Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle. The word "diameter" derives from Greek διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure"^[1]).

In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. See also Tangent lines to circles.

Generalizations[link]

The four definitions given above are special cases of a more general definition. The diameter of a subset of a metric space is the least upper bound of the distances between pairs of points in the subset. So, if A is the subset, the diameter is

sup { d(x, y) | x, y ∈ A } .

Some authors prefer to treat the empty set (Failed to parse (Missing texvc executable; please see math/README to configure.): A=\emptyset ) as a special case.^[2]

In differential geometry, the diameter is an important global Riemannian invariant. In plane and coordinate geometry, a diameter of a conic section is any chord which passes through the conic's centre; such diameters are not necessarily of uniform length, except in the case of the circle, which has eccentricity e = 0.

In medical parlance the diameter of a lesion is the longest line segment whose endpoints are within the lesion.

Diameter symbol[link]

The symbol or variable for diameter, ⌀, is similar in size and design to ø, the Latin small letter o with stroke. Unicode provides character number 8960 (hexadecimal 2300) for the symbol, which can be encoded in HTML webpages as ⌀ or ⌀. The character can be obtained in Microsoft Windows by holding the Alt key down while entering 8960 on the numeric keypad. On an Apple Macintosh, the diameter symbol can be entered via the character palette (this is opened by pressing ⌥ Opt⌘ CmdT in most applications), where it can be found in the Technical Symbols category.

The character often will not display correctly, however, since most fonts do not include it. In most situations the letter ø is acceptable, which is unicode 0248 (hexadecimal 00F8). It can be obtained in UNIX-like operating systems using a Compose key by pressing, in sequence, Compose/o and on a Macintosh by pressing ⌥ Opt O (in both cases, that is the letter o, not the number 0).

In LaTeX the symbol is achieved with the command \diameter which is part of the wasysym package.

The diameter symbol ⌀ is distinct from the empty set symbol ∅, from an (italic) uppercase phi Φ, and from the Nordic vowel Ø.^[3]

See also[link]

• Graph or network diameter
• Angular diameter
• Hydraulic diameter
• Caliper, micrometer, tools for measuring diameters
• Eratosthenes, who calculated the diameter of the Earth around 240 BC.
• Jung's theorem, an inequality relating the diameter to the radius of the smallest enclosing ball
• Sauter mean diameter
• Inside diameter

Notes[link]

Roy Lichtenstein (October 27, 1923 – September 29, 1997) was a prominent American pop artist. During the 1960s, his paintings were exhibited at the Leo Castelli Gallery in New York City and along with Andy Warhol, Jasper Johns, James Rosenquist and others he became a leading figure in the new art movement. His work defined the basic premise of pop art better than any other through parody.^[2] Favoring the old-fashioned comic strip as subject matter, Lichtenstein produced hard-edged, precise compositions that documented while it parodied often in a tongue-in-cheek humorous manner. His work was heavily influenced by both popular advertising and the comic book style. He described Pop Art as, "not 'American' painting but actually industrial painting".^[3]

Early years[link]

Roy Lichtenstein was born in New York into an upper-middle-class Jewish New York City^[1] family and attended public school until the age of 12. He then enrolled at New York's Franklin School for Boys, remaining there for his secondary education. Lichtenstein first became interested in art and design as a hobby, and through school.^[4] He was an avid jazz fan, often attending concerts at the Apollo Theater in Harlem.^[4] He frequently drew portraits of the musicians playing their instruments.^[4] After graduation from Franklin, Lichtenstein enrolled in summer classes at the Art Students League of New York, where he worked under the tutelage of Reginald Marsh.^[5]

Lichtenstein then left New York to study at the Ohio State University, which offered studio courses and a degree in fine arts.^[1] His studies were interrupted by a three-year stint in the army during and after World War II between 1943 and 1946.^[1] After being in training programs for languages, engineering, and pilot training; all of which were cancelled, he served as an orderly, draftsman, and artist.^[1] Lichtenstein returned home to visit his dying father and was discharged from the army with eligibility for the G.I. Bill.^[4] He returned to studies in Ohio under the supervision of one of his teachers, Hoyt L. Sherman, who is widely regarded to have had a significant impact on his future work (Lichtenstein would later name a new studio he funded at OSU as the Hoyt L. Sherman Studio Art Center).^[6] Lichtenstein entered the graduate program at Ohio State and was hired as an art instructor, a post he held on and off for the next ten years. In 1949 Lichtenstein received a M.F.A. degree from the Ohio State University and in the same year married Isabel Wilson (divorced in 1965) who was previously married to Ohio artist Michael Sarisky.^[7] In 1951 Lichtenstein had his first one-man exhibition at the Carlebach Gallery in New York.^[1][8] He moved to Cleveland in the same year, where he remained for six years, although he frequently traveled back to New York. During this time he undertook jobs as varied as a draftsman to a window decorator in between periods of painting.^[1] His work at this time fluctuated between Cubism and Expressionism.^[4] In 1954, his first son, David Hoyt Lichtenstein, now a songwriter, was born. He then had his second son, Mitchell Lichtenstein in 1956.^[9] In 1957, he moved back to upstate New York and began teaching again.^[3] It was at this time that he adopted the Abstract Expressionism style, a late convert to this style of painting.^[10] Lichtenstein began teaching in upstate New York at the State University of New York at Oswego in 1958. However, the brutal upstate winters were taking a toll on him and his wife.^[11] He married his second wife, Dorothy Herzka in 1968.^[12] From 1970 until his death, Lichtenstein split his time between New York city and a house near the beach in Southampton.^[13]

Rise to fame[link]

In 1960, he started teaching at Rutgers University where he was heavily influenced by Allan Kaprow, who was also a teacher at the University. This environment helped reignite his interest in Proto-pop imagery.^[1] In 1961, Lichtenstein began his first pop paintings using cartoon images and techniques derived from the appearance of commercial printing. This phase would continue to 1965, and included the use of advertising imagery suggesting consumerism and homemaking.^[4] His first work to feature the large-scale use of hard-edged figures and Ben-Day dots was Look Mickey (1961, National Gallery of Art, Washington, D.C.).^[14] This piece came from a challenge from one of his sons, who pointed to a Mickey Mouse comic book and said; "I bet you can't paint as good as that, eh, Dad?"^[15] In the same year he produced six other works with recognizable characters from gum wrappers and cartoons.^[16] In 1961, Leo Castelli started displaying Lichtenstein's work at his gallery in New York. Lichtenstein had his first one-man show at the Castelli gallery in 1962; the entire collection was bought by influential collectors before the show even opened.^[1] A group of paintings produced between 1961-1962 focussed on solitary household objects such as sneakers, hot dogs, and golf balls.^[17] In September 1963 he took a leave of absence from his teaching position at Douglass College at Rutgers.^[18]

Fame[link]

It was at this time, that Lichtenstein began to find fame not just in America but worldwide. He moved back to New York to be at the center of the art scene and resigned from Rutgers University in 1964 to concentrate on his painting.^[19] Lichtenstein used oil and Magna paint in his best known works, such as Drowning Girl (1963), which was appropriated from the lead story in DC Comics' Secret Hearts #83. (Drowning Girl now hangs in the Museum of Modern Art, New York.^[20]) Also featuring thick outlines, bold colors and Ben-Day dots to represent certain colors, as if created by photographic reproduction. Lichtenstein would say of his own work: Abstract Expressionists "put things down on the canvas and responded to what they had done, to the color positions and sizes. My style looks completely different, but the nature of putting down lines pretty much is the same; mine just don't come out looking calligraphic, like Pollock's or Kline's."^[21]

Rather than attempt to reproduce his subjects, his work tackled the way mass media portrays them. Lichtenstein would never take himself too seriously however: "I think my work is different from comic strips- but I wouldn't call it transformation; I don't think that whatever is meant by it is important to art".^[22] When his work was first released, many art critics of the time challenged its originality. His work was harshly criticized as vulgar and empty. The title of a Life magazine article in 1964 asked, “Is He the Worst Artist in the U.S.?”^[23] Lichtenstein responded to such claims by offering responses such as the following: "The closer my work is to the original, the more threatening and critical the content. However, my work is entirely transformed in that my purpose and perception are entirely different. I think my paintings are critically transformed, but it would be difficult to prove it by any rational line of argument".^[24] He discussed experiencing this heavy criticism in interview with April Bernard and Mimi Thompson in 1986. Suggesting that it was at times difficult to be criticized, Lichtenstein said, “I don’t doubt when I’m actually painting, it’s the criticism that makes you wonder, it does.”^[25]

In the early 1960s, Lichtenstein reproduced masterpieces by Cézanne, Mondrian and Picasso before embarking on the Brushstroke series in 1965.^[26] Lichtenstein continued to revisit this theme later in his career with works such as Bedroom at Arles that derived from Vincent van Gogh's Bedroom in Arles.

His most famous image is arguably Whaam! (1963, Tate Modern, London^[27]), one of the earliest known examples of pop art, adapted a comic-book panel from a 1962 issue of DC Comics' All-American Men of War.^[28] The painting depicts a fighter aircraft firing a rocket into an enemy plane, with a red-and-yellow explosion. The cartoon style is heightened by the use of the onomatopoeic lettering "Whaam!" and the boxed caption "I pressed the fire control... and ahead of me rockets blazed through the sky..." This diptych is large in scale, measuring 1.7 x 4.0 m (5 ft 7 in x 13 ft 4 in).^[27]

Lichtenstein began experimenting with sculpture around 1964, demonstrating a knack for the form that was at odds with the insistent flatness of his paintings. For Head of Girl (1964), and Head with Red Shadow (1965), he collaborated with a ceramicist who sculpted the form of the head out of clay. Lichtenstein then applied a glaze to create the same sort of graphic motifs that he used in his paintings; the application of black lines and Ben-day dots to three-dimensional objects resulted in a flattening of the form^[29]

Most of his best-known artworks are relatively close, but not exact, copies of comic book panels, a subject he largely abandoned in 1965. (He would occasionally incorporate comics into his work in different ways in later decades.) These panels were originally drawn by such comics artists as Jack Kirby and DC Comics artists Russ Heath, Tony Abruzzo, Irv Novick, and Jerry Grandenetti, who rarely received any credit. Jack Cowart, executive director of the Lichtenstein Foundation, contests the notion that Lichtenstein was a copyist, saying: "Roy's work was a wonderment of the graphic formulae and the codification of sentiment that had been worked out by others. The panels were changed in scale, color, treatment, and in their implications. There is no exact copy."^[30] However, some^[31] have been critical of Lichtenstein's use of comic-book imagery and art pieces, especially insofar as that use has been seen as endorsement of a patronizing view of comics by the art mainstream;^[31] noted comics author Art Spiegelman commented that "Lichtenstein did no more or less for comics than Andy Warhol did for soup."^[31]

In 1966, Lichtenstein moved on from his much-celebrated imagery of the early 1960s, and began his Modern Paintings series, including over 60 paintings and accompanying drawings. Using his characteristic Ben Day dots and geometric shapes and lines, he rendered incongruous, challenging images out of familiar architectural structures, patterns borrowed from Art Déco and other subtly evocative, often sequential, motifs.^[32] The Modern Sculpture series of 1967–8 made reference to motifs from Art Déco architecture.^[33]

Later work[link]

In 1970, Lichtenstein was commissioned by the Los Angeles County Museum of Art (within its Art and Technology program developed between 1967 and 1971) to make a film. With the help of Universal Film Studios, the artist conceived of, and produced, Three Landscapes, a film of marine landscapes, directly related to a series of collages with landscape themes he created between 1964 and 1966.^[34] Although Lichtenstein had planned on producing 15 short films, the three-screen installation — made with New York-based independent filmmaker Joel Freedman — turned out to be the artist's only venture into the medium.^[35]

In the 1970s and 1980s, Lichtenstein's style began to loosen and he expanded on what he had done before. Lichtenstein began a series of Mirrors paintings in 1969. By 1970, while continuing on the Mirrors series, he started work on the subject of entablatures. The Entablatures consisted of a first series of paintings from 1971-72, followed by a second series in 1974-76, and the publication of a series of relief prints in 1976.^[36] He produced a series of "Artists Studios" which incorporated elements of his previous work. A notable example being Artist's Studio, Look Mickey (1973, Walker Art Center, Minneapolis) which incorporates five other previous works, fitted into the scene.^[1]

In the late 1970s, this style was replaced with more surreal works such as Pow Wow (1979, Ludwig Forum für Internationale Kunst, Aachen). A major series of Surrealist-Pop paintings from 1979–81 is based on Native American themes.^[37] These works range Amerind Figure (1981), a stylized life-size sculpture reminiscent of a streamlined totem pole in black-patinated bronze, to the monumental wool tapestry Amerind Landscape (1979). The "Indian" works took their themes, like the other parts of the Surrealist series, from contemporary art and other sources, including books on American Indian design from Lichtenstein's small library.^[38]

Lichtenstein's Still Life paintings, sculptures and drawings, which span from 1972 through the early 1980s, cover a variety of motifs and themes, including the most traditional such as fruit, flowers, and vases.^[39] In his Reflection series, produced between 1988 and 1990, Lichtenstein reused his own motifs from previous works.^[40] Interiors (1991-1992) is a series of works depicting banal domestic environments inspired by furniture ads the artist found in telephone books or on billboards.^[41] Having garnered inspiration from the monochromatic prints of Edgar Degas featured in a 1994 exhibition at the Metropolitan Museum of Art in New York, the motifs of his Landscapes in the Chinese Style series are formed with simulated Benday dots and block contours, rendered in hard, vivid color, with all traces of the hand removed.^[42] The nude is a recurring element in Lichtenstein's work of the 1990s, such as in Collage for Nude with Red Shirt (1995).

In addition to paintings and sculptures, Lichtenstein also made over 300 prints, mostly in screenprinting.^[43]

He died of pneumonia in 1997^[15] at New York University Medical Center. He was survived by his second wife, Dorothy, and by his sons, David and Mitchell, from his first marriage.

Commissions[link]

In 1969, Lichtenstein was commissioned by Gunter Sachs to create Composition and Leda and the Swan, for the collector's famous Pop Art bedroom suite at the Palace Hotel in Sankt Moritz. In the late 1970s and during the 1980s, Lichtenstein received major commissions for works in public places: the sculptures Lamp (1978) in St. Mary’s, Georgia; Mermaid (1979) in Miami Beach; the 26 feet tall Brushstrokes in Flight (1984, moved in 1998) at Port Columbus International Airport; the five-storey high Mural with Blue Brushstrokes (1984–85) at the Equitable Center, New York; and El Cap de Barcelona (1992) in Barcelona.^[33] In 1994, Lichtenstein created the 53-foot-long, enamel-on-metal Times Square Mural that now hovers over pedestrians in the Times Square subway station.^[44] In 1977, he was commissioned by BMW to paint a Group 5 Racing Version of the BMW 320i for the third installment in the BMW Art Car Project. The DreamWorks Records logo was his last completed project.^[1] "I'm not in the business of doing anything like that (a corporate logo) and don't intend to do it again," allows Lichtenstein. "But I know Mo Ostin and David Geffen and it seemed interesting."^[45]

Relevance[link]

Pop art continues to influence the 21st century. Lichtenstein and Andy Warhol were used in U2's 1997, 1998 PopMart Tour and in an exhibition in 2007 at the British National Portrait Gallery.

Among many other works of art destroyed in the World Trade Center attacks on September 11, 2001, a painting from Lichtenstein’s The Entablature Series was destroyed in the subsequent fire.^[46]

His work Crying Girl was one of the artworks brought to life in Night at the Museum: Battle of the Smithsonian.

Exhibitions[link]

In 1964, Lichtenstein became the first American to exhibit at the Tate Gallery, London, on the occasion of the show "'54–'64: Painting and Sculpture of a Decade". In 1967, his first museum retrospective exhibition was held at the Pasadena Art Museum in California. Also in this year, his first solo exhibition in Europe was held at museums in Amsterdam, London, Bern and Hannover.^[7] Lichtenstein later participated in documentas IV (1968) and VI in (1977). Lichtenstein had his first retrospective at the Guggenheim Museum in 1969, organized by Diane Waldman. The Guggenheim presented a second Lichtenstein retrospective in 1994.^[36] Lichtenstein became the first living artist to have a solo drawing exhibitions at the Museum of Modern Art from March – June 1987.^[47] Recent retrospective surveys include "All About Art," Louisiana Museum, Humelbaek (2003, traveled to the Hayward Gallery, London, Museo Reina Sofia, Madrid, and the San Francisco Museum of Modern Art through 2005); and "Classic of the New", Kunsthaus Bregenz (2005), "Roy Lichtenstein: Meditations on Art" Museo Triennale, Milan (2010, traveled to the Museum Ludwig, Cologne). In late 2010 The Morgan Library & Museum showed Roy Lichtenstein: The Black-and-White Drawings, 1961–1968.^[48] Another major retrospective will open at the Art Institute of Chicago in May 2012 before going to the National Gallery of Art in Washington, Tate Modern in London, and the Centre Pompidou in Paris in 2013.^[49]

Collections[link]

In 1996 the National Gallery of Art in Washington, D.C. became the largest single repository of the artist's work when Lichtenstein donated 154 prints and 2 books. The Art Institute of Chicago has several important works by Lichtenstein in its permanent collection, including Brushstroke with Spatter (1966) and Mirror No. 3 (Six Panels) (1971). In Europe, the Museum Ludwig has one of the most comprehensive Lichtenstein holdings. In total there are some 4,500 works thought to be in circulation.^[1]

Recognition[link]

• 1995 National Medal of the Arts, Washington D.C.
• 1995 Kyoto Prize, Inamori Foundation, Kyoto, Japan.
• 1993 Amici de Barcelona, from Mayor Pasqual Maragall, L’Alcalde de Barcelona.
• 1991 Creative Arts Award in Painting, Brandeis University, Waltham, Massachusetts.
• 1989 American Academy in Rome, Rome, Italy. Artist in residence.
• 1979 American Academy of Arts and Letters, New York.
• 1977 Skowhegan Medal for Painting, Skowhegan School, Skowhegan, Maine.

Lichtenstein received numerous Honorary Doctorate degrees from, among others, the George Washington University (1996), Ohio State University (1987), Southampton College (1980), and the California Institute of the Arts (1977).

Art market[link]

Since the 1950s Lichtenstein's work has been exhibited in New York and elsewhere with Leo Castelli at his gallery and at Castelli Graphics as well as with Ileana Sonnabend in her gallery in Paris, and at the Ferus Gallery, Pace Gallery, Gagosian Gallery, Mitchell-Innes & Nash, Mary Boone, Brooke Alexander, Carlebach, Rosa Esman, Marilyn Pearl, James Goodman, John Heller, Blum Helman, Hirschl & Adler, Phyllis Kind, Getler Pall, Condon Riley, 65 Thompson Street, Holly Solomon, and Sperone Westwater Galleries among others.

Beginning in 1962, the Leo Castelli Gallery, New York, held regular exhibitions of the artist’s work.^[60] Gagosian Gallery has been exhibiting work by Lichtenstein since 1996.^[61]

Big Painting No. 6 (1965) became the highest priced Lichtenstein work in 1970.^[50] Like the entire Brushstrokes series, the subject of the painting is the process of Abstract Expressionist painting via sweeping brushstrokes and drips, but the result of Lichtenstein's simplification that uses a Ben-Day dots background is a representation of the mechanical/industrial color printing reproduction.^[62]

Lichtenstein's painting Torpedo...Los! (1963) sold at Christie's for $5.5 million in 1989, a record sum at the time, making him one of only three living artists to have attracted such huge sums.^[7] In 2005, In the Car was sold for a then record $16.2m (£10m).

In 2010, his cartoon-style 1964 painting Ohhh...Alright..., previously owned by Steve Martin and later by Steve Wynn,^[63] was sold at a record US $42.6m (£26.7m) at a sale at Christies in New York.^[56][64]

Based on a 1961 William Overgard drawing for a Steve Roper cartoon story^[65], Lichtenstein’s I Can See the Whole Room!...and There's Nobody in It! (1961) depicts a man looking through a hole in a door. It was sold by collector Courtney Sale Ross for $43 million, double its estimate, at Christie's in New York City in 2011; the seller's husband, Steve Ross had acquired it at auction in 1988 for $2.1 million.^[57] The painting measures four-foot by four-foot and is in graphite and oil.^[66]

In 2012, the comic painting Sleeping Girl (1964) from the collection of Beatrice and Phillip Gersh established a new Lichtenstein record $44.8 million at Sotheby's.^[58][59]

References[link]

Citations

Bibliography

Further reading[link]

• Roy Lichtenstein Interview with Chris Hunt Image Entertainment video, 1991
• Roy Lichtenstein Interview with Melvyn Bragg video
• Adelman, Bob (1999). Roy Lichtenstein's ABC's. Boston: Bulfinch Press. ISBN 978-0-8212-2591-2. 
• Waldman, Diane (1988) [1st Pub. 1970]. Roy Lichtenstein : Drawing and Prints. Secaucus, N.J.: Wellfleet Books. ISBN 9781555213015. 

External links[link]

Biography portal

Wikiquote has a collection of quotations related to: Roy Lichtenstein

Wikimedia Commons has media related to: Roy Lichtenstein

• Roy Lichtenstein Foundation
• Roy Lichtenstein at the Museum of Modern Art
• Roy Lichtenstein Image Duplicator
• Deconstructing Roy Lichtenstein (sources for Lichtenstein's comic-book paintings)
• Inside Roy Lichtenstein's Studio 1990–92
• Roy Lichtenstein at Find a Grave
• Roy Lichtenstein – slideshow by The New York Times
• 1977 BMW 320i with special paintjob by Roy Lichtenstein
• Roy Lichtenstein's public artwork at Times Square-42nd Street, commissioned by MTA Arts for Transit.
• Roy Lichtenstein: Pop Art's Most Popular; His Whimsical Paintings Once Evoked the "Shock of the New"; Now They Evoke Record Prices on the Auction Block
• Roy Lichtenstein in the National Gallery of Australia's Kenneth Tyler collection