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The Perks of Being a Wallflower (film)
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The Perks of Being a Wallflower
Theatrical release poster
Directed by
Stephen Chbosky
Produced by
Lianne Halfon
Russell Smith
John Malkovich
Screenplay by
Stephen Chbosky
Based on
The Perks of Being a Wallflower
by Stephen Chbosky
Starring
Logan Lerman
Emma Watson
Ezra Miller
Mae Whitman
Kate Walsh
Dylan McDermott
Joan Cusack
Paul Rudd
Music by
Michael Brook
Cinematography
Andrew Dunn
Edited by
Mary Jo Markey
Production
company
Mr. Mudd
Distributed by
Summit Entertainment
Release date
September 8, 2012 (2012-09-08) (TIFF)
September 21, 2012 (2012-09-21) (United States)
Running time
103 minutes[1]
Country
United States
Language
English
Budget
$13 million[2]
Box office
$33.4 million[3]
The Perks of Being a Wallflower is a 2012 American coming-of-age drama film.[4] An adaptation of the 1999 epistolary novel of the same name, it was written and directed by the novel's author, Stephen Chbosky. Filmed in Pittsburgh, Pennsylvania, the film was released on September 21, 2012, to positive critical response and commercial success, earning $33.4 million[3] to a budget of $13 million.[2] The film stars Logan Lerman, Emma Watson and Ezra Miller. Two or three years after the release of film, Chbosky began to speak more openly concerning the mental health care aspects of the film which were of significance to him in the original writing of the book and the production of the film as he conceived it.[5] This is one of the three films from John Malkovich, Lianne Halfon and Russell Smith's Mr. Mudd Productions that feature struggling teenagers; the other two are Ghost World and Juno.[3][6][7][8]
Contents
[hide]
1 Plot
2 Cast
3 Development
3.1 Filming
4 Music
4.1 Soundtrack
4.2 Score
5 Release
5.1 Rating
5.2 Box office
6 Reception
6.1 Critical response
6.2 Accolades
7 References
8 External links
Plot
The film is set against the background of a young student, Charlie (Logan Lerman), who has been suffering from clinical depression from childhood setbacks and has recently been discharged from a mental health care institution to begin his adaptation to a normal lifestyle as a young high school student. Charlie is uneasy about beginning his freshman year of high school; he is shy and finds difficulty in making friends, but he connects with his English teacher, Mr. Anderson (Paul Rudd).
When he sits with two seniors, Sam (Emma Watson) and her stepbrother Patrick (Ezra Miller), at a football game, they invite him to tag along to several social activities with them. At a party, Charlie unwittingly eats a cannabis brownie, gets high and discloses to Sam that the year before, his best friend committed suicide. He also walks in on Patrick and Brad (Johnny Simmons), a popular athlete, kissing. Sam realizes that Charlie has no other friends so she and Patrick make a special effort to bring Charlie into their group. Sam needs to improve her SAT scores to be accepted to Pennsylvania State University, so Charlie offers to tutor her. On the way home from the party, when the three hear a song with which they are unfamiliar, Sam instructs Patrick to drive through a tunnel so she can stand up in the back of the pickup while the music blasts.
At Christmas, Sam gives Charlie a vintage typewriter to help his aspirations of being a writer. The two discuss relationships, and Charlie reveals he has never been kissed. Sam, though already involved with someone else, tells Charlie she wants his first kiss to be from someone who loves him, and kisses him. Charlie, in love with Sam, begins to try to find ways to show her how he feels.
At a regular Rocky Horror Picture Show performance, Charlie is asked to fill in for Sam's boyfriend Craig, who is unavailable. Their friend Mary Elizabeth (Mae Whitman) is impressed and asks Charlie to the Sadie Hawkins dance. The two enter into a desultory relationship. Finally, at a party, when Charlie is dared to kiss the most beautiful girl in the room, he chooses Sam, upsetting both her and Mary Elizabeth. Patrick recommends Charlie stay away from the group for a while, and the isolation causes him to sink back into depression. He experiences flashbacks of his Aunt Helen (Melanie Lynskey), who died in a car accident when he was seven years old.
When Brad shows up at school with a black eye having been caught by his father having sex with Patrick, he lies, saying that he was jumped and beaten up. Brad distances himself from Patrick, calling him a "faggot". Brad's friends begin beating Patrick, but Charlie forcefully intervenes, then blacks out. He recovers to find he has bruised knuckles and Brad's friends are on the floor, incapacitated. Charlie threatens, "Touch my friends again, and I'll blind you," then leaves. Sam and Patrick express their gratitude to Charlie, and the three become friends again.
Sam is accepted into Penn State, and breaks up with Craig on prom night after learning he has been cheating on her. The night before she departs, she brings Charlie to her room and asks him "Why do I and everyone I love pick people who treat us like we're nothing?" to which he repeats advice he received from Mr. Anderson, "We accept the love we think we deserve." They confide in each other and kiss, but when Sam touches Charlie's thigh, he experiences a momentary flashback of his Aunt Helen, which he passes off as nothing, and they continue to kiss. After she leaves for college, though, his emotional state deteriorates and his flashbacks worsen. He calls his sister blaming himself for Helen's death, and admits he may have wished it upon her. His sister realizes he is in trouble and calls the police. Charlie passes out as they burst through the door and wakes up in a hospital, where psychiatrist Dr. Burton (Joan Cusack) manages to bring out Charlie's repressed memories of his aunt sexually abusing him.
Charlie then is later visited by Sam and Patrick. Sam explains what college life is like, and how she has found "The Tunnel Song" — "Heroes" by David Bowie. The three revisit the tunnel, where Charlie kisses Sam again and stands up in the back of the truck. Charlie acknowledges that he feels alive and in that moment—"We are infinite."
Cast
Logan Lerman as Charlie Kelmeckis
Emma Watson as Sam
Ezra Miller as Patrick
Mae Whitman as Mary Elizabeth
Paul Rudd as Mr. Anderson, Charlie's English teacher
Nina Dobrev as Candace Kelmeckis, Charlie's sister
Johnny Simmons as Brad
Erin Wilhelmi as Alice
Adam Hagenbuch as Bob
Kate Walsh as Mrs. Kelmeckis
Dylan McDermott as Mr. Kelmeckis
Melanie Lynskey as Aunt Helen
Joan Cusack as Dr. Burton
Zane Holtz as Chris Kelmeckis, Charlie's older brother
Reece Thompson as Craig, Sam's college boyfriend
Nicholas Braun as Ponytail Derek, Candace's boyfriend
Landon Pigg as Peter
Tom Savini as Mr. Callahan
Julia Garner as Susan
Development
John Hughes read the novel and attempted to write a screenplay after he got the rights from Chbosky; however, he never finished this screenplay. Hughes was going to use the project as a directorial comeback with more of a black comedy style. He had in mind particular actors while writing the screenplay, namely, Shia LaBeouf as Charlie; Kirsten Dunst (The Virgin Suicides) as Sam; and Patrick Fugit (Almost Famous) as Patrick.
Other filmmakers who were interested in the project were Ron Howard, Richard Linklater, Josh Schwartz, McG, Joel Schumacher, Ryan Murphy and British filmmaker Danny Boyle.
Mr. Mudd Productions (producers of Juno) became interested in the project and wanted Chbosky to adapt the film. The producers—John Malkovich, Lianne Halfon, and Russell Smith—hired Chbosky to write a screenplay adaptation (instead of Hughes) and to direct the film. Chbosky found value in half of Hughes' screenplay, so he negotiated for the rights from Hughes' heirs and added his own touches. In January 2011, Summit acquired distribution rights.[9] The following month, Summit sought a buyer for the project at the European Film Market held simultaneously with the Berlin International Film Festival.[10]
In May 2010, actors Logan Lerman and Emma Watson were reported as in talks for the project[11] and confirmed the following year.[12] In April 2011, Mae Whitman signed on as Mary Elizabeth and Nina Dobrev was cast as Candace. Paul Rudd was cast as Mr Anderson later that month.[13] On May 9, 2011, Kate Walsh announced that she was cast in the film as Charlie's mother and had begun filming.[14]
Filming
The film was shot in the Pittsburgh metropolitan area from May 9 to June 29, 2011.[15] Initial filming began in Pittsburgh's South Hills, including South Park, Upper St. Clair, and Peters Township High School.[16][17]
The Rocky Horror Picture Show scenes were filmed at The Hollywood Theater in Dormont[18] after Chbosky learned that the theater was re-opening; he had seen The Rocky Horror Picture Show there when younger.[19]
The film also has scenes within Pittsburgh city limits inside the Fort Pitt Tunnel, Fort Pitt Bridge on Interstate 376 and on Mount Washington.[20]
Music
Soundtrack
The Perks of Being a Wallflower (Original Motion Picture Soundtrack)
Soundtrack album by Various Artists
Released
August 1, 2012
Genre
Alternative rock, dream pop, new wave, jangle pop, pop rock, folk rock
Length
51:58
Label
Atlantic Records
Original Motion Picture Soundtrack
No.
Title
Music
Length
1. "Could It Be Another Change?" The Samples 3:27
2. "Come On Eileen" Dexys Midnight Runners 4:12
3. "Tugboat" Galaxie 500 3:54
4. "Temptation" New Order 5:22
5. "Evensong" The Innocence Mission 3:40
6. "Asleep" The Smiths 4:10
7. "Low" Cracker 4:34
8. "Teen Age Riot" Sonic Youth 6:57
9. "Dear God" XTC 3:36
10. "Pearly-Dewdrops' Drops" Cocteau Twins 4:10
11. "Charlie's Last Letter" Michael Brook 1:48
12. "'Heroes'" David Bowie 6:08
Chart (2012/2013)
Peak
position
US Billboard Top Soundtracks[21]
7
Score
The Perks of Being a Wallflower (Original Motion Picture Score)
Soundtrack album by Michael Brook
Released
September 25, 2012
Genre
Score
Length
23:41
Label
Lionsgate Records
Release
The film was scheduled to be released on September 14, 2012, but it was announced in August 2012 that it would be released a week later, on September 21, 2012, in selected cities.[22] The film continued to expand on September 28, 2012, with a nationwide release on October 12, 2012. The UK premiere was on September 23[23] at the Cambridge Film Festival.
Rating
The film originally received an R rating for "teen drug and alcohol use, and some sexual references". The filmmakers appealed and the MPAA changed it to PG-13 for "mature thematic material, drug and alcohol use, sexual content including references, and a fight—all involving teens".[24]
Box office
The Perks of Being a Wallflower received a limited release of four theaters in the United States on September 21, 2012, and grossed $228,359 on its limited opening weekend, averaging $57,089 per theater. The film earned $17,742,948 in North America and $15,641,179 in other countries, for a worldwide total of $33,384,127.[3][25][26]
Reception
Critical response
The film received mainly positive reviews. Review aggregation website Rotten Tomatoes gives the film a "Certified Fresh" score of 86%, based on reviews from 151 critics, with an average score of 7.4/10. The site's consensus states: "The Perks of Being a Wallflower is a heartfelt and sincere adaptation that's bolstered by strong lead performances."[27] On Metacritic, which assigns a normalised rating out of 100 based on reviews from critics, the film has a score of 67 based on 36 reviews, indicating "generally favorable reviews".[28]
The lead cast also received positive notices. Ian Buckwalter of The Atlantic said "The primary trio of actors delivers outstanding performances, starting with Watson, who sheds the memory of a decade playing Hermione in the Harry Potter series with an about-face as a flirtatious but insecure free spirit. Miller also plays against his most recent performance, which was as the tightly wound eponymous teenage psychopath in We Need to Talk About Kevin, to deliver a giddy, scene-stealing turn as Patrick. Lerman, best known from the Percy Jackson series, shines as Charlie, a role that demands he be immediately likeable while still holding onto some deep darkness that can't be fully revealed until the end."[29]
John Anderson of Newsday also praised the cast saying "As Sam, the quasi-bad girl trying to reinvent herself before college, she (Emma Watson) brings honesty and a lack of cliche to a character who might have been a standard-issue student. But equally fine are her co-stars: Ezra Miller, who plays the gay character Patrick as something messy and unusual; Paul Rudd, as their English teacher, is refreshingly thoughtful. And Charlie is portrayed by Lerman as quietly observant, yearning and delicate in a way that will click with audiences regardless of age".[30]
Allison M. Lyzenga of My Film Habit praised the film saying "This movie especially recognizes that even while high-school can be a battlefield of insecurity and bullying, you can find allies to help you through the struggle. It also shows that we all have a brighter future ahead if we let ourselves reach for it."[31]
Some critics had a less positive response to the film, with the main criticism being that the portrayal of teenage issues is idealized and the casting uninspired. The Miami Herald critic Connie Ogle notes that "the suicide of Charlie’s best friend, which takes place before the film opens, seems glossed over too quickly" despite the event being Charlie's main character motivation in the film.[32] Jack Wilson of The Age writes, "the script is transparently fake at almost every moment, congratulating the gang on their non-conformity while soft-pedalling any aspect of adolescent behaviour—drug use, sex, profanity—that might upset the American mainstream."[33] Richard Corliss of Time criticized the casting of actors in their twenties to play teenagers, unlike the film Heathers where the cast were actually teenagers.[34]
MTV, Us Weekly and Complex named The Perks of Being a Wallflower one of the best films of the year.[35][36][37]
Accolades
Year
Award
Category
Recipient
Result
2012 Boston Society of Film Critics Awards Best Supporting Actor Ezra Miller Won
Best Supporting Actress Emma Watson Nominated
Chicago Film Critics Association Awards Best Adapted Screenplay Stephen Chbosky Nominated
Most Promising Filmmaker Nominated
Detroit Film Critics Society Awards Breakthrough Performance Nominated
Best Screenplay Nominated
Best Supporting Actor Ezra Miller Nominated
Hollywood Film Festival Spotlight Award Won
Indiana Film Critics Association Awards Best Adapted Screenplay Stephen Chbosky Won
National Board of Review Awards Top Films The Perks of Being a Wallflower Won
Phoenix Film Critics Society Awards Best Supporting Actor Ezra Miller Nominated
Best Supporting Actress Emma Watson Nominated
Best Adapted Screenplay Stephen Chbosky Nominated
Most Overlooked Film The Perks of Being a Wallflower Nominated
Best Breakthrough Performance Behind the Camera Stephen Chbosky Nominated
San Diego Film Critics Society Awards Best Adapted Screenplay Nominated
Best Supporting Actress Emma Watson Won
Best Ensemble Performance Cast Won
St. Louis Gateway Film Critics Association Awards Best Supporting Actress Emma Watson Nominated
Best Adapted Screenplay Stephen Chbosky Nominated
Utah Film Critics Association Awards Best Adapted Screenplay Won
Washington D.C. Area Film Critics Association Awards Best Adapted Screenplay Nominated
Best Youth Performance Logan Lerman Nominated
2013 Broadcast Film Critics Association Awards Best Young Performer Nominated
Best Adapted Screenplay Stephen Chbosky Nominated
GLAAD Media Awards[38] Outstanding Film - Wide Release The Perks of Being a Wallflower Won
Independent Spirit Awards[39] Best First Feature Stephen Chbosky Won
MTV Movie Awards[40] Best Female Performance Emma Watson Nominated
Best Kiss Emma Watson and Logan Lerman Nominated
Best Breakthrough Performance Ezra Miller Nominated
Best Musical Moment Emma Watson, Logan Lerman and Ezra Miller Nominated
People's Choice Awards Favorite Drama Movie The Perks of Being a Wallflower Won
Favorite Dramatic Movie Actress Emma Watson Won
Writers Guild of America Awards Best Adapted Screenplay Stephen Chbosky Nominated
Teen Choice Awards Choice Movie: Drama The Perks of Being a Wallflower Won
Choice Movie Actor: Drama Logan Lerman Won
Choice Movie Actress: Drama Emma Watson Won
Choice Movie Breakout: Actor Ezra Miller Nominated
Choice Movie Liplock Logan Lerman and Emma Watson Nominated
References
Jump up ^ "THE PERKS OF BEING A WALLFLOWER (12A)". British Board of Film Classification. 2012-07-27. Retrieved 2012-08-18.
^ Jump up to: a b Mark Olsen (November 1, 2012). "'The Perks of Being a Wallflower' steadily blossoms". Los Angeles Times.
^ Jump up to: a b c d "The Perks of Being a Wallflower (film)". Box Office Mojo. IMDB. Retrieved April 14, 2013.
Jump up ^ "The Perks of Being a Wallflower". Rotten Tomatoes. Flixster. Retrieved 2013-02-26.
Jump up ^ Jana Kasperkevic."The cost of mental health". The Guardian, 17 Dec 2014.[1]
Jump up ^ "Catching Up With The Perks of Being A Wallflower". Paste.com. Retrieved September 29, 2012.
Jump up ^ "'Perks Of Being A Wallflower' updates plus filming locations in Pittsburgh May 9–13". Retrieved May 12, 2011.
Jump up ^ "A message from Emma". EmmaWatson.com. Retrieved May 12, 2011.
Jump up ^ McNary, Dave (January 25, 2011). "Summit circles 'Wallflower'". Variety.
Jump up ^ Kay, Jeremy (February 17, 2011). "Buyers leave EFM with deals despite slow festival". Screen Daily.
Jump up ^ McNary, Dave (May 19, 2010). "Watson, Lerman in talks for 'Perks'". Variety.
Jump up ^ Lodderhose, Diana (February 9, 2011). "Emma Watson to star in 'Wallflower'". Variety.
Jump up ^ Finke, Nikki (April 15, 2011). "Nina Dobrev Goes From 'Vampire Diaries' To 'The Perks Of Being A Wallflower'". Retrieved April 17, 2011.
Jump up ^ Wilkinson, Amy (May 10, 2011). "Kate Walsh Signs On For 'Perks Of Being A Wallflower'". MTV. Retrieved May 19, 2011.
Jump up ^ "Movie Filming In Pittsburgh Wants To Make Your Car A Star". WPXI. April 27, 2011. Retrieved May 13, 2011.
Jump up ^ "Movie Begins Filming in Upper St. Clair". Upper St. Clair Patch. Retrieved May 19, 2011.
Jump up ^ Emmers, Becky (May 19, 2011). "Kings Restaurant Closing for 'Perks' Movie Shoot". Peters Patch. Retrieved May 19, 2011.
Jump up ^ Vancheri, Barbara (April 21, 2011). "Film Notes: Newly resurrected Hollywood Theater to appear in film". Pittsburgh Post-Gazette. Retrieved May 14, 2011.
Jump up ^ "USC Native to Film Scenes for Movie at Dormont's Hollywood Theater". Dormont-Brookline Patch. April 25, 2011. Retrieved May 14, 2011.
Jump up ^ Anya Sostek (September 28, 2012). "The 'Perks' Fort Pitt Tunnel stunt: Don't try it". Pittsburgh Post-Gazette.
Jump up ^ "Soundtracks : 1 – 10". Billboard. Retrieved 2013-03-16.
Jump up ^ "Release Date Round-Up: ‘Oblivion’ and ‘Perks’ Get Pushed, ‘Rush’ and ‘Mama’ Get Dated". FilmSchoolRejects. Retrieved 12 August 2012.
Jump up ^ "'Cambridge Film Festival – Programme for Sunday 23rd of September'".
Jump up ^ "MPAA Grants 'Perks of Being a Wallflower' PG-13 Rating". The Wrap. Sharon Waxman. 2012-03-08. Retrieved 2012-04-07.
Jump up ^ Deadline, The (September 23, 2012). "Indie Box Office - Perks Of Being A Wallflower, Diana Vreeland, The Master". Deadline.com. Retrieved 2013-02-26.
Jump up ^ "Box Office: Jake Gyllenhaal Tops Jennifer Lawrence; Dredd 3D Bombs | E! Online". Ca.eonline.com. Retrieved 2013-02-26.
Jump up ^ "The Perks of Being a Wallflower". Rotten Tomatoes. Flixster. Retrieved 2013-02-26.
Jump up ^ "The Perks of Being a Wallflower Reviews". Metacritic. CBS Interactive. Retrieved 2013-02-26.
Jump up ^ Buckwalter, Ian. "How 'Perks of Being a Wallflower' Breaks an Old Filmmaking Curse". The Atlantic. Retrieved 7 December 2012.
Jump up ^ Anderson, John. "'Perks of Being a Wallflower' review: Life in high school". Retrieved 12 December 2012.
Jump up ^ Lyzenga, Allison M. (September 3, 2015). "The Perks of Being a Wallflower - High School Hell". My Film Habit.
Jump up ^ Ogle, Connie. "'The Perks of Being a Wallflower' (PG-13". The Miami Herald. Retrieved 2012-09-27.
Jump up ^ Wilson, Jack. "Bohemian fantasy shies away from adolescent truths". Melbourne: theage.com.au. Retrieved November 29, 2012.
Jump up ^ Corliss, Richard (September 13, 2012). "The Perks of Being a Wallflower: A Teen Angel’s Dreamy Angst". Time Entertainment.
Jump up ^ "Best Movies Of 2012". MTV. Retrieved December 16, 2012.
Jump up ^ "Top Ten Movies of 2012". US Weekly. Retrieved January 19, 2013.
Jump up ^ "The 25 Best Movies of 2012". Complex. Retrieved February 16, 2013.
Jump up ^ Megan Townsend (April 20, 2013). "The New Normal, The Perks of Being a Wallflower among GLAAD Media Award Recipients in Los Angeles". GLAAD.org.
Jump up ^ "Independent Spirit Awards 2013: Winners List". The Hollywood Reporter. 23 February 2013. Retrieved 23 February 2013.
Jump up ^ "2013 MTV Movie Awards Winners". MTV.com. April 14, 2013.
External links
Wikiquote has quotations related to: The Perks of Being a Wallflower (film)
Official website
The Perks of Being a Wallflower on IMDb
The Perks of Being a Wallflower at AllMovie
The Perks of Being a Wallflower at Rotten Tomatoes
The Perks of Being a Wallflower at Metacritic
The Perks of Being a Wallflower at Box Office Mojo
[show]
v
t
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GLAAD Media Award for Outstanding Film – Wide Release
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Fried Green Tomatoes/Frankie and Johnny (1992)
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Kinsey (2005)
Brokeback Mountain (2006)
Little Miss Sunshine (2007)
Stardust (2008)
Milk (2009)
A Single Man (2010)
The Kids Are All Right (2011)
Beginners (2012)
The Perks of Being a Wallflower (2013)
Philomena (2014)
The Imitation Game (2015)
Carol (2016)
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[show]
v
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Teen Choice Award for Choice Movie – Drama
Cruel Intentions (1999)
The Sixth Sense (2000)
Pearl Harbor (2001)
Spider-Man (2002)
None (2003)
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The Blind Side (2010)
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[show]
v
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Films by Stephen Chbosky
Screenplay and directed
The Four Corners of Nowhere (1995)
The Perks of Being a Wallflower (2012)
Wonder (2017)
Screenplay only
Rent (2005)
Beauty and the Beast (2017)
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Equations for a falling body
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A set of equations describe the resultant trajectories when objects move owing to a constant gravitational force under normal Earth-bound conditions. For example, Newton's law of universal gravitation simplifies to F = mg, where m is the mass of the body. This assumption is reasonable for objects falling to earth over the relatively short vertical distances of our everyday experience, but is untrue over larger distances, such as spacecraft trajectories.
Contents
[hide]
1 History
2 Overview
3 Equations
4 Examples
5 Acceleration relative to the rotating Earth
6 See also
7 Notes
8 References
9 External links
History[edit]
Galileo was the first to demonstrate and then formulate these equations. He used a ramp to study rolling balls, the ramp slowing the acceleration enough to measure the time taken for the ball to roll a known distance.[1][2] He measured elapsed time with a water clock, using an "extremely accurate balance" to measure the amount of water.[note 1]
The equations ignore air resistance, which has a dramatic effect on objects falling an appreciable distance in air, causing them to quickly approach a terminal velocity. The effect of air resistance varies enormously depending on the size and geometry of the falling object — for example, the equations are hopelessly wrong for a feather, which has a low mass but offers a large resistance to the air. (In the absence of an atmosphere all objects fall at the same rate, as astronaut David Scott demonstrated by dropping a hammer and a feather on the surface of the Moon.)
The equations also ignore the rotation of the Earth, failing to describe the Coriolis effect for example. Nevertheless, they are usually accurate enough for dense and compact objects falling over heights not exceeding the tallest man-made structures.
Overview[edit]
An initially stationary object which is allowed to fall freely under gravity falls a distance proportional to the square of the elapsed time. This image, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 0.05s the ball drops one unit of distance (about 12 mm), by 0.10s it has dropped at total of 4 units, by 0.15s 9 units, and so on.
Near the surface of the Earth, the acceleration due to gravity g = 9.81 m/s2 (meters per second squared; which might be thought of as "meters per second, per second", or 32.2 ft/s2 as "feet per second per second") approximately. For other planets, multiply g by the appropriate scaling factor. A coherent set of units for g, d, t and v is essential. Assuming SI units, g is measured in meters per second squared, so d must be measured in meters, t in seconds and v in meters per second.
In all cases, the body is assumed to start from rest, and air resistance is neglected. Generally, in Earth's atmosphere, all results below will therefore be quite inaccurate after only 5 seconds of fall (at which time an object's velocity will be a little less than the vacuum value of 49 m/s (9.8 m/s2 × 5 s) due to air resistance). Air resistance induces a drag force on any body that falls through any atmosphere other than a perfect vacuum, and this drag force increases with velocity until it equals the gravitational force, leaving the object to fall at a constant terminal velocity.
Atmospheric drag, the coefficient of drag for the object, the (instantaneous) velocity of the object, and the area presented to the airflow determine terminal velocity.
Apart from the last formula, these formulas also assume that g negligibly varies with height during the fall (that is, they assume constant acceleration). The last equation is more accurate where significant changes in fractional distance from the center of the planet during the fall cause significant changes in g. This equation occurs in many applications of basic physics.
Equations[edit]
Distance d {\displaystyle \ d\ } travelled by an object falling for time t {\displaystyle \ t\ } : d = 1 2 g t 2 {\displaystyle \ d={\frac {1}{2}}gt^{2}}
Time t {\displaystyle \ t\ } taken for an object to fall distance d {\displaystyle \ d\ } : t = 2 d g {\displaystyle \ t=\ {\sqrt {\frac {2d}{g}}}}
Instantaneous velocity v i {\displaystyle \ v_{i}\ } of a falling object after elapsed time t {\displaystyle \ t\ } : v i = g t {\displaystyle \ v_{i}=gt}
Instantaneous velocity v i {\displaystyle \ v_{i}\ } of a falling object that has travelled distance d {\displaystyle \ d\ } : v i = 2 g d {\displaystyle \ v_{i}={\sqrt {2gd}}\ }
Average velocity v a {\displaystyle \ v_{a}\ } of an object that has been falling for time t {\displaystyle \ t\ } (averaged over time): v a = 1 2 g t {\displaystyle \ v_{a}={\frac {1}{2}}gt}
Average velocity v a {\displaystyle \ v_{a}\ } of a falling object that has travelled distance d {\displaystyle \ d\ } (averaged over time): v a = 2 g d 2 {\displaystyle \ v_{a}={\frac {\sqrt {2gd}}{2}}\ }
Instantaneous velocity v i {\displaystyle \ v_{i}\ } of a falling object that has travelled distance d {\displaystyle \ d\ } on a planet with mass M {\displaystyle \ M\ } , with the combined radius of the planet and altitude of the falling object being r {\displaystyle \ r\ } , this equation is used for larger radii where g {\displaystyle \ g\ } is smaller than standard g {\displaystyle \ g\ } at the surface of Earth, but assumes a small distance of fall, so the change in g {\displaystyle \ g\ } is small and relatively constant: v i = 2 G M d r 2 {\displaystyle \ v_{i}={\sqrt {\frac {2GMd}{r^{2}}}}\ }
Instantaneous velocity v i {\displaystyle \ v_{i}\ } of a falling object that has travelled distance d {\displaystyle \ d\ } on a planet with mass M {\displaystyle \ M\ } and radius r {\displaystyle \ r\ } (used for large fall distances where g {\displaystyle \ g\ } can change significantly): v i = 2 G M ( 1 r − 1 r + d ) {\displaystyle \ v_{i}={\sqrt {2GM{\Big (}{\frac {1}{r}}-{\frac {1}{r+d}}{\Big )}}}\ }
Measured fall time of a small steel sphere falling from various heights. The data is in good agreement with the predicted fall time of 2 h / g {\displaystyle {\sqrt {2h/g}}} , where h is the height and g is the acceleration of gravity.
Examples[edit]
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 12 = 4.9 meters. After two seconds it will have fallen 1/2 × 9.8 × 22 = 19.6 meters; and so on. The second to last equation becomes grossly inaccurate at great distances. If an object fell 10,000 meters to Earth, then the results of both equations differ by only 0.08%; however, if it fell from geosynchronous orbit, which is 42,164 km, then the difference changes to almost 64%.
Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e., face down) free-fall position is about 195 km/h (122 mph or 54 m/s). This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.
Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s), which is almost the terminal velocity of the peregrine falcon diving down on its prey. The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to earth having been fired upwards, or dropped from a tower—according to a 1920 U.S. Army Ordnance study.
Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 1,357.6 km/h (843.6 mph/Mach 1.25) by Felix Baumgartner who skydived from 38,969.4 m (127,852.4 ft) above earth on 14 October 2012. The record was set due to the high altitude where the lesser density of the atmosphere decreased drag.
For astronomical bodies other than Earth, and for short distances of fall at other than "ground" level, g in the above equations may be replaced by G(M+m)/r2 where G is the gravitational constant, M is the mass of the astronomical body, m is the mass of the falling body, and r is the radius from the falling object to the center of the body.
Removing the simplifying assumption of uniform gravitational acceleration provides more accurate results. We find from the formula for radial elliptic trajectories:
The time t taken for an object to fall from a height r to a height x, measured from the centers of the two bodies, is given by:
t = arccos  ( x r ) + x r ( 1 − x r ) 2 μ r 3 / 2 {\displaystyle t={\frac {\arccos {\Big (}{\sqrt {\frac {x}{r}}}{\Big )}+{\sqrt {{\frac {x}{r}}\ (1-{\frac {x}{r}})}}}{\sqrt {2\mu }}}\,r^{3/2}}
where μ = G ( m 1 + m 2 ) {\displaystyle \mu =G(m_{1}+m_{2})} is the sum of the standard gravitational parameters of the two bodies. This equation should be used whenever there is a significant difference in the gravitational acceleration during the fall.
Acceleration relative to the rotating Earth[edit]
Centripetal force causes the acceleration measured on the rotating surface of the Earth to differ from the acceleration that is measured for a free-falling body: the apparent acceleration in the rotating frame of reference is the total gravity vector minus a small vector toward the north-south axis of the Earth, corresponding to staying stationary in that frame of reference.
See also[edit]
Gravitation portal
De Motu Antiquiora and Two New Sciences (the earliest modern investigations of the motion of falling bodies)
Equations of motion
Free fall
Gravitation
Mean speed theorem, the foundation of the law of falling bodies
Radial trajectory
Notes[edit]
Jump up ^ See the works of Stillman Drake, for a comprehensive study of Galileo and his times, the Scientific Revolution.
References[edit]
Jump up ^ Jespersen, James; Fitz-Randolph, Jane. From Sundials to Clocks: Understanding Time and Frequency (PDF). National Institute of Standards and Technology Monograph 155 (Report) (1999 ed.). U.S. Department of Commerce Technology Administration and National Institute of Standards and Technology. pp. 188–190.
Jump up ^ MacDougal, D.W. (2012). "Chapter 2 - Galileo's Great Discovery: How Things Fall". Newton’s Gravity: An Introductory Guide to the Mechanics of the Universe, Undergraduate Lecture Notes in Physics (PDF). New York: Springer Science+Business Media. doi:10.1007/978-1-4614-5444-1_2.

External links[edit]
Wikimedia Commons has media related to Free fall.
Falling body equations calculator
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Hector
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other uses, see Hector (disambiguation).
"Hektor" redirects here. For other uses, see Hektor (disambiguation).
Hector brought back to Troy, from a Roman sarcophagus of c. 180–200 AD
This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.
Coin from Troy, 177–192 AD; Obverse: Bust of Commodus; Reverse: Hector, brandishing shield and spear, on a two-horse chariot; Inscription ΕΚΤΩΡ (Hektor) above, ΙΛΙΕΩΝ (Ilion meaning Troy) in exergue
The bronze coin struck in 350–300 BC in Ophryneion which was considered to be the site of the Tomb of Hector. Obverse depicts bearded Hector wearing triple crested helmet and reverse depicts infant Dionysos.
In Greek mythology and Roman Mythology, Hector (Ἕκτωρ Hektōr, pronounced [héktɔːr]) was a Trojan prince and the greatest fighter for Troy in the Trojan War. As the first-born son of King Priam and Queen Hecuba, who was a descendant of Dardanus and Tros, the founder of Troy,[1] he was a prince of the royal house and the heir apparent to his father's throne. He was married to Andromache, with whom he had an infant son, Scamandrius (whom the people of Troy called Astyanax). He acted as leader of the Trojans and their allies in the defense of Troy, "killing 31,000 Greek fighters", offers Hyginus.[2] During the European Middle Ages, Hector figures as one of the Nine Worthies noted by Jacques de Longuyon, known not only for his courage but also for his noble and courtly nature. Indeed, Homer places Hector as peace-loving, thoughtful as well as bold, a good son, husband and father, and without darker motives. James Redfield writes of Hector as a "martyr to loyalties, a witness to the things of this world, a hero ready to die for the precious imperfections of ordinary life."[3]
Contents
[hide]
1 Etymology
2 Greek mythology
2.1 Greatest warrior of Troy
2.1.1 Duel with Protesilaus
2.1.2 Duel with Ajax
2.1.3 Duel with Achilles
2.2 Trojan counter attack
2.3 Hector's last fight
3 Historical references
4 In literature
5 See also
6 References
7 External links
Etymology[edit]
In Greek, Héktōr is a derivative of the verb ἔχειν ékhein, archaic form *ἕχειν hékhein, 'to have' or 'to hold' from Proto-Indo-European *seǵh- 'to hold'.[4] Héktōr, or Éktōr as found in Aeolic poetry, is also an epithet of Zeus in his capacity as 'he who holds [everything together]'. Hector's name could thus be taken to mean 'holding fast'.[5]
Greek mythology[edit]
Greatest warrior of Troy[edit]
Hector Admonishes Paris for His Softness and Exhorts Him to Go to War by J. H. W. Tischbein (1751–1828)
According to the Iliad, Hector does not approve of war between the Greeks and the Trojans.
For ten years, the Achaeans besieged Troy and their allies in the east. Hector commanded the Trojan army, with a number of subordinates including Polydamas, and his brothers Deiphobus, Helenus, and Paris. By all accounts, Hector was the best warrior the Trojans and all their allies could field, and his fighting prowess was admired by Greeks and his own people alike.
Diomedes and Odysseus, when faced with his attack, described him as what Robert Fagles translated as an 'incredible dynamite', and a 'maniac'.
Duel with Protesilaus[edit]
In the Iliad, Hector's exploits in the war prior to the events of the book are recapitulated. He had fought the Greek champion Protesilaus in single combat at the start of the war and killed him. A prophecy had stated that the first Greek to land on Trojan soil would die. Thus, Protesilaus, Ajax, and Odysseus would not land. Finally, Odysseus threw his shield out and landed on that, and Protesilaus jumped next from his own ship. In the ensuing fight, Hector killed him, fulfilling the prophecy.
Ajax and Hector exchange gifts (woodcut in Andreas Alciatus, Emblematum libellus, 1591).
Duel with Ajax[edit]
At the advice of his brother, Helenus (who also is divinely inspired), and being told by him that he is not destined to die yet, Hector managed to get both armies seated and challenges any one of the Greek warriors to single combat.[6] The Argives were initially reluctant to accept the challenge. However, after Nestor's chiding, nine Greek heroes stepped up to the challenge and drew by lot to see who was to face Hector. Ajax wins and fights Hector to a stalemate for the entire day. With neither able to achieve victory, they express admiration for each other's courage, skill, and strength. Hector gave Ajax his sword, which Ajax later uses to kill himself. Ajax gives Hector his girdle, which later was used to attach Hector's corpse to Achilles' chariot by which he is dragged around the walls of Troy.
The Greek and the Trojans make a truce to bury the dead. In the early dawn the next day the Greeks take advantage of it to build a wall and ditch around the ships. Zeus is watching in a distance.[7]
Duel with Achilles[edit]
Another mention of Hector's exploits in the early years of war was given in the Iliad book 9. During the embassy to Achilles, Odysseus, Phoenix and Ajax all try to persuade Achilles to rejoin the fight. In his response, Achilles points out that while Hector was terrorizing the Greek forces now, and that while he himself had fought in their front lines, Hector had 'no wish' to take his force far beyond the walls and out from the Skiaian Gate and nearby oak tree. He then claims, 'There he stood up to me alone one day, and he barely escaped my onslaught.' Another duel that took place, although Hector got help from Aeneas and Deiphobus, was when Hector rushed to try to save his brother Troilus from Achilles' hands. But he came too late and Troilus had already perished. All Hector could do was to take the lifeless body of Troilus while Achilles escaped after he fought his way through from the Trojans reinforcement.
A 2004 film version of Troy has Achilles slaying Hector following a duel, whereas in the Iliad it is rather different. In the Iliad, Hector remains outside the walls, while his army flees into the city. As Achilles approaches, Hector stands his ground, fights and dies upon looking up at Troy. The film version of his death more resembles the single combat between the champions mentioned by Achilles in the Iliad, book 9.
Hector's last visit with his wife, Andromache, and infant son Astyanax, startled by his father's helmet (Apulian red-figure vase, 370–360 BC)
In the tenth year of the war, observing Paris avoiding combat with Menelaus, Hector upbraids him with having brought trouble on his whole country and now refusing to fight. Paris therefore proposes single combat between himself and Menelaus, with Helen to go to the victor, ending the war.[8] The duel, however, leads to inconclusive results due to intervention by Aphrodite who leads Paris off the field. After Pandarus wounds Menelaus with an arrow the fight begins again.
The Greeks attack and drive the Trojans back. Hector must now go out to lead a counter-attack. His wife, Andromache, carrying in her arms their son Astyanax, intercepts him at the gate, pleading with him not to go out for her sake as well as his son's. Hector knows that Troy and the house of Priam are doomed to fall and that the gloomy fate of his wife and infant son will be to die or go into slavery in a foreign land. With understanding, compassion, and tenderness he explains that he cannot personally refuse to fight, and comforts her with the idea that no one can take him until it is his time to go.[9] The gleaming bronze helmet frightens Astyanax and makes him cry.[10] Hector takes it off, embraces his wife and son, and for his sake prays aloud to Zeus that his son might be chief after him, become more glorious in battle than he, and to bring home the blood of his enemies and make Hector's wife, his mother, proud. Once he left back for battle those in the house began to mourn as they knew he would not return.[9]
Hector and Paris pass through the gate and rally the Trojans, raising havoc among the Greeks.
Trojan counter attack[edit]
Zeus weighs the fates of the two armies in the balance, and that of the Greeks sinks down. The Trojans press the Greeks into their camp over the ditch and wall and would have laid hands on the ships, but Agamemnon rallies the Greeks in person. The Trojans are driven off, night falls, and Hector resolves to take the camp and burn the ships next day. The Trojans bivouac in the field.
A thousand camp-fires gleamed upon the plain ....[11]
The next day Agamemnon rallies the Greeks and drives the Trojans
like a herd of cows maddened with fright when a lion has attacked them ...[12]
Hector refrains from battle until Agamemnon leaves the field, wounded in the arm by a spear. Then Hector rallies the Trojans:
... like some fierce tempest that swoops down upon the sea ....
Diomedes and Odysseus hinder Hector and win the Greeks some time to retreat, but the Trojans sweep down upon the wall and rain blows upon it. The Greeks in the camp contest the gates to secure entrance for their fleeing warriors. The Trojans try to pull down the ramparts while the Greeks rain arrows upon them. Hector smashes open a gate with a large stone, clears the gate and calls on the Trojans to scale the wall, which they do, and
... all was uproar and confusion.[13]
Battle at the ships, on a Roman-era sarcophagus, 225–250 AD
The battle rages inside the camp. Hector goes down, hit by a stone thrown by Ajax, but Apollo arrives from Olympus and infuses strength into "the shepherd of the people", who orders a chariot attack, with Apollo clearing the way. Many combats, deaths, boasts, threats, epithets, figures of speech, stories, lines of poetry and books of the Iliad later, Hector lays hold of Protesilaus' ship and calls for fire. The Trojans cannot bring it to him, as Ajax kills everyone who tries. Eventually, Hector breaks Ajax' spear with his sword, forcing him to give ground, and he sets the ship on fire.[14]
These events are all according to the will of the gods, who have decreed the fall of Troy, and therefore intend to tempt Achilles back into the war. Patroclus, Achilles' closest companion, disguised in the armor of Achilles, enters the combat leading the Myrmidons and the rest of the Achaeans to force a Trojan withdrawal. After Patroclus has routed the Trojan army, Hector, with the aid of Apollo and Euphorbus, kills Patroclus, vaunting over him:
"Wretch! Achilleus, great as he was, could do nothing to help you."[15]
The dying Patroclus foretells Hector's death:
"You yourself are not one who shall live long, but now already death and powerful destiny are standing beside you, to go down under the hands of Aiakos' great son, Achilleus"[15]
Hector's last fight[edit]
Alas! the gods have lured me on to my destruction. ... death is now indeed exceedingly near at hand and there is no way out of it – for so Zeus and his son Apollo the far-darter have willed it, though heretofore they have been ever ready to protect me. My doom has come upon me; let me not then die ingloriously and without a struggle, but let me first do some great thing that shall be told among men hereafter.
—  Spoken by Hector facing Achilles, after a missed spear-throw; Iliad, Book XXII, lines 299–305
Hector strips the armor of Achilles off the fallen Patroclus and gives it to his men to take back to the city. Glaucus accuses Hector of cowardice for not challenging Ajax. Stung, Hector calls for the armor, puts it on, and uses it to rally the Trojans. Zeus regards the donning of a hero's armor as an act of insolence by a fool about to die, but it makes Hector strong for now.[16]
The next day, the enraged Achilles renounces the wrath that kept him out of action and routs the Trojans, forcing them back to the city. Hector chooses to remain outside the gates of Troy to face Achilles, partly because had he listened to Polydamas and retreated with his troops the previous night, Achilles would not have killed so many Trojans. When he sees Achilles, however, Hector is seized by fear and turns to flee. Achilles chases him around the city three times before Hector masters his fear and turns to face Achilles. But Athena, in the disguise of Hector's brother Deiphobus, has deluded Hector. He requests from Achilles that the victor should return the other's body after the duel, (though Hector himself made it clear he planned to throw the body of Patroclus to the dogs) but Achilles refuses. Achilles hurls his spear at Hector, who dodges it, but Athena brings it back to Achilles' hands without Hector noticing. Hector then throws his own spear at Achilles; it hits his shield and does no injury. When Hector turns to face his supposed brother to retrieve another spear, he sees no one there. At that moment he realizes that he is doomed. Hector decides that he will go down fighting and that men will talk about his bravery in years to come. The desire to achieve ever-lasting honor was one of the most fierce for soldiers living in the timocratic (honor based) society of the age.
Triumphant Achilles dragging Hector's lifeless body in front of the Gates of Troy. (From a panoramic fresco on the upper level of the main hall of the Achilleion)
Hector pulls out his sword, now his only weapon, and charges. But Achilles grabbed his thrown spears that delivered to him by the unseen Athena who wore the Hades helmet. And then Achilles aimed his spear and pierced the collar bone section of Hector, the only part that the stolen Armor of Achilles that not protected Hector from it. That wound was fatal yet that wound also allowed Hector to speak to Achilles. Hector, in his final moments, begs Achilles for an honorable funeral, but Achilles replies that he will let the dogs and vultures devour Hector's flesh. (Throughout the Homeric poems, several references are made to dogs, vultures, and other creatures that devour the dead. It can be seen as another way of saying one will die.) Hector dies, prophesying that Achilles' death will follow soon:
Be careful now; for I might be made into the gods' curse ... upon you, on that day when Paris and Phoibos Apollo...destroy you in the Skainan gates, for all your valor.[17]
After his death, Achilles slits Hector's heels and passes the girdle that Ajax had given Hector through the slits. He then fastens the girdle to his chariot and drives his fallen enemy through the dust to the Danaan camp. For the next twelve days, Achilles mistreats the body, but it remains preserved from all injury by Apollo and Aphrodite. After these twelve days, the gods can no longer stand watching it and send down two messengers: Iris, another messenger god, and Thetis, the mother of Achilles. Thetis has told Achilles to allow King Priam to come and take the body for ransom. Once King Priam has been notified that Achilles will allow him to claim the body, he goes to his strongroom to withdraw the ransom. The ransom King Priam offers includes twelve fine robes, twelve white mantles, several richly embroidered tunics, ten bars of yellow gold, a special gold cup, and several cauldrons. Priam himself goes to claim his son's body, and Hermes grants him safe passage by casting a charm that will make anyone who looks at him fall asleep.
Think of thy father, and this helpless face behold
See him in me, as helpless and as old!
Though not so wretched: there he yields to me,
The first of men in sovereign misery!
Thus forced to kneel, thus groveling to embrace
The scourge and ruin of my realm and race;
Suppliant my children’s murderer to implore,
And kiss those hands yet reeking with their gore!
—  Spoken by Priam to Achilles; Iliad, Book XXIV, Pope's translation
Achilles, moved by Priam's actions and following his mother's orders sent by Zeus, returns Hector's body to Priam and promises him a truce of twelve days to allow the Trojans to perform funeral rites for Hector. Priam returns to Troy with the body of his son, and it is given full funeral honors. Even Helen mourns Hector, for he had always been kind to her and protected her from spite. The last lines of the Iliad are dedicated to Hector's funeral. Homer concludes by referring to the Trojan prince as the "Breaker of Horses."[18]
Historical references[edit]
The most valuable historical evidence for the Battle of Troy are treaties and letters mentioned in Hittite cuneiform texts of the same approximate era, which mention an unruly Western Anatolian warlord named Piyama-Radu (possibly Priam) and his successor Alaksandu (possibly Alexander, the nickname of Paris) both based in Wilusa (possibly Ilion/Ilios), as well as the god Apaliunas (possibly Apollo).
Other such pieces of evidence are names of Trojan heroes in Linear B tablets. Twenty out of fifty-eight men's names also known from Homer, including 𐀁𐀒𐀵, E-ko-to (Hector),[19] are Trojan warriors and some, including Hector, are in a servile capacity.[20] No such conclusion that they are the offspring of Trojan captive women is warranted. Generally the public has to be content with the knowledge that these names existed in Greek in Mycenaean times, although Page[21] hypothesizes that Hector "may very well be ... a familiar Greek form impressed on a similar-sounding foreign name."
When Pausanias visited Thebes in Boeotia, in the second century AD, he was shown Hector's tomb and was told that the bones had been transported to Thebes according to a Delphic oracle. Moses I. Finley observes[22] "this typical bit of fiction must mean that there was an old Theban hero Hector, a Greek, whose myths antedated the Homeric poems. Even after Homer had located Hector in Troy for all time, the Thebans held on to their hero, and the Delphic oracle provided the necessary sanction."
The pseudepigraphical writer Dares Phrygius states that Hector "spoke with a slight lisp. His complexion was fair, his hair curly. His eyes would blink attractively. His movements were swift. His face, with its beard, was noble. He was handsome, fierce, and high-spirited, merciful to the citizens, and deserving of love."[23]
In literature[edit]
The Grief and Recriminations of Andromache over the Body of Hector Her Husband (1783) by Jacques-Louis David
In Dante Alighieri's Inferno (which is part of the Divine Comedy series), Hector and his family are placed in Limbo, the outer circle wherein the virtuous non-Christians dwell.
Roland's sword in early 12th century French poem Song of Roland, was named Durendal. According to Ludovico Ariosto's Orlando Furioso it once belonged to Hector of Troy, and was given to Roland by Malagigi (Maugris).
In William Shakespeare's Troilus and Cressida, Hector's death is used to mark the conclusion of the play. His nobility is shown in stark contrast to the deceit and pridefulness of the Greeks, especially Achilles.
See also[edit]
List of King Priam's children
Nine Worthies
References[edit]
Jump up ^ Iliad, XX, 215 ff.
Jump up ^ Hyginus, Fabulae 115.
Jump up ^ Redfield, James M. (1994). Nature and Culture in the Iliad: The Tragedy of Hector. Durham: Duke University Press. p. ix.
Jump up ^ R. S. P. Beekes, Etymological Dictionary of Greek, Brill, 2009, p. 399.
Jump up ^ This etymology is given under Hector in the Online Etymological Dictionary, which, if true, would make it an Indo-European name, of root *seĝh-. The Dardanians would not have been Greek, but the language of the city of Troy is still an open question.
Jump up ^ Iliad, VII.
Jump up ^ Iliad, VII, 433 ff.)
Jump up ^ Iliad, III.
^ Jump up to: a b Iliad, VI.
Jump up ^ This Trojan helmet was made famous by Denys L. Page in History and the Homeric Iliad, Chapter VI, "Some Mycenaean relics in the Iliad", as the Greeks do not wear bronze helmets in the poem's epic formulae, but they did in the Homeric Age; therefore, scholar Denys L. Page concludes (on other evidence as well) that the bronze helmet of Hector descends in oral poetry from Mycenaean times.
Jump up ^ Iliad, VIII, 542 ff.
Jump up ^ Iliad, XI, 171 ff.
Jump up ^ Iliad, XII.
Jump up ^ Iliad, XV, end.
^ Jump up to: a b The Iliad, book XVI
Jump up ^ Iliad, XVII
Jump up ^ Lattimore, Richmond (2011). The Iliad. University of Chicago Press. p. 467. ISBN 978-0-226-47049-8.
Jump up ^ Pseudo-Apollodorus. Bibliotheca. III, xii, 5–6; "Epitome" IV, 2.
Jump up ^ "The Linear B word e-ko-to". Palaeolexicon: Word study tool for ancient languages.
Jump up ^ Template:Cite book editor1-first=Michael
Jump up ^ Page, Denys Lionel (1972) [1959]. "V". History and the Homeric Iliad. Sather Classical Lectures. University of California Press.
Jump up ^ Finley, Moses I. (1978) [1954]. The World of Odysseus (Revised ed.). Viking Press. p. 44.
Jump up ^ Dares of Phrygia. History of the Fall of Troy 12. A short prose work which purports to be a first hand account of the Trojan War by Dares, a Trojan priest of Hephaestus in the Iliad.
External links[edit]
Media related to Hector at Wikimedia Commons
"Hector". Encyclopedia Americana. 1920.
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A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation.[1] For example, James Bond's famous identifier, 007, has two leading zeros.[2] When leading zeros occupy the most significant digits of an integer, they could be left blank or omitted for the same numeric value.[3] Therefore, the usual decimal notation of integers does not use leading zeros except for the zero itself, which would be denoted as an empty string otherwise.[4] However, in decimal fractions strictly between −1 and 1, the leading zeros digits between the decimal point and the first nonzero digit are necessary for conveying the magnitude of a number and cannot be omitted,[1] while trailing zeroes- zeroes occurring after the decimal point and after the last nonzero digit- can be omitted without changing the meaning.
Contents
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1 Occurrence
2 Advantages
3 0 as a prefix
4 See also
5 References
Occurrence[edit]
Often, leading zeros are found on non-electronic digital displays or on such electronic ones as seven-segment displays, that contain fixed sets of digits. These devices include manual counters, stopwatches,[5] odometers,[6] and digital clocks.[5] Leading zeros are also generated by many older computer programs when creating values to assign to new records, accounts and other files, and as such are likely to be used by utility billing systems, human resources information systems and government databases. Many digital cameras and other electronic media recording devices use leading zeros when creating and saving new files to make names of the equal length.
Leading zeros also present whenever the number of digits is technically fixed (such as in a memory register), but the stored value is not large enough to result in a non-zero most significant digit.[7] The count leading zeros operation efficiently determines the number of leading zero bits in a machine word.[8]
A leading zero appears in roulette in the United States, where "00" is distinct from "0" (a wager on "0" will not win if the ball lands in "00", and vice versa). Sports where competitors are numbered follow this as well; a stock car numbered "07" would be considered distinct from one numbered "7". Benito Santiago, a Major League Baseball catcher who wore the number 09 for several years, is the only major professional sports league player to use a jersey number with a leading zero, not counting several who have worn the number 00. This is most common with single-digit numbers.
Advantages[edit]
Collation
Leading zeros are used to make ascending order of numbers correspond with alphabetical order: e.g., 11 comes alphabetically before 2, but after 02. (See, e.g., ISO 8601.) This does not work with negative numbers, though, whether leading zeroes are used or not: −23 comes alphabetically after −01, −1, and −22, although it is less than all of them.
Error prevention
Leading zeros in a sentence also make it less likely that a careless reader will overlook the decimal point. For example, in modern pharmacy there is a widely followed convention that leading zeros must not be omitted from any dose or dosage value in drug prescribing. Likewise, just as leading zeros are mandatory, trailing zeros are forbidden. In both cases, the reason is the same: to prevent misreading and the resultant misdose by one or several orders of magnitude.
Fraud prevention
Leading zeros can also be used to prevent fraud by filling in character positions that might normally be empty. For example, adding leading zeros to the amount of a check (or similar financial document) makes it more difficult for fraudsters to alter the amount of the check before presenting it for payment.
0 as a prefix[edit]
See also: Octal § In computers, and Data types
A prefix 0 is used in C to specify string representations of octal numbers, as required by the ANSI C standard for the "strtol" function (the string to long integer converter) in the "stdlib.h" library. Many other programming languages, such as Python 2, Perl, Ruby, PHP, and the Unix shell bash also follow this specification for converting strings to numbers. As an example, "0020" does not represent 2010 (2×101 + 0×100), but rather 208 = 1610 (2×81 + 0×80 = 1×101 + 6×100). Decimal numbers written with leading zeros will be interpreted as octal by languages that follow this convention and will generate errors (not just unexpected results) if they contain "8" or "9", since these digits do not exist in octal. This behavior can be quite a nuisance when working with sequences of strings with embedded, zero-padded decimal numbers (typically file names) to facilitate alphabetical sorting (see above) or when validating inputs from users who would not know that adding a leading zero triggers this base conversion.
See also[edit]
Trailing zero
00 (disambiguation)
References[edit]
^ Jump up to: a b Miller, Jane E. (2008), The Chicago Guide to Writing about Numbers, University of Chicago Press, p. 276, ISBN 9780226526324 .
Jump up ^ Lafore, Robert W. (1987), Microsoft C: programming for the IBM, H.W. Sams, p. 294, ISBN 9780672225154 .
Jump up ^ Zegarelli, Mark (2014), Basic Math and Pre-Algebra Workbook For Dummies (2nd ed.), John Wiley & Sons, p. 8, ISBN 9781118828304 .
Jump up ^ Flynt, Clif (2012), Tcl/Tk: A Developer's Guide, Elsevier, pp. 752–753, ISBN 9780123847171 .
^ Jump up to: a b Greene, Jennifer; Stellman, Andrew (2013), Head First C#, O'Reilly Media, Inc., p. 770, ISBN 9781449358884 .
Jump up ^ Dueck, Robert; Reid, Ken (2011), Digital Electronics, Cengage Learning, p. 48, ISBN 9781133708964 .
Jump up ^ Kuc, Roman (1999), The digital information age: an introduction to electrical engineering, PWS Pub. Co., p. 67, ISBN 9780534953157 .
Jump up ^ Dandamudi, Sivarama P. (2005), Guide to RISC Processors: for Programmers and Engineers, Springer, p. 139, ISBN 9780387274461 .
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Manis (orangutan)
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Manis was the trained orangutan that played Clyde as Clint Eastwood's sidekick in the 1978 box office hit Every Which Way But Loose. Its 1980 sequel, Any Which Way You Can (1980), did not feature Manis, as the "child actor" had grown too much between productions. In the sequel two orangutans, C.J. and Buddha, shared the role.[1] Although rumors about the cause of death of Buddha in 1980 point to abuse by his trainer on set, at least one source for the rumors may originate from a 1985 National Enquirer article.
Manis returned to working with his trainers' act in Las Vegas.[2]
References[edit]
Jump up ^ "Any Which Way You Can, Full Cast & Crew". IMDB.
Jump up ^ "The Daily Cleaner". The Gleaner. Gleaner Company. 1979-09-12. p. 5. Retrieved 2008-06-18.
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