Time Enough at Last
"Time Enough at Last" is the eighth episode of the American television anthology series The Twilight Zone. The episode was adapted from a short story written by Lynn Venable; the short story appeared in the January 1953 edition of the science fiction magazine If: Worlds of Science Fiction about seven years before the television episode first aired. "Time Enough at Last" became one of the most famous episodes of the original Twilight Zone and has been parodied since. It is "the story of a man who seeks salvation in the rubble of a ruined world" and tells of Henry Bemis, played by Burgess Meredith, who loves books, yet is surrounded by those who would prevent him from reading them; the episode follows Bemis through the post-apocalyptic world, touching on such social issues as anti-intellectualism, the dangers of reliance upon technology, the difference between aloneness and loneliness. Witness Mr. Henry Bemis, a charter member in the fraternity of dreamers. A bookish little man whose passion is the printed page, but, conspired against by a bank president and a wife and a world full of tongue-cluckers and the unrelenting hands of a clock.
But in just a moment, Mr. Bemis will enter a world without bank presidents or wives or clocks or anything else. He'll have a world all to himself... without anyone. Henpecked, far sighted bank teller and avid bookworm Henry Bemis works at his window in a bank, while reading David Copperfield, which causes him to shortchange an annoyed customer. Bemis's angry boss, his nagging wife, both complain to him that he wastes far too much time reading "doggerel"; as a cruel joke, his wife asks him to read poetry from one of his books to her. Seconds she destroys the book by ripping the pages from it, much to Henry's dismay; the next day, as usual, Henry takes his lunch break in the bank's vault, where his reading will not be disturbed. Moments after he sees a newspaper headline, which reads "H-Bomb Capable of Total Destruction", an enormous explosion outside the bank violently shakes the vault, knocking Bemis unconscious. After regaining consciousness and recovering the thick glasses required for him to see, Bemis emerges from the vault to find the bank demolished and everyone in it dead.
Leaving the bank, he sees that the entire city has been destroyed, realizes that a nuclear war has devastated Earth, but that his being in the vault has saved him. Seconds, hours, they crawl by on hands and knees for Mr. Henry Bemis, who looks for a spark in the ashes of a dead world. A telephone connected to nothingness. A neighborhood bar, a movie, a baseball diamond, a hardware store, the mailbox of what was once his house and is now a rubble, they lie at his feet as battered monuments to what is no more. Mr. Henry Bemis on an eight-hour tour of a graveyard. Finding himself alone in a shattered world with canned food to last him a lifetime and no means of leaving to look for other survivors, Bemis succumbs to despair; as he prepares to commit suicide using a revolver he has found, Bemis sees the ruins of the public library in the distance. Investigating, he finds that the books are still legible, his despair gone, Bemis contentedly sorts the books he looks forward to reading for years to come, with no obligations to get in the way.
Just as he bends down to pick up the first book, he stumbles, his glasses fall off and shatter. In shock, he picks up the broken remains of the glasses he is blind without, says, "That's not fair. That's not fair at all. There was time now. There was—was all the time I needed…! It's not fair! It's not fair!" and bursts into tears, surrounded by books he now can never read. The best laid plans of mice and men... and Henry Bemis... the small man in the glasses who wanted nothing but time. Henry Bemis, now just a part of a smashed landscape, just a piece of the rubble, just a fragment of what man has deeded to himself. Mr. Henry Bemis... in the Twilight Zone. "Time Enough at Last" was one of the first episodes written for The Twilight Zone. It introduced Burgess Meredith to the series, he narrated for the 1983 film Twilight Zone: The Movie, which made reference to "Time Enough at Last" during its opening sequence, with the characters discussing the episode in detail. Footage of the exterior steps of the library was filmed several months after production had been completed.
These steps can be seen on the exterior of an Eloi public building in MGM's 1960 version of The Time Machine. John Brahm was nominated for a Directors Guild award for his work on the episode; the book that Bemis was reading in the vault and that flips open when the bomb explodes is A History of the Life and Voyages of Christopher Columbus by Washington Irving. Although the overriding message may seem to "be careful what you wish for, you just might get it", there are other themes throughout the episode as well. Paramount among these is the question of solitude versus loneliness, as embodied by Bemis' moment of near-suicide. Additionally, the portrayal of societal attitudes towards books speaks to the contemporary decline of traditional literature and how, given enough time, reading may become a relic of the past. At the same time, the ending "punishes Bemis for his antisocial behavior, his greatest desire is thwarted". Rod Serl
Third from the Sun
"Third from the Sun" is episode 14 of the American television anthology series The Twilight Zone. It is based on a short story of the same name by Richard Matheson which first appeared in the first issue of the magazine Galaxy Science Fiction in October 1950. Will Sturka, a scientist who works at a military base, has been producing a great number of H-bombs in preparation for imminent nuclear war. Sturka realizes that there is only one way to escape—steal an experimental, top-secret spacecraft stored at the base, he plans to bring Sturka's daughter Jody. The two plot for months, making arrangements for their departure; when production of the bombs increases, Sturka realizes. He and Riden decide to put their plan in action—take their families to the craft to tour it, overpower the guards and take off. Sturka's superior Carling overhears the two men talking; that night, everyone gathers for a game of cards where Riden reveals that he has found a place to go—a small planet 11 million miles away. During the game, Carling unexpectedly appears at the door and hints that he knows what the group is planning.
He hints at trouble: "A lot can happen in forty-eight hours." After he leaves and Riden inform the women that they must leave that moment. When the five arrive at the site of the spacecraft and Riden spot their contact, who flashes a light; when the contact steps forward, though, he is revealed to be Carling, armed with a gun. He prepares to call the authorities; the women, who have been waiting in the car, watch as Carling orders them out. Jody throws the car's door open, knocking the gun from Carling's hand and giving the men enough time to overpower him; the group rushes into the ship. That evening, the group has safely escaped their doomed planet and are on course. Sturka comments. Riden smiles as he points out on the ship's viewer their mysterious destination, 11 million miles away—the third planet from the Sun, called "Earth". Todd VanDerWerff of The A. V. Club rated it A and called the twist "justifiably famous". "Probe 7, Over and Out", another Twilight Zone episode with a similar plot. "The Invaders", another episode in which a farm woman encounters tiny "alien" astronauts, who are Earthlings.
"Death Ship" is a TZ episode again featuring the Forbidden Planet Cruiser, where explorers find their ship E-89 has somehow crashed on the alien planet they have just found. Ancient astronaut theory DeVoe, Bill.. Trivia from The Twilight Zone. Albany, GA: Bear Manor Media. ISBN 978-1-59393-136-0 Grams, Martin.. The Twilight Zone: Unlocking the Door to a Television Classic. Churchville, MD: OTR Publishing. ISBN 978-0-9703310-9-0 "Third from the Sun" on IMDb "Third from the Sun" at TV.com Matheson, Richard. "Third from the Sun". Galaxy Science Fiction. P. 61. Retrieved 17 October 2013
Hobo
A hobo is a migrant worker or homeless vagrant one, impoverished. The term originated in the Western—probably Northwestern—United States around 1890. Unlike a "tramp", who works only when forced to, a "bum", who does not work at all, a "hobo" is a traveling worker; the origin of the term is unknown. According to etymologist Anatoly Liberman, the only certain detail about its origin is the word was first noticed in American English circa 1890. Liberman points out that many folk etymologies fail to answer the question: "Why did the word become known in California by the early Nineties?" Author Todd DePastino has suggested it may be derived from the term hoe-boy meaning "farmhand", or a greeting such as Ho, boy! Bill Bryson suggests in Made in America that it could either come from the railroad greeting, "Ho, beau!" or a syllabic abbreviation of "homeward bound". It could come from the words "homeless boy". H. L. Mencken, in his The American Language, wrote: Tramps and hobos are lumped together, but see themselves as differentiated.
A hobo or bo is a migrant laborer. Lower than either is the bum, who neither works nor travels, save when impelled to motion by the police, it is unclear when hobos first appeared on the American railroading scene. With the end of the American Civil War in the 1860s, many discharged veterans returning home began hopping freight trains. Others looking for work on the American frontier followed the railways west aboard freight trains in the late 19th century. In 1906, Professor Layal Shafee, after an exhaustive study, put the number of tramps in the United States at about 500,000, his article "What Tramps Cost Nation" was published by The New York Telegraph in 1911, when he estimated the number had surged to 700,000. The number of hobos increased during the Great Depression era of the 1930s. With no work and no prospects at home, many decided to travel for free by freight train and try their luck elsewhere. Life as a hobo was dangerous. In addition to the problems of being itinerant and far from home and support, plus the hostility of many train crews, they faced the railroads' security staff, nicknamed "bulls", who had a reputation of violence against trespassers.
Moreover, riding on a freight train is dangerous in itself. British poet W. H. Davies, author of The Autobiography of a Super-Tramp, lost a foot when he fell under the wheels when trying to jump aboard a train, it was easy to be trapped between cars, one could freeze to death in bad weather. When freezer cars were loaded at an ice factory, any hobo inside was to be killed. According to Ted Conover in Rolling Nowhere, at some unknown point in time, as many as 20,000 people were living a hobo life in North America. Modern freight trains are much faster and thus harder to ride than in the 1930s, but they can still be boarded in railyards. Many hobo terms have become part of common language, such as "big House", "glad rags", "main drag", others. To cope with the uncertainties of hobo life, hobos developed a system of a visual code. Hobos would write this code with chalk or coal to provide directions and warnings to others in "the brotherhood". A symbol would indicate "turn right here", "beware of hostile railroad police", "dangerous dog", "food available here", so on.
Some used signs: A cross signifies "angel food", that is, food served to the hobos after a sermon. A triangle with hands signifies. A horizontal zigzag signifies a barking dog. A square missing its top line signifies. A top hat and a triangle signify wealth. A spearhead signifies a warning to defend oneself. A circle with two parallel arrows means get out fast. Two interlocked circles, representing handcuffs, warn. A caduceus symbol signifies. A cross with a smiley face in one of the corners means the doctor at this office will treat hobos free of charge. A cat signifies. A wavy line above an X means a campsite. Three diagonal lines mean. A square with a slanted roof with an X through it means that the house has been "burned" or "tricked" by another hobo and is not a trusting house. Two shovels signify. Another version of the hobo code exists as a display in the Steamtown National Historic Site at Scranton, operated by the National Park Service. There is an exhibit of hobo codes at the National Cryptologic Museum in Annapolis Junction, Maryland.
The Free Art and Technology Lab released a QR Hobo Code, with a QR stenciler, in July 2011. An ethical code was created by Tourist Union #63 during its 1889 National Hobo Convention in St. Louis, Missouri; this code was voted upon as a concrete set of laws to govern the Nationwide Hobo Body. When in town, always respect the local law and officials, try to be a gentleman at all times. Don't take advantage of someone, in a vulnerable situation, locals or other hobos. Always try to find work if temporary, always seek out jobs nobody wants. By doing so you not only help a business along, but ensure employment should you return to that town again; when no employment is available, make your own work by using your added talents at crafts. Do not allow yourself to become a stupid drunk and set a bad example for locals' treatment of other hobos; when jungling in town, respect handouts, do not
Anthology series
An anthology series is a radio, television or book series that presents a different story and a different set of characters in each episode or season. These have a different cast each week, but several series in the past, such as Four Star Playhouse, employed a permanent troupe of character actors who would appear in a different drama each week; some anthology series, such as Studio One, began on radio and expanded to television. Medieval Greek anthologiā, collection of epigrams, from Greek, flower gathering, from anthologein, to gather flowers: antho-, antho- + logos, a gathering. Many popular old-time radio programs were anthology series. On some series, such as Inner Sanctum Mysteries, the only constant was the host, who introduced and concluded each dramatic presentation. One of the earliest such programs was The Collier Hour, broadcast on the NBC Blue Network from 1927 to 1932; as radio's first major dramatic anthology, it adapted stories and serials from Collier's Weekly in a calculated move to increase subscriptions and compete with The Saturday Evening Post.
Airing on the Wednesday prior to each week's distribution of the magazine, the program soon moved to Sundays in order to avoid spoilers with dramatizations of stories appearing in the magazine. Radio drama anthology series include: Academy Award Theater Arch Oboler's Plays The Campbell Playhouse Cavalcade of America CBS Radio Workshop Earplay Four Star Playhouse Lux Radio Theater The Mercury Theatre on the Air The Screen Guild Theater Stars over Hollywood Radio anthology series provided a format for science fiction, horror and mystery genres: Mystery House The Witch's Tale Lights Out The Hermit's Cave Famous Jury Trials Dark Fantasy Inner Sanctum Mysteries The Whistler Suspense The Mysterious Traveler Creeps by Night Mystery Playhouse The Strange Dr. Weird The Haunting Hour The Sealed Book Mystery in the Air The Weird Circle Quiet, Please! Escape The Unexpected The Hall of Fantasy 2000 Plus Dimension X ABC Mystery Theater, anthology and mystery series Sleep No More Theater 10:30 X Minus One The final episode of Suspense was broadcast on September 30, 1962, a date that has traditionally been seen as marking the end of the old-time radio era.
However, genre series produced since 1962 include: The Black Mass The Creaking Door Beyond Midnight The Zero Hour Mystery Theater Nightfall The Cabinet of Dr. Fritz 2000X The Twilight Zone In the history of television, live anthology dramas were popular during the Golden Age of Television of the 1950s with series such as The United States Steel Hour and The Philco Television Playhouse. Dick Powell came up with an idea for an anthology series, Four Star Playhouse, with a rotation of established stars every week, four stars in all; the stars would own the studio and the program, as Lucille Ball and Desi Arnaz had done with Desilu studio. Powell had intended for the program to feature himself, Charles Boyer, Joel McCrea, Rosalind Russell; when Russell and McCrea backed out, David Niven came on board as the third star. The fourth star was a guest star. CBS liked the idea, Four Star Playhouse made its debut in fall of 1952, it ran on alternate weeks only during the first season, alternating with Andy.
It was successful enough to be renewed and became a weekly program from the second season until the end of its run in 1956. Ida Lupino was brought on board as the de facto fourth star, though unlike Powell and Niven, she owned no stock in the company. American television networks would sometimes run summer anthology series which consisted of unsold television pilots. Beginning in 1971, the long-run Masterpiece Theatre drama anthology series brought British productions to American television. In 2011, American Horror Story debuted a new type of anthology format in the U. S; each season, rather than each episode, is a standalone story. Several actors have appeared in the various seasons, but playing different roles—in an echo of the Four Star Playhouse format; the success of American Horror Story has spawned other season-long anthologies such as American Crime Story and Feud. The 20th Century Fox Hour ABC Movie of the Week ABC Stage 67 Academy Theatre Actors Studio Alcoa-Goodyear Theatre The Alcoa Hour Alcoa Premiere American Crime American Crime Story American Horror Story American Film Theatre American Playhouse The American Playwrights Theater: The One Acts Th
Doll
A doll is a model of a human being used as a toy for girls. Dolls have traditionally been used in magic and religious rituals throughout the world, traditional dolls made of materials such as clay and wood are found in the Americas, Asia and Europe; the earliest documented dolls go back to the ancient civilizations of Egypt and Rome. They have been made as rudimentary playthings as well as elaborate art. Modern doll manufacturing has its roots from the 15th century. With industrialization and new materials such as porcelain and plastic, dolls were mass-produced. During the 20th century, dolls became popular as collectibles; the earliest dolls were made from available materials such as clay, wood, ivory, leather, or wax. Archaeological evidence places dolls as the foremost candidate for the oldest known toy. Wooden paddle dolls have been found in Egyptian tombs dating to as early as the 21st century BC. Dolls with movable limbs and removable clothing date back to at least 200 BC. Archaeologists have discovered Greek dolls articulated at the hips and shoulders.
Rag dolls and stuffed animals were also popular, but no known examples of these have survived to the present day. Stories from ancient Greece around 100 AD show. In ancient Rome, dolls were made of wood or ivory. Dolls have been found in the graves of Roman children. Like children today, the younger members of Roman civilization would have dressed their dolls according to the latest fashions. In Greece and Rome, it was customary for boys to dedicate their toys to the gods when they reached puberty and for girls to dedicate their toys to the goddesses when they married. Rag dolls are traditionally home-made from spare scraps of cloth material. Roman rag dolls have been found dating back to 300 BC. Traditional dolls are sometimes used as children's playthings, but they may have spiritual and ritual value. There is no defined line between spiritual toys. In some cultures dolls, used in rituals were given to children, they were used in children's education and as carriers of cultural heritage. In other cultures dolls were considered too laden with magical powers to allow children to play with them.
African dolls are used to entertain. Their shape and costume vary according to custom. Dolls are handed down from mother to daughter. Akuaba are wooden ritual fertility dolls from nearby areas; the best known akuaba are those of the Ashanti people, whose akuaba have disc-like heads. Other tribes in the region have their own distinctive style of akuaba. There is a rich history of Japanese dolls dating back to the Dogū figures and Haniwa funerary figures. By the eleventh century, dolls were used as playthings as well as for protection and in religious ceremonies. During Hinamatsuri, the doll festival, hina dolls are displayed; these are made of straw and wood and dressed in elaborate, many-layered textiles. Daruma dolls are white faces without pupils, they represent Bodhidharma, the East Indian who founded Zen, are used as good luck charms. Wooden Kokeshi dolls have no arms or legs, but a large head and cylindrical body, representing little girls; the use of an effigy to perform a spell on someone is documented in African, Native American, European cultures.
Examples of such magical devices include the European poppet and the nkisi or bocio of West and Central Africa. In European folk magic and witchcraft, poppet dolls are used to represent a person for casting spells on that person; the intention is that whatever actions are performed upon the effigy will be transferred to the subject through sympathetic magic. The practice of sticking pins in voodoo dolls have been associated with African-American Hoodoo folk magic. Voodoo dolls are not a feature of Haitian Vodou religion, but have been portrayed as such in popular culture, stereotypical voodoo dolls are sold to tourists in Haiti; the voodoo doll concept in popular culture is influenced by the European poppet dolls. A kitchen witch is a poppet originating in Northern Europe, it resembles a stereotypical witch or crone and is displayed in residential kitchens as a means to provide good luck and ward off bad spirits. Hopi Kachina dolls are effigies made of cottonwood that embody the characteristics of the ceremonial Kachina, the masked spirits of the Hopi Native American tribe.
Kachina dolls are objects meant to be treasured and studied in order to learn the characteristics of each Kachina. Inuit dolls are made out of soapstone and bone, materials common to the Inuit people. Many are clothed with animal skin, their clothing articulates the traditional style of dress necessary to survive cold winters and snow. The tea dolls of the Innu people were filled with tea for young girls to carry on long journeys. Apple dolls are traditional North American dolls with a head made from dried apples. In Inca mythology, Sara Mama was the goddess of grain, she was associated with maize that grew in multiples or was strange. These strange plants were sometimes dressed as dolls of Sara Mama. Corn husk dolls are traditional Native American dolls made out of the dried leaves or husk of a corncob. Traditionally, they do not have a face; the making of corn husk dolls was adopted by early European settlers in the United States. Early settlers made rag dolls and carved wooden dolls, called Pennywoods.
La última muñeca, or "the last doll", is a tradition of the Quinceañera, the celebration of a girl's fifteenth birthday in parts of Latin America. During this ritu
Cube (film)
Cube is a 1997 Canadian science-fiction horror film directed and co-written by Vincenzo Natali. A product of the Canadian Film Centre's First Feature Project, the film follows a group of people as they cross industrialized cube-shaped rooms, some rigged with various traps designed to kill. Cube has gained notoriety and a cult following, for its surreal atmosphere and Kafkaesque setting and concept of industrial, cube-shaped rooms; the film received polarizing reviews, was followed by two sequels. A remake is in development at Lionsgate. After a man named Alderson dies in a mysterious cube-shaped room, five people – Quentin, Holloway and Leaven – meet in another room. None know how they got there. Quentin informs the others. Rennes assumes each trap is triggered by a motion detector and tests each room by throwing one of his boots in first. Leaven notices numbers inscribed in the passageways between rooms. Quentin recognizes Rennes as "The Wren", a convict. After declaring one room trap-free, Rennes is killed when he is sprayed with acid.
The others realize that there are different kinds of detectors, Quentin deduces that this trap was triggered by heat. Quentin believes, he is a police officer, Leaven a mathematics student, Holloway a physician and conspiracy theorist, the surly Worth declines to talk about himself. Leaven hypothesizes, they find a mentally challenged man named Kazan. When Quentin injures his leg in a room deemed safe by Leaven's calculations, tensions rise due to personality conflicts and lack of faith in Leaven's system. Quentin provokes Worth into an argument about finding the exit, Worth accidentally reveals that he has knowledge of the Cube. Worth admits that he designed the Cube's outer shell for a shadowy bureaucracy and guesses that its original purpose has been forgotten. Worth's knowledge of the outer shell's size allows Leaven to determine that each side of the Cube is 26 rooms across and that there are 17,576 rooms in total, she guesses. The group moves toward the nearest edge as determined by her theory, but each of the rooms near the outer wall is trapped.
Rather than backtrack, they travel silently through a room with a sound-activated trap. After Kazan makes a sound and nearly causes Quentin's death, Quentin threatens Kazan. Holloway provokes Quentin into an argument by calling him a Nazi; the acrimonious argument escalates until Quentin slaps her, further increasing tension within the group. When they reach the edge, Holloway scouts the gap between the Cube and its outer shell but slips during a violent quake, he reports it to the others as an accident. Quentin attempts to persuade Leaven to abandon the others with him and makes a sexual advance, but she rejects him; when Quentin becomes aggressive, Worth intervenes. Worth laughs hysterically -- Rennes's corpse; the group is demoralized by the thought of having been wandering in circles. Worth realizes that the rooms move periodically through the Cube, this is the source of the quaking. Leaven deduces that traps are not by powers of prime numbers. Much to Quentin's surprise, Kazan reveals himself to be an autistic savant who can do prime factorizations mentally.
With Kazan's help, Leaven guides them to a bridge room which will lead them out of the maze in two movements. Worth preemptively leaves him behind. Kazan opens the supposed final door, revealing a bright white light, but Worth declines to leave the Cube, as he has lost faith in humanity. Leaven objects and attempts to convince Worth to join her, but Quentin reappears, kills her, mortally wounds Worth; as Quentin moves to kill Kazan, Worth expends the last of his strength to grab Quentin's leg, pinning him in the passageway as the rooms shift again. Quentin is torn apart, Worth crawls back to Leaven's corpse and dies next to her. Kazan walks into the bright light, his ultimate fate unknown. Maurice Dean Wint as Quentin McNeil, a police officer, he is a aggressive man who takes charge and undertakes most of the dangerous tasks. He is said to be in his 40s. Nicole de Boer as Joan Leaven, a young student with mathematical skills, she is said to be in her early 20s. David Hewlett as David Worth, a chronic malcontent and cynic who unwittingly designed the outer shell of the Cube.
He is said to be in late 20s to early 30s. Andrew Miller as Kazan, an autistic man with the ability to and perform prime number calculations, he is said to be in his 20s. Nicky Guadagni as Dr. Helen Holloway, a free clinic doctor and a paranoid conspiracy theorist, she is said to be in her early 50s. Wayne Robson as Rennes known as "the Wren", an escape artist who has gotten out of seven prisons, he is said to be in his early 60s. Julian Richings as a prisoner and a mysterious character, he never met the rest of the group. Each character's name is connected with a real-world prison: An episode of the original The Twilight Zone television series, "Five Characters in Search of an Exit", was an inspiration for the film. Though Vincenzo Natali had the initial inspiration to make a film "set in hell" in 1990, it was not until 1994, when he was working as a storyboard artist's assistant at Canada's Nelvana animat
Cylinder
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on bottom; this traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology. The shift in the basic meaning has created some ambiguity with terminology, it is hoped that context makes the meaning clear. In this article both points of view are presented and distinguished by referring to solid cylinders and cylindrical surfaces, but keep in mind that in the literature the unadorned term cylinder could refer to either of these or to an more specialized object, the right circular cylinder; the definitions and results in this section are taken from the 1913 text and Solid Geometry by George Wentworth and David Eugene Smith. A cylindrical surface is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line.
Any line in this family of parallel lines is called an element of the cylindrical surface. From a kinematics point of view, given a plane curve, called the directrix, a cylindrical surface is that surface traced out by a line, called the generatrix, not in the plane of the directrix, moving parallel to itself and always passing through the directrix. Any particular position of the generatrix is an element of the cylindrical surface. A solid bounded by a cylindrical surface and two parallel planes is called a cylinder; the line segments determined by an element of the cylindrical surface between the two parallel planes is called an element of the cylinder. All the elements of a cylinder have equal lengths; the region bounded by the cylindrical surface in either of the parallel planes is called a base of the cylinder. The two bases of a cylinder are congruent figures. If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder.
If the bases are disks the cylinder is called a circular cylinder. In some elementary treatments, a cylinder always means a circular cylinder; the height of a cylinder is the perpendicular distance between its bases. The cylinder obtained by rotating a line segment about a fixed line that it is parallel to is a cylinder of revolution. A cylinder of revolution is a right circular cylinder; the height of a cylinder of revolution is the length of the generating line segment. The line that the segment is revolved about is called the axis of the cylinder and it passes through the centers of the two bases; the bare term cylinder refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in the figure. The cylindrical surface without the ends is called an open cylinder; the formulae for the surface area and the volume of a right circular cylinder have been known from early antiquity. A right circular cylinder can be thought of as the solid of revolution generated by rotating a rectangle about one of its sides.
These cylinders are used in an integration technique for obtaining volumes of solids of revolution. A cylindric section is the intersection of a cylinder's surface with a plane, they are, in general and are special types of plane sections. The cylindric section by a plane that contains two elements of a cylinder is a parallelogram; such a cylindric section of a right cylinder is a rectangle. A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a right section. If a right section of a cylinder is a circle the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a conic section the solid cylinder is said to be parabolic, elliptic or hyperbolic respectively. For a right circular cylinder, there are several ways. First, consider planes that intersect a base in at most one point. A plane is tangent to the cylinder; the right sections are circles and all other planes intersect the cylindrical surface in an ellipse.
If a plane intersects a base of the cylinder in two points the line segment joining these points is part of the cylindric section. If such a plane contains two elements, it has a rectangle as a cylindric section, otherwise the sides of the cylindric section are portions of an ellipse. If a plane contains more than two points of a base, it contains the entire base and the cylindric section is a circle. In the case of a right circular cylinder with a cylindric section, an ellipse, the eccentricity e of the cylindric section and semi-major axis a of the cylindric section depend on the radius of the cylinder r and the angle α between the secant plane and cylinder axis, in the following way: e = cos α, a = r sin α. If the base of a circular cylinder has a radius r and the cylinder has height h its volume is given by V = πr2h; this formula holds. This formula may be established by using Cavalieri's principle. In more generality, by the same principle, the volume of an
