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75-424: A whorl ( / w ɜːr l / or / w ɔːr l / ) is an individual circle , oval , volution or equivalent in a whorled pattern , which consists of a spiral or multiple concentric objects (including circles , ovals and arcs ). For mollusc whorls , the body whorl in a mollusc shell is the most recently formed whorl of a spiral shell, terminating in the aperture. This geometry-related article

150-412: A 2 − r 0 2 sin 2 ⁡ ( θ − ϕ ) . {\displaystyle r=r_{0}\cos(\theta -\phi )\pm {\sqrt {a^{2}-r_{0}^{2}\sin ^{2}(\theta -\phi )}}.} Without the ± sign, the equation would in some cases describe only half a circle. In the complex plane , a circle with a centre at c and radius r has

225-570: A ) ( x − a ) + ( y 1 − b ) ( y − b ) = r 2 . {\displaystyle (x_{1}-a)(x-a)+(y_{1}-b)(y-b)=r^{2}.} If y 1 ≠ b , then the slope of this line is d y d x = − x 1 − a y 1 − b . {\displaystyle {\frac {dy}{dx}}=-{\frac {x_{1}-a}{y_{1}-b}}.} This can also be found using implicit differentiation . When

300-853: A Circle (1911); František Kupka had painted the Orphist works, Discs of Newton (Study for Fugue in Two Colors ), 1912 and Amorpha, Fugue en deux couleurs ( Fugue in Two Colors ), 1912; Robert Delaunay painted a series entitled Simultaneous Windows and Formes Circulaires, Soleil n°2 (1912–13); Léopold Survage created Colored Rhythm (Study for the film), 1913; Piet Mondrian , painted Tableau No. 1 and Composition No. 11 , 1913. With his expressive use of color and his free and imaginative drawing Henri Matisse comes very close to pure abstraction in French Window at Collioure (1914), View of Notre-Dame (1914), and The Yellow Curtain from 1915. And

375-507: A basis for a diversity of modes of abstraction. The following extract from The World Backwards gives some impression of the inter-connectedness of culture at the time: " David Burliuk 's knowledge of modern art movements must have been extremely up-to-date, for the second Knave of Diamonds exhibition , held in January 1912 (in Moscow) included not only paintings sent from Munich, but some members of

450-407: A certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre. In Plato 's Seventh Letter there is a detailed definition and explanation of the circle. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation. Early science , particularly geometry and astrology and astronomy ,

525-551: A chord, between the midpoint of that chord and the arc of the circle. Given the length y of a chord and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle that will fit around the two lines: r = y 2 8 x + x 2 . {\displaystyle r={\frac {y^{2}}{8x}}+{\frac {x}{2}}.} Another proof of this result, which relies only on two chord properties given above,

600-480: A compass, a halo, the vesica piscis and its derivatives (fish, eye, aureole, mandorla, etc.), the ouroboros, the Dharma wheel , a rainbow, mandalas, rose windows and so forth. Magic circles are part of some traditions of Western esotericism . The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius

675-433: A concept (she organized an exhibit in 1871). Expressionist painters explored the bold use of paint surface, drawing distortions and exaggerations, and intense color. Expressionists produced emotionally charged paintings that were reactions to and perceptions of contemporary experience; and reactions to Impressionism and other more conservative directions of late 19th-century painting. The Expressionists drastically changed

750-715: A few directions relating to abstraction in the second half of the 20th century. In the United States, Art as Object as seen in the Minimalist sculpture of Donald Judd and the paintings of Frank Stella are seen today as newer permutations. Other examples include Lyrical Abstraction and the sensuous use of color seen in the work of painters as diverse as Robert Motherwell , Patrick Heron , Kenneth Noland , Sam Francis , Cy Twombly , Richard Diebenkorn , Helen Frankenthaler , Joan Mitchell , and Veronica Ruiz de Velasco . One socio-historical explanation that has been offered for

825-799: A few of the exiled Europeans who arrived in New York. The rich cultural influences brought by the European artists were distilled and built upon by local New York painters. The climate of freedom in New York allowed all of these influences to flourish. The art galleries that primarily had focused on European art began to notice the local art community and the work of younger American artists who had begun to mature. Certain artists at this time became distinctly abstract in their mature work. During this period Piet Mondrian's painting Composition No. 10 , 1939–1942, characterized by primary colors, white ground and black grid lines clearly defined his radical but classical approach to

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900-459: A generalised circle is either a (true) circle or a line . The tangent line through a point P on the circle is perpendicular to the diameter passing through P . If P = ( x 1 , y 1 ) and the circle has centre ( a , b ) and radius r , then the tangent line is perpendicular to the line from ( a , b ) to ( x 1 , y 1 ), so it has the form ( x 1 − a ) x + ( y 1 – b ) y = c . Evaluating at ( x 1 , y 1 ) determines

975-500: A manifesto defining an abstract art in which the line, color and surface only are the concrete reality. Abstraction-Création founded in 1931 as a more open group, provided a point of reference for abstract artists, as the political situation worsened in 1935, and artists again regrouped, many in London. The first exhibition of British abstract art was held in England in 1935. The following year

1050-457: A new art had been made by James McNeill Whistler who, in his painting Nocturne in Black and Gold: The Falling Rocket , (1872), placed greater emphasis on visual sensation than the depiction of objects. Even earlier than that, with her "spirit" drawings, Georgiana Houghton 's choice to work with abstract shapes correlate with the unnatural nature of her subject, in a time when abstraction was not yet

1125-448: A region of the plane called a disc . The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel , which, with related inventions such as gears , makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus . All of

1200-407: A technician, learning to use the tools and materials of modern production. Art into life! was Vladimir Tatlin 's slogan, and that of all the future Constructivists. Varvara Stepanova and Alexandre Exter and others abandoned easel painting and diverted their energies to theatre design and graphic works. On the other side stood Kazimir Malevich , Anton Pevsner and Naum Gabo . They argued that art

1275-558: A view from a single point, with modulated color in flat areas – became the basis of a new visual art, later to be developed into Cubism . Additionally in the late 19th century in Eastern Europe mysticism and early modernist religious philosophy as expressed by theosophist Mme. Blavatsky had a profound impact on pioneer geometric artists like Hilma af Klint and Wassily Kandinsky . The mystical teaching of Georges Gurdjieff and P.D. Ouspensky also had an important influence on

1350-409: Is 2 π . Thus the circumference C is related to the radius r and diameter d by: C = 2 π r = π d . {\displaystyle C=2\pi r=\pi d.} As proved by Archimedes , in his Measurement of a Circle , the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals

1425-421: Is a stub . You can help Misplaced Pages by expanding it . Circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre . The distance between any point of the circle and the centre is called the radius . The length of a line segment connecting two points on the circle and passing through the centre is called the diameter . A circle bounds

1500-414: Is as follows. Given a chord of length y and with sagitta of length x , since the sagitta intersects the midpoint of the chord, we know that it is a part of a diameter of the circle. Since the diameter is twice the radius, the "missing" part of the diameter is ( 2 r − x ) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting

1575-575: Is impossible. Artwork which takes liberties, e.g. altering color or form in ways that are conspicuous, can be said to be partially abstract. Total abstraction bears no trace of any reference to anything recognizable. In geometric abstraction , for instance, one is unlikely to find references to naturalistic entities. Figurative art and total abstraction are almost mutually exclusive . But figurative and representational (or realistic ) art often contain partial abstraction. Both geometric abstraction and lyrical abstraction are often totally abstract. Among

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1650-735: Is sometimes called a generalised circle . This becomes the above equation for a circle with p = 1 ,   g = − c ¯ ,   q = r 2 − | c | 2 {\displaystyle p=1,\ g=-{\overline {c}},\ q=r^{2}-|c|^{2}} , since | z − c | 2 = z z ¯ − c ¯ z − c z ¯ + c c ¯ {\displaystyle |z-c|^{2}=z{\overline {z}}-{\overline {c}}z-c{\overline {z}}+c{\overline {c}}} . Not all generalised circles are actually circles:

1725-1307: The ⁠ x {\displaystyle x} ⁠ – ⁠ y {\displaystyle y} ⁠ plane can be broken into two semicircles each of which is the graph of a function , ⁠ y + ( x ) {\displaystyle y_{+}(x)} ⁠ and ⁠ y − ( x ) {\displaystyle y_{-}(x)} ⁠ , respectively: y + ( x ) = y 0 + r 2 − ( x − x 0 ) 2 , y − ( x ) = y 0 − r 2 − ( x − x 0 ) 2 , {\displaystyle {\begin{aligned}y_{+}(x)=y_{0}+{\sqrt {r^{2}-(x-x_{0})^{2}}},\\[5mu]y_{-}(x)=y_{0}-{\sqrt {r^{2}-(x-x_{0})^{2}}},\end{aligned}}} for values of ⁠ x {\displaystyle x} ⁠ ranging from ⁠ x 0 − r {\displaystyle x_{0}-r} ⁠ to ⁠ x 0 + r {\displaystyle x_{0}+r} ⁠ . The equation can be written in parametric form using

1800-654: The Abstract expressionists and the New York School . In New York City there was an atmosphere which encouraged discussion and there was a new opportunity for learning and growing. Artists and teachers John D. Graham and Hans Hofmann became important bridge figures between the newly arrived European Modernists and the younger American artists coming of age. Mark Rothko , born in Russia, began with strongly surrealist imagery which later dissolved into his powerful color compositions of

1875-456: The Bauhaus . By the mid-1920s the revolutionary period (1917 to 1921) when artists had been free to experiment was over; and by the 1930s only socialist realism was allowed. As visual art becomes more abstract, it develops some characteristics of music : an art form which uses the abstract elements of sound and divisions of time. Wassily Kandinsky , himself an amateur musician, was inspired by

1950-505: The Nebra sky disc and jade discs called Bi . The Egyptian Rhind papyrus , dated to 1700 BCE, gives a method to find the area of a circle. The result corresponds to ⁠ 256 / 81 ⁠ (3.16049...) as an approximate value of π . Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from

2025-501: The Renaissance up to the middle of the 19th century, underpinned by the logic of perspective and an attempt to reproduce an illusion of visible reality. By the end of the 19th century many artists felt a need to create a new kind of art which would encompass the fundamental changes taking place in technology , science and philosophy . The sources from which individual artists drew their theoretical arguments were diverse, and reflected

2100-555: The angle that the ray from ( a ,  b ) to ( x ,  y ) makes with the positive x  axis. An alternative parametrisation of the circle is x = a + r 1 − t 2 1 + t 2 , y = b + r 2 t 1 + t 2 . {\displaystyle {\begin{aligned}x&=a+r{\frac {1-t^{2}}{1+t^{2}}},\\y&=b+r{\frac {2t}{1+t^{2}}}.\end{aligned}}} In this parameterisation,

2175-493: The circular points at infinity . In polar coordinates , the equation of a circle is r 2 − 2 r r 0 cos ⁡ ( θ − ϕ ) + r 0 2 = a 2 , {\displaystyle r^{2}-2rr_{0}\cos(\theta -\phi )+r_{0}^{2}=a^{2},} where a is the radius of the circle, ( r , θ ) {\displaystyle (r,\theta )} are

2250-401: The circumscribing square (whose side is of length d ). The circle is the plane curve enclosing the maximum area for a given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality . If a circle of radius r is centred at the vertex of an angle , and that angle intercepts an arc of the circle with an arc length of s , then

2325-741: The equation of the circle , follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the radius is the hypotenuse of a right-angled triangle whose other sides are of length | x − a | and | y − b |. If the circle is centred at the origin (0, 0), then the equation simplifies to x 2 + y 2 = r 2 . {\displaystyle x^{2}+y^{2}=r^{2}.} The circle of radius ⁠ r {\displaystyle r} ⁠ with center at ⁠ ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} ⁠ in

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2400-451: The radian measure 𝜃 of the angle is the ratio of the arc length to the radius: θ = s r . {\displaystyle \theta ={\frac {s}{r}}.} The circular arc is said to subtend the angle, known as the central angle , at the centre of the circle. The angle subtended by a complete circle at its centre is a complete angle , which measures 2 π radians, 360 degrees , or one turn . Using radians,

2475-401: The trigonometric functions sine and cosine as x = a + r cos ⁡ t , y = b + r sin ⁡ t , {\displaystyle {\begin{aligned}x&=a+r\,\cos t,\\y&=b+r\,\sin t,\end{aligned}}} where t is a parametric variable in the range 0 to 2 π , interpreted geometrically as

2550-565: The Bauhaus went to America. During the 1930s Paris became the host to artists from Russia, Germany, the Netherlands and other European countries affected by the rise of totalitarianism . Sophie Tauber and Jean Arp collaborated on paintings and sculpture using organic/geometric forms. The Polish Katarzyna Kobro applied mathematically based ideas to sculpture. The many types of abstraction now in close proximity led to attempts by artists to analyse

2625-628: The German Die Brücke group, while from Paris came work by Robert Delaunay , Henri Matisse and Fernand Léger , as well as Picasso. During the Spring David Burliuk gave two lectures on cubism and planned a polemical publication, which the Knave of Diamonds was to finance. He went abroad in May and came back determined to rival the almanac Der Blaue Reiter which had emerged from the printers while he

2700-527: The Paris art world with "wild", multi-colored, expressive landscapes and figure paintings that the critics called Fauvism . The raw language of color as developed by the Fauves directly influenced another pioneer of abstraction, Wassily Kandinsky . Cubism , based on Cézanne's idea that all depiction of nature can be reduced to cube , sphere and cone became, along with Fauvism , the art movement that directly opened

2775-538: The ancient wisdom of the sacred books of India and China in the early years of the century. It was in this context that Piet Mondrian , Wassily Kandinsky, Hilma af Klint and other artists working towards an 'objectless state' became interested in the occult as a way of creating an 'inner' object. The universal and timeless shapes found in geometry : the circle, square and triangle become the spatial elements in abstract art; they are, like color, fundamental systems underlying visible reality. The Bauhaus at Weimar, Germany

2850-427: The blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the central angle is 180°). The sagitta (also known as the versine ) is a line segment drawn perpendicular to

2925-461: The centre of the circle is at the origin, then the equation of the tangent line becomes x 1 x + y 1 y = r 2 , {\displaystyle x_{1}x+y_{1}y=r^{2},} and its slope is d y d x = − x 1 y 1 . {\displaystyle {\frac {dy}{dx}}=-{\frac {x_{1}}{y_{1}}}.} An inscribed angle (examples are

3000-1774: The circle determined by three points ( x 1 , y 1 ) , ( x 2 , y 2 ) , ( x 3 , y 3 ) {\displaystyle (x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})} not on a line is obtained by a conversion of the 3-point form of a circle equation : ( x − x 1 ) ( x − x 2 ) + ( y − y 1 ) ( y − y 2 ) ( y − y 1 ) ( x − x 2 ) − ( y − y 2 ) ( x − x 1 ) = ( x 3 − x 1 ) ( x 3 − x 2 ) + ( y 3 − y 1 ) ( y 3 − y 2 ) ( y 3 − y 1 ) ( x 3 − x 2 ) − ( y 3 − y 2 ) ( x 3 − x 1 ) . {\displaystyle {\frac {({\color {green}x}-x_{1})({\color {green}x}-x_{2})+({\color {red}y}-y_{1})({\color {red}y}-y_{2})}{({\color {red}y}-y_{1})({\color {green}x}-x_{2})-({\color {red}y}-y_{2})({\color {green}x}-x_{1})}}={\frac {(x_{3}-x_{1})(x_{3}-x_{2})+(y_{3}-y_{1})(y_{3}-y_{2})}{(y_{3}-y_{1})(x_{3}-x_{2})-(y_{3}-y_{2})(x_{3}-x_{1})}}.} In homogeneous coordinates , each conic section with

3075-408: The circle has been used directly or indirectly in visual art to convey the artist's message and to express certain ideas. However, differences in worldview (beliefs and culture) had a great impact on artists' perceptions. While some emphasised the circle's perimeter to demonstrate their democratic manifestation, others focused on its centre to symbolise the concept of cosmic unity. In mystical doctrines,

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3150-419: The circle mainly symbolises the infinite and cyclical nature of existence, but in religious traditions it represents heavenly bodies and divine spirits. The circle signifies many sacred and spiritual concepts, including unity, infinity, wholeness, the universe, divinity, balance, stability and perfection, among others. Such concepts have been conveyed in cultures worldwide through the use of symbols, for example,

3225-496: The circle's radius, which comes to π multiplied by the radius squared: A r e a = π r 2 . {\displaystyle \mathrm {Area} =\pi r^{2}.} Equivalently, denoting diameter by d , A r e a = π d 2 4 ≈ 0.7854 d 2 , {\displaystyle \mathrm {Area} ={\frac {\pi d^{2}}{4}}\approx 0.7854d^{2},} that is, approximately 79% of

3300-520: The circle). For a circle centred on the origin, i.e. r 0 = 0 , this reduces to r = a . When r 0 = a , or when the origin lies on the circle, the equation becomes r = 2 a cos ⁡ ( θ − ϕ ) . {\displaystyle r=2a\cos(\theta -\phi ).} In the general case, the equation can be solved for r , giving r = r 0 cos ⁡ ( θ − ϕ ) ±

3375-417: The compass. Apollonius of Perga showed that a circle may also be defined as the set of points in a plane having a constant ratio (other than 1) of distances to two fixed foci, A and B . (The set of points where the distances are equal is the perpendicular bisector of segment AB , a line.) That circle is sometimes said to be drawn about two points. Abstract art Western art had been, from

3450-521: The development of abstract art were Romanticism , Impressionism and Expressionism . Artistic independence for artists was advanced during the 19th century. An objective interest in what is seen can be discerned from the paintings of John Constable , J. M. W. Turner , Camille Corot and from them to the Impressionists who continued the plein air painting of the Barbizon school . Early intimations of

3525-429: The door to abstraction in the early 20th century. During the 1912 Salon de la Section d'Or , where František Kupka exhibited his abstract painting Amorpha, Fugue en deux couleurs ( Fugue in Two Colors ) (1912), the poet Guillaume Apollinaire named the work of several artists including Robert Delaunay , Orphism . He defined it as, "the art of painting new structures out of elements that have not been borrowed from

3600-702: The early 1950s. The expressionistic gesture and the act of painting itself, became of primary importance to Jackson Pollock , Robert Motherwell , and Franz Kline . While during the 1940s Arshile Gorky 's and Willem de Kooning 's figurative work evolved into abstraction by the end of the decade. New York City became the center, and artists worldwide gravitated towards it; from other places in America as well. Digital art , hard-edge painting , geometric abstraction , minimalism , lyrical abstraction , op art, abstract expressionism, color field painting, monochrome painting , assemblage , neo-Dada, shaped canvas painting, are

3675-686: The early 20th century, geometric objects became an artistic subject in their own right. Wassily Kandinsky in particular often used circles as an element of his compositions. From the time of the earliest known civilisations – such as the Assyrians and ancient Egyptians, those in the Indus Valley and along the Yellow River in China, and the Western civilisations of ancient Greece and Rome during classical Antiquity –

3750-410: The early formations of the geometric abstract styles of Piet Mondrian and his colleagues in the early 20th century. The spiritualism also inspired the abstract art of Kasimir Malevich and František Kupka . At the beginning of the 20th century Henri Matisse and several other young artists including the pre-cubist Georges Braque , André Derain , Raoul Dufy and Jean Metzinger revolutionized

3825-460: The emphasis on subject matter in favor of the portrayal of psychological states of being. Although artists like Edvard Munch and James Ensor drew influences principally from the work of the Post-Impressionists they were instrumental to the advent of abstraction in the 20th century. Paul Cézanne had begun as an Impressionist but his aim – to make a logical construction of reality based on

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3900-514: The equation | z − c | = r . {\displaystyle |z-c|=r.} In parametric form, this can be written as z = r e i t + c . {\displaystyle z=re^{it}+c.} The slightly generalised equation p z z ¯ + g z + g z ¯ = q {\displaystyle pz{\overline {z}}+gz+{\overline {gz}}=q} for real p , q and complex g

3975-461: The equation of a circle has the form x 2 + y 2 − 2 a x z − 2 b y z + c z 2 = 0. {\displaystyle x^{2}+y^{2}-2axz-2byz+cz^{2}=0.} It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane ) the points I (1: i : 0) and J (1: − i : 0). These points are called

4050-407: The first chord, we find that ( 2 r − x ) x = ( y / 2) . Solving for r , we find the required result. There are many compass-and-straightedge constructions resulting in circles. The simplest and most basic is the construction given the centre of the circle and a point on the circle. Place the fixed leg of the compass on the centre point, the movable leg on the point on the circle and rotate

4125-446: The formula for the arc length s of a circular arc of radius r and subtending a central angle of measure 𝜃 is s = θ r , {\displaystyle s=\theta r,} and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.} In

4200-431: The growing prevalence of the abstract in modern art—an explanation linked to the name of Theodor W. Adorno —is that such abstraction is a response to (and a reflection of) the growing abstraction of social relations in industrial society . Frederic Jameson similarly sees modernist abstraction as a function of the abstract power of money, equating all things equally as exchange-values. The social content of abstract art

4275-861: The more international Abstract and Concrete exhibition was organized by Nicolete Gray including work by Piet Mondrian , Joan Miró , Barbara Hepworth and Ben Nicholson . Hepworth, Nicholson and Gabo moved to the St. Ives in Cornwall to continue their constructivist work. During the Nazi rise to power in the 1930s many artists fled Europe to the United States. By the early 1940s the main movements in modern art, expressionism, cubism, abstraction, surrealism , and dada were represented in New York: Marcel Duchamp , Fernand Léger , Piet Mondrian , Jacques Lipchitz , André Masson , Max Ernst , and André Breton , were just

4350-407: The polar coordinates of a generic point on the circle, and ( r 0 , ϕ ) {\displaystyle (r_{0},\phi )} are the polar coordinates of the centre of the circle (i.e., r 0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x  axis to the line connecting the origin to the centre of

4425-419: The possibility of marks and associative color resounding in the soul. The idea had been put forward by Charles Baudelaire , that all our senses respond to various stimuli but the senses are connected at a deeper aesthetic level. Closely related to this, is the idea that art has The spiritual dimension and can transcend 'every-day' experience, reaching a spiritual plane. The Theosophical Society popularized

4500-406: The ratio of t to r can be interpreted geometrically as the stereographic projection of the line passing through the centre parallel to the x  axis (see Tangent half-angle substitution ). However, this parameterisation works only if t is made to range not only through all reals but also to a point at infinity; otherwise, the leftmost point of the circle would be omitted. The equation of

4575-457: The rectangle and abstract art in general. Some artists of the period defied categorization, such as Georgia O'Keeffe who, while a modernist abstractionist, was a pure maverick in that she painted highly abstract forms while not joining any specific group of the period. Eventually American artists who were working in a great diversity of styles began to coalesce into cohesive stylistic groups. The best-known group of American artists became known as

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4650-449: The school was moved to Dessau and, as the Nazi party gained control in 1932, The Bauhaus was closed. In 1937 an exhibition of degenerate art , 'Entartete Kunst' contained all types of avant-garde art disapproved of by the Nazi party. Then the exodus began: not just from the Bauhaus but from Europe in general; to Paris, London and America. Paul Klee went to Switzerland but many of the artists at

4725-602: The search continued: The Rayist (Luchizm) drawings of Natalia Goncharova and Mikhail Larionov , used lines like rays of light to make a construction. Kasimir Malevich completed his first entirely abstract work, the Suprematist , Black Square , in 1915. Another of the Suprematist group' Liubov Popova , created the Architectonic Constructions and Spatial Force Constructions between 1916 and 1921. Piet Mondrian

4800-432: The social and intellectual preoccupations in all areas of Western culture at that time. Abstraction indicates a departure from reality in depiction of imagery in art. This departure from accurate representation can be slight, partial, or complete. Abstraction exists along a continuum. Even art that aims for verisimilitude of the highest degree can be said to be abstract, at least theoretically, since perfect representation

4875-506: The special case 𝜃 = 2 π , these formulae yield the circumference of a complete circle and area of a complete disc, respectively. In an x – y Cartesian coordinate system , the circle with centre coordinates ( a , b ) and radius r is the set of all points ( x , y ) such that ( x − a ) 2 + ( y − b ) 2 = r 2 . {\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}.} This equation , known as

4950-670: The specified regions may be considered as open , that is, not containing their boundaries, or as closed , including their respective boundaries. The word circle derives from the Greek κίρκος/κύκλος ( kirkos/kuklos ), itself a metathesis of the Homeric Greek κρίκος ( krikos ), meaning "hoop" or "ring". The origins of the words circus and circuit are closely related. Prehistoric people made stone circles and timber circles , and circular elements are common in petroglyphs and cave paintings . Disc-shaped prehistoric artifacts include

5025-457: The value of c , and the result is that the equation of the tangent is ( x 1 − a ) x + ( y 1 − b ) y = ( x 1 − a ) x 1 + ( y 1 − b ) y 1 , {\displaystyle (x_{1}-a)x+(y_{1}-b)y=(x_{1}-a)x_{1}+(y_{1}-b)y_{1},} or ( x 1 −

5100-532: The various conceptual and aesthetic groupings. An exhibition by forty-six members of the Cercle et Carré group organized by Joaquín Torres-García assisted by Michel Seuphor contained work by the Neo-Plasticists as well as abstractionists as varied as Kandinsky, Anton Pevsner and Kurt Schwitters . Criticized by Theo van Doesburg to be too indefinite a collection he published the journal Art Concret setting out

5175-429: The very numerous art movements that embody partial abstraction would be for instance fauvism in which color is conspicuously and deliberately altered vis-a-vis reality, and cubism , which alters the forms of the real-life entities depicted. Patronage from the church diminished and private patronage from the public became more capable of providing a livelihood for artists. Three art movements which contributed to

5250-463: The visual sphere, but had been created entirely by the artist...it is a pure art." Since the turn of the century, cultural connections between artists of the major European cities had become extremely active as they strove to create an art form equal to the high aspirations of modernism . Ideas were able to cross-fertilize by means of artist's books, exhibitions and manifestos so that many sources were open to experimentation and discussion, and formed

5325-402: Was connected to the divine for most medieval scholars , and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles. In 1880 CE, Ferdinand von Lindemann proved that π is transcendental , proving that the millennia-old problem of squaring the circle cannot be performed with straightedge and compass. With the advent of abstract art in

5400-672: Was essentially a spiritual activity; to create the individual's place in the world, not to organize life in a practical, materialistic sense. During that time, representatives of the Russian avant-garde collaborated with other Eastern European Constructivist artists, including Władysław Strzemiński , Katarzyna Kobro , and Henryk Stażewski . Many of those who were hostile to the materialist production idea of art left Russia. Anton Pevsner went to France, Gabo went first to Berlin, then to England and finally to America. Kandinsky studied in Moscow then left for

5475-428: Was evolving his abstract language, of horizontal and vertical lines with rectangles of color, between 1915 and 1919, Neo-Plasticism was the aesthetic which Mondrian, Theo van Doesburg and other in the group De Stijl intended to reshape the environment of the future. Many of the abstract artists in Russia became Constructivists believing that art was no longer something remote, but life itself. The artist must become

5550-557: Was founded in 1919 by Walter Gropius . The philosophy underlying the teaching program was unity of all the visual and plastic arts from architecture and painting to weaving and stained glass. This philosophy had grown from the ideas of the Arts and Crafts movement in England and the Deutscher Werkbund . Among the teachers were Paul Klee , Wassily Kandinsky , Johannes Itten , Josef Albers , Anni Albers , and László Moholy-Nagy . In 1925

5625-563: Was in Germany". From 1909 to 1913 many experimental works in the search for this 'pure art' had been created by a number of artists: Francis Picabia painted Caoutchouc , c. 1909, The Spring , 1912, Dances at the Spring and The Procession, Seville , 1912; Wassily Kandinsky painted Untitled (First Abstract Watercolor) , 1913, Improvisation 21A , the Impression series, and Picture with

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