performing Arts Center at SUNY Purchase.[13]
Reception[edit]
The first season of the series received positive reviews from critics. Review aggregator Rotten Tomatoes gave the series a 'fresh' 95% rating based on 20 critic reviews, with the critical consensus "Though confined to the isolated world of classical music, Mozart in the Jungle's Gael Garcia Bernal makes this charming little show sing."[14] Metacritic gave the series a 73 out of 100, indicating 'generally favorable reviews.'[15] Cory Barker, writing for TV.com, praised the series. "What works so well is that Mozart isn't afraid to throw you into a world you're likely unfamiliar with, but it doesn't swim so far into the deep end that you immediately drown in jargon and distanced dramatic stakes."[16] Robert Lloyd, writing for The Los Angeles Times, also lauded the first season. He stated that "Characters who were mouthpieces for attitudes start to seem like people, more complicated than a thumbnail description can accommodate. You grow interested in what will become of them without expecting or rooting for any particular outcome."[17] Kory Grow of Rolling Stone also praised the series, writing that "[t]hanks to quirky scripts and a smart ensemble cast... it comes off whimsical without ringing off-pitch."[18]
Tim Goodman of The Hollywood Reporter also gave the first season a positive review. "Bernal is both likable and magnetic, and makes the eclectic maestro surge on the screen. He alone is worth streaming the series, but, thankfully, there's a lot more going on here."[19] Brian Lowry, writing for Variety, also lauded the series. "While Mozart is surely a niche confection, the show generally shines by proving long on charm even when it's short on laughs."[20] In a more mixed review, Jeff Jensen of Entertainment Weekly gave the series a "B-".
Accolades[edit]
Year
Award
Category
Recipients
Result
Ref.
2015 Imagen Foundation Awards Best Actor - Television Gael Garcia Bernal Won [21]
2016 Golden Globe Awards Best Television Series – Comedy Mozart in the Jungle Won [22]
Best Actor in a Television Series – Musical or Comedy Gael Garcia Bernal Won
Primetime Emmy Awards Outstanding Sound Mixing for a Comedy or Drama Series (Half-Hour) and Animation Thomas Varga, Andy D'Addario, Bill Higley, Chris Navarro (for "Nothing Resonates Like Rhinoceros Foreskin") Won [23]
Imagen Foundation Awards Best Actor - Television Gael García Bernal Won [24]
2017 Golden Globe Awards Best Television Series – Comedy Mozart in the Jungle Nominated [25]
Best Actor in a Television Series – Musical or Comedy Gael Garcia Bernal Nominated
Primetime Emmy Awards Outstanding Cinematography for a Single-Camera Series (Half-Hour) Tobias Datum (for "Now I Will Sing") Nominated [26]
Outstanding Production Design for a Narrative Program (Half-Hour or Less) Tommaso Ortino, Susanna Codognato, Letizia Santucci (for "Now I Will Sing") Nominated
Outstanding Sound Mixing for a Comedy or Drama Series (Half-Hour) and Animation Andy D'Addario, Gary Gegan, Marco Fiumara (for "Now I Will Sing") Won
References[edit]
Jump up ^ Gans, Andrew (2014-03-12). "Amazon Studios Picks Up "Mozart in the Jungle" Pilot Starring Bernadette Peters". Retrieved 2015-12-31.
Jump up ^ Burton, Louise (2013-12-11). "Amazon's TV Pilot 'Mozart in the Jungle,' with Joshua Bell and Malcolm McDowell, Is a Tale of Sex, Drugs and…Classical Music?". Classicalite. Archived from the original on 2014-01-21. Retrieved 2015-12-31.
Jump up ^ Ramey, Corinne (2013-12-06). "Amazon Studios' 'Mozart in the Jungle' Offers New View of Music World". The Wall Street Journal. Retrieved 2015-12-31.
Jump up ^ Vlessing, Etan (2014-11-20). "Amazon Announces Premiere Date for 'Mozart in the Jungle' Comedy-Drama". The Hollywood Reporter. Retrieved 2015-12-31.
Jump up ^ Tartaglione, Nancy (2015-02-18). "Amazon Tunes Up Second Season Order For 'Mozart In The Jungle'". deadline.com. Retrieved 2015-12-31.
Jump up ^ Gans, Andrew. " 'Mozart in the Jungle,' Starring Bernadette Peters, Renewed for Third Season" playbill.com, February 9, 2016
Jump up ^ Mozart in the Jungle [@MITJAmazon] (7 August 2016). "A whole new tune. December 9" (Tweet) – via Twitter. https://twitter.com/MITJAmazon/status/762329084693188608
Jump up ^ Mitovich, Matt (January 30, 2017). "'Mozart in the Jungle' Renewed for Season 4, 'Red Oaks' Gets Final Season". TV Line. Retrieved January 31, 2017.
Jump up ^ Graham, Will. "It'll be early 2018". Twitter. Twitter. Retrieved 2 December 2017.
Jump up ^ Ng, David (2014-02-10). "'Mozart in the Jungle': Is 'Rodrigo' a parody of Gustavo Dudamel?". The Los Angeles Times. Retrieved 2016-01-26.
Jump up ^ Swed, Mark (2015-07-31). "L.A. Phil, Dudamel dive into the 'Mozart in the Jungle' act at the Bowl". The Los Angeles Times. Retrieved 2016-01-26.
Jump up ^ Midgette, Anne (2015-12-30). "'Mozart in the Jungle' finds its feet". The Washington Post. Retrieved 2016-01-26.
Jump up ^ "Amazon's 'Mozart In The Jungle' Films At SUNY Purchase". Harrison Daily Voice. Retrieved 14 May 2017.
Jump up ^ "Mozart in the Jungle: Season 1". Rotten Tomatoes. Retrieved 2015-12-31.
Jump up ^ "Mozart in the Jungle - Season 1". Metacritic. Retrieved 2015-12-31.
Jump up ^ Barker, Cory (2015-01-06). "4 Reasons Why You Should Binge-Watch Amazon's Mozart in the Jungle This Week". TV.com. Retrieved 2015-12-31.
Jump up ^ Lloyd, Robert (2014-12-23). "Review 'Mozart in the Jungle' on Amazon gets good after woeful pilot". The Los Angeles Times. Retrieved 2015-12-31.
Jump up ^ Grow, Kory (2014-12-22). "Bittersweet Symphony: Inside the Sex and Drugs of 'Mozart in the Jungle'". Rolling Stone. Retrieved 2015-12-31.
Jump up ^ Goodman, Tim (2014-12-23). "'Mozart In the Jungle': TV Review". The Hollywood Reporter. Retrieved 2015-12-31.
Jump up ^ Lowry, Brian (2014-12-17). "TV Review: Amazon's 'Mozart in the Jungle'". Variety. Retrieved 2015-12-31.
Jump up ^ "2015 Imagen Awards Winners, Honorees & Nominees". The Imagen Foundation. Retrieved 2016-09-29.
Jump up ^ "Winners & Nominees 2016". Hollywood Foreign Press Association. Retrieved 2016-09-29.
Jump up ^ "68th Emmy Awards Nominees and Winners". Academy of Television Arts & Sciences. Retrieved 2016-09-29.
Jump up ^ "Winners of 31st Annual Imagen Awards Announced". The Imagen Foundation. Retrieved 2016-09-29.
Jump up ^ "Winners & Nominees 2017". Hollywood Foreign Press Association. Retrieved 2016-12-12.
Jump up ^ "69th Emmy Awards Nominees and Winners". Academy of Television Arts & Sciences. Retrieved 2017-07-22.
External links[edit]
Mozart in the Jungle on IMDb
Mozart in the Jungle at TV Guide
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Isosceles triangle
From Wikipedia, the free encyclopedia
Jump to: navigation, search
"Isosceles" redirects here. For other uses, see Isosceles (disambiguation).
Isosceles triangle
Isosceles triangle with vertical axis of symmetry
Type
triangle
Edges and vertices
3
Schläfli symbol
( ) ∨ { }
Symmetry group
Dih2, [ ], (*), order 2
Dual polygon
Self-dual
Properties
convex, cyclic
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
By the isosceles triangle theorem, the two angles opposite the equal sides are themselves equal, while if the third side is different then the third angle is different.
By the Steiner–Lehmus theorem, every triangle with two angle bisectors of equal length is isosceles.
Contents
[hide]
1 Etymology
2 Terminology
3 Symmetry
4 Acute, right and obtuse
5 Euler line
6 Steiner inellipse
7 Formulas
7.1 Area
8 The isosceles triangle theorem
9 Partitioning into isosceles triangles
10 Miscellaneous
11 Fallacy of the isosceles triangle
12 See also
13 Notes
14 References
Etymology[edit]
The compound is made from "isos"(equal) and skelos (leg).
Terminology[edit]
In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.[1] The vertex opposite the base is called the apex.
Euclid defined an isosceles triangle as one having exactly two equal sides,[2] but modern treatments prefer to define them as having at least two equal sides, making equilateral triangles (with three equal sides) a special case of isosceles triangles.[3] In the equilateral triangle case, since all sides are equal, any side can be called the base, if needed, and the term leg is not generally used.
Symmetry[edit]
A triangle with exactly two equal sides has exactly one axis of symmetry, which goes through the vertex angle and also goes through the midpoint of the base. Thus the axis of symmetry coincides with (1) the angle bisector of the vertex angle, (2) the median drawn to the base, (3) the altitude drawn from the vertex angle, and (4) the perpendicular bisector of the base.[4]
Acute, right and obtuse[edit]
Isosceles right triangle
Whether the isosceles triangle is acute, right or obtuse depends on the vertex angle. In Euclidean geometry, the base angles cannot be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle. Since a triangle is obtuse or right if and only if one of its angles is obtuse or right, respectively, an isosceles triangle is obtuse, right or acute if and only if its vertex angle is respectively obtuse, right or acute.
Euler line[edit]
The Euler line of any triangle goes through the triangle's orthocenter (the intersection of its three altitudes), its centroid (the intersection of its three medians), and its circumcenter (the intersection of the perpendicular bisectors of its three sides, which is also the center of the circumcircle that passes through the three vertices). In an isosceles triangle with exactly two equal sides, the Euler line coincides with the axis of symmetry. This can be seen as follows. Since as pointed out in the previous section the axis of symmetry coincides with an altitude, the intersection of the altitudes, which must lie on that altitude, must therefore lie on the axis of symmetry; since the axis coincides with a median, the intersection of the medians, which must lie on that median, must therefore lie on the axis of symmetry; and since the axis coincides with a perpendicular bisector, the intersection of the perpendicular bisectors, which must lie on that perpendicular bisector, must therefore lie on the axis of symmetry.
If the vertex angle is acute (so the isosceles triangle is an acute triangle), then the orthocenter, the centroid, and the circumcenter all fall inside the triangle. If the vertex angle, and therefore the triangle, is obtuse, then the centroid still falls in the triangle's interior, but the circumcenter falls outside it (beyond the base), and the orthocenter also falls outside the triangle (beyond the apex).
In an isosceles triangle the incenter (the intersection of its angle bisectors, which is the center of the incircle, that is, the circle which is internally tangent to the triangle's three sides) lies on the Euler line.
Steiner inellipse[edit]
The Steiner inellipse of any triangle is the unique ellipse that is internally tangent to the triangle's three sides at their midpoints. In an isosceles triangle, if the legs are longer than the base then the Steiner inellipse's major axis coincides with the triangle's axis of symmetry; if the legs are shorter than the base, then the ellipse's minor axis coincides with the triangle's axis of symmetry.
Formulas[edit]
For an isosceles triangle with equal sides of length a and base of length b, the general triangle formulas for (1) the length of the triangle-interior portion of the angle bisector of the vertex angle, (2) the length of the median drawn to the base, (3) length of the altitude drawn to the base, and (4) the length of the triangle-interior portion of the perpendicular bisector of the base all simplify to 1 2 4 a 2 − b 2 . {\displaystyle {\tfrac {1}{2}}{\sqrt {4a^{2}-b^{2}}}.}
For any isosceles triangle with area T and perimeter p, we have[5]:Eq.(1)
2 p b 3 − p 2 b 2 + 16 T 2 = 0. {\displaystyle 2pb^{3}-p^{2}b^{2}+16T^{2}=0.}
Area[edit]
The area of an isosceles triangle can be derived using the Pythagorean Theorem: The sum of the squares of half the base b {\displaystyle b} and the height h {\displaystyle h} is the square of either of the other two sides of length a {\displaystyle a} :
( b 2 ) 2 + h 2 = a 2 {\displaystyle \left({\frac {b}{2}}\right)^{2}+h^{2}=a^{2}} ,
h = 4 a 2 − b 2 2 {\displaystyle h={\frac {\sqrt {4a^{2}-b^{2}}}{2}}} .
By substituting the height, the formula for the area of an isosceles triangle can be derived from the general formula one-half the base times the height:
T = b 4 4 a 2 − b 2 {\displaystyle T={\frac {b}{4}}{\sqrt {4a^{2}-b^{2}}}} .
This is what Heron's formula reduces to in the isosceles case.
If the apex angle ( θ ) {\displaystyle (\theta )} and leg lengths ( a ) {\displaystyle (a)} of an isosceles triangle are known, then the area of that triangle is:
T = 2 ( 1 2 a sin  ( θ 2 ) a cos  ( θ 2 ) ) {\displaystyle T=2\left({\frac {1}{2}}a\sin \left({\frac {\theta }{2}}\right)a\cos \left({\frac {\theta }{2}}\right)\right)}
= a 2 sin  ( θ 2 ) cos  ( θ 2 ) {\displaystyle =a^{2}\sin \left({\frac {\theta }{2}}\right)\cos \left({\frac {\theta }{2}}\right)} .
This is derived by drawing a perpendicular line from the base of the triangle, which bisects the vertex angle and creates two right triangles. The bases of these two right triangles are both equal to the hypotenuse times the sine of the bisected angle by definition of the term "sine". For the same reason, the heights of these triangles are equal to the hypotenuse times the cosine of the bisected angle. Using the trigonometric identity sin  θ = 2 sin  ( θ 2 ) cos  ( θ 2 ) {\displaystyle \sin \theta =2\sin {\left({\frac {\theta }{2}}\right)}\cos {\left({\frac {\theta }{2}}\right)}} , we get
T = 1 2 a 2 sin  θ {\displaystyle T={\frac {1}{2}}a^{2}\sin \theta } ,
which is a special case of the general triangle area formula one-half the product of two sides times the sine of the included angle.
The isosceles triangle theorem[edit]
The theorem which states that the base angles of an isosceles triangle are equal appears as Proposition I.5 in Euclid.[6] This result has been called the pons asinorum (the bridge of asses). Some say that this is probably because of the diagram used by Euclid in his demonstration of the result. Others claim that the name stems from the fact that this is the first difficult result in Euclid, and acts to separate those who can understand Euclid's geometry from those who can't.[7]
Partitioning into isosceles triangles[edit]
For any integer n ≥ 4 {\displaystyle n\geq 4} , any triangle can be partitioned into n {\displaystyle n} isosceles triangles.[8]
In a right triangle, the median from the hypotenuse (that is, the line segment from the midpoint of the hypotenuse to the right-angled vertex) divides the right triangle into two isosceles triangles. This is because the midpoint of the hypotenuse is the center of the circumcircle of the right triangle, and each of the two triangles created by the partition has two equal radii as two of its sides.[9]:p.24
The golden triangle is isosceles and has a ratio of either leg to the base equal to the golden ratio, and has angles 72°, 72°, and 36° in the ratios 2:2:1. It can be partitioned into another golden triangle and a golden gnomon, also isosceles, with ratio of base to leg equaling the golden ratio and with angles 36°, 36°, and 108° in the ratios 1:1:3.[9]:p.30–31
Miscellaneous[edit]
If a cubic equation has two complex roots and one real root, then when these roots are plotted in the complex plane they are the vertices of an isosceles triangle whose axis of symmetry coincides with the horizontal (real) axis. This is because the complex roots are complex conjugates and hence are symmetric about the real axis.
Either diagonal of a rhombus divides it into two congruent isosceles triangles.
The Calabi triangle, which is isosceles, is the unique non-equilateral triangle in which the largest square that fits in its interior can be positioned in any of three different ways.
If an isosceles triangle ABC with equal legs AB and BC has a segment drawn from A to a point D on ray BC, and if the reflection of AD around AC intersects ray BC at E, then BC2 = BD × BE.[10]
There are exactly two distinct isosceles triangles with given area T and perimeter p if the isoperimetric inequality holds strictly as p 2 > 12 3 T . {\displaystyle p^{2}>12{\sqrt {3}}T.} If the inequality is replaced by the corresponding equality, there is only one such triangle, which is equilateral.[5]:Thm.2
If the two equal sides have length a and the other side has length c, then the internal angle bisector t from one of the two equal-angled vertices satisfies[11]:p.169,# η {\displaystyle \eta } 44
2 a c a + c > t > a c 2 a + c {\displaystyle {\frac {2ac}{a+c}}>t>{\frac {ac{\sqrt {2}}}{a+c}}}
as well as[12]
t < 4 a 3 {\displaystyle t<{\frac {4a}{3}}} ;
and conversely, if the latter condition holds, an isosceles triangle parametrized by a and t exists.
Fallacy of the isosceles triangle[edit]
A well known fallacy is the false proof of the statement that all triangles are isosceles. This argument has been attributed to Lewis Carroll,[13] but W.W. Rouse Ball claims priority in this matter.[14] The fallacy is rooted in Euclid's lack of recognition of the concept of betweenness and the resulting ambiguity of inside versus outside of figures.[15]
See also[edit]
Equilateral triangle
Golden triangle, an isosceles triangle with sides in the golden ratio
Isosceles right triangle
Dragon's Eye (symbol)
Scalene triangle
Notes[edit]
Jump up ^ Jacobs 1974, p. 144
Jump up ^ Heath 1956, p. 187, Definition 20
Jump up ^ Stahl 2003, p. 37
Jump up ^ Ostermann & Wanner 2012, p. 55, Exercise 7
^ Jump up to: a b George Baloglou and Michel Helfgott. "Angles, area, and perimeter caught in a cubic", Forum Geometricorum 8, 2008, 13-25. http://forumgeom.fau.edu/FG2008volume8/FG200803.pdf
Jump up ^ Heath 1956, p. 251
Jump up ^ Venema 2006, p. 89
Jump up ^ Lord, N. J. (June 1982), "Isosceles subdivisions of triangles", Mathematical Gazette, 66: 136–137, doi:10.2307/3617750
^ Jump up to: a b Posamentier, Alfred S.; Lehmann, Ingmar (2012). The Secrets of Triangles. Prometheus Books. ISBN 978-1-61614-587-3.
Jump up ^ Dutta, Surajit (2014). "A simple property of isosceles triangles with applications". Forum Geometricorum. 14: 237–240.
Jump up ^ Inequalities proposed in “Crux Mathematicorum”, [1].
Jump up ^ Oxman, Victor (2005). "On the existence of triangles with given lengths of one side, the opposite and one adjacent angle bisectors" (PDF). Forum Geometricorum. 5: 21–22.
Jump up ^ Robin Wilson (2008). Lewis Carroll in Numberland. Penguin Books. pp. 169–170. ISBN 978-0-14-101610-8.
Jump up ^ Ball, W.W. Rouse; Coxeter, H.S.M. (1987) [1892], Mathematical Recreations and Essays (13th ed.), Dover, p. 77 footnote, ISBN 0-486-25357-0
Jump up ^ A description of the fallacy is given in "Fallacy of the Isosceles Triangle".
References[edit]
Heath, Thomas L. (1956), The Thirteen Books of Euclid's Elements, 1 (2nd ed. [Facsimile. Original publication: Cambridge University Press, 1925] ed.), New York: Dover Publications, ISBN 0-486-60088-2
Jacobs, Harold R. (1974), Geometry, W. H. Freeman and Co., ISBN 0-7167-0456-0
Ostermann, Alexander; Wanner, Gerhard (2012), Geometry by Its History, Springer, ISBN 978-3-642-29162-3
Stahl, Saul (2003), Geometry from Euclid to Knots, Prentice-Hall, ISBN 0-13-032927-4
Venema, Gerard A. (2006), Foundations of Geometry, Prentice-Hall, ISBN 0-13-143700-3
Weisstein, Eric W. "Isosceles triangle". MathWorld.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Isosceles_triangle&oldid=821162675"
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