Sky and Water I
Sky and Water I is a woodcut print by the Dutch artist M. C. Escher first printed in June 1938; the basis of this print is a regular division of the plane consisting of birds and fish. Both prints have the horizontal series of these elements—fitting into each other like the pieces of a jigsaw puzzle—in the middle, transitional portion of the prints. In this central layer the pictorial elements are equal: birds and fish are alternately foreground or background, depending on whether the eye concentrates on light or dark elements; the birds take on an increasing three-dimensionality in the upward direction, the fish, in the downward direction. But as the fish progress upward and the birds downward they lose their shapes to become a uniform background of sky and water, respectively. According to Escher: "In the horizontal center strip there are birds and fish equivalent to each other. We associate flying with sky, so for each of the black birds the sky in which it is flying is formed by the four white fish which encircle it.
Swimming makes us think of water, therefore the four black birds that surround a fish become the water in which it swims." This print has been used in physics, chemistry, in psychology for the study of visual perception. In the pictures a number of visual elements unite into a simple visual representation, but separately each forms a point of departure for the elucidation of a theory in one of these disciplines. M. C Escher and Water I best exemplify figure ground-reversal. Sky and Water II Tessellation M. C. Escher—The Graphic Work. M. C. Escher—29 Master Prints. Publishers. Locher, J. L.. The Magic of M. C. Escher. Harry N. Abrams, Inc. ISBN 0-8109-6720-0
National Gallery of Canada
The National Gallery of Canada, located in the capital city of Ottawa, Ontario, is Canada's premier art gallery. The Gallery is now housed in a glass and granite building on Sussex Drive with a notable view of the Canadian Parliament buildings on Parliament Hill; the building was designed by Moshe Safdie and opened in 1988. The Gallery's former director, Jean Sutherland Boggs, was chosen by Prime Minister Pierre Trudeau to oversee construction of the national gallery and museums. Marc Mayer was named the museum's director, succeeding Pierre Théberge, on 19 January 2009; the Gallery was first formed in 1880 by Canada's Governor General, John Campbell, 9th Duke of Argyll, and, in 1882, moved into its first home on Parliament Hill in the same building as the Supreme Court. In 1911, the Gallery moved to the Victoria Memorial Museum, now the home of the Canadian Museum of Nature. In 1913, the first National Gallery Act was passed. In 1962, the Gallery moved to the Lorne Building site, a rather nondescript office building on Elgin Street.
Adjacent to the British High Commission, the building has since been demolished for a 17-storey office building, to house the Federal Finance Department. The museum moved into its current building beside Nepean Point. In 1985, the newly created Canadian Museum of Contemporary Photography the Stills Photography Division of the National Film Board of Canada, was affiliated to the National Gallery; the CMCP's mandate and staff moved to its new location in 1992, at 1 Rideau Canal, next to the Château Laurier. In 1998, the CMCP's administration was amalgamated to that of the National Gallery's. In 2000, the Royal Architectural Institute of Canada chose the National Gallery as one of the top 500 buildings produced in Canada during the last millennium; the Gallery has a large and varied collection of paintings, drawings and photographs. Although its focus is on Canadian art, it holds works by many noted European artists, it has a strong contemporary art collection with some of Andy Warhol's most famous works.
In 1990 the Gallery bought Barnett Newman's Voice of Fire for $1.8 million, igniting a storm of controversy. Since that time its value has appreciated sharply. In 2005, the Gallery acquired a painting by Italian Renaissance painter Francesco Salviati for $4.5 million. Its most famous painting is The Death of General Wolfe by Anglo-American artist Benjamin West. In 2005, a sculpture of a giant spider, Louise Bourgeois's Maman, was installed in the plaza in front of the Gallery. In 2011 the gallery installed Canadian sculptor Joe Fafard's Running Horses next to the Sussex Drive entrance, American artist Roxy Paine's stainless steel sculpture One Hundred Foot Line in Nepean Point behind the gallery; the Canadian collection, the most comprehensive in Canada, holds works by Louis-Philippe Hébert, Tom Thomson, the Group of Seven, Emily Carr, Alex Colville, Jean-Paul Riopelle and Jack Bush. The Gallery organizes its own exhibits which travel across Canada and beyond, hosts shows from around the world co-sponsored with other national art galleries and museums.
The Gallery's collection has been built up through purchase and donations. Much of the collection was donated, notably the British paintings donated by former Governor General Vincent Massey and that of the Southam family; the museum features Canadian and Inuit art and European painting, sculpture and drawings, modern and contemporary art and photographs. The largest work in the Gallery is the entire interior of the Rideau Street Chapel, which formed part of the Convent of Our Lady Sacred Heart, The interior decorations of the Rideau Street Chapel were designed by Georges Couillon in 1887. After the convent was demolished in 1972, the chapel was dismantled and reconstructed within the gallery as a work of art in 1988. Auguste Rodin, Age of Bronze, 1875–1876, cast in 1901. M. C. Escher, Stars, 1948. Barnett Newman, Voice of Fire, 1967; the Museum is affiliated with: CMA, Ontario Association of Art Galleries, CHIN, Virtual Museum of Canada. Ord, The National Gallery of Canada: ideas, architecture, McGill-Queen's University Press, ISBN 0-7735-2509-2 Robert Fulford, "Turning the absurd into an art form: Canada's National Gallery has a history filled with bizarre decisions," National Post, 9 September 2003, http://www.robertfulford.com/2003-09-09-gallery.html Official website
In geometry, orbifold notation is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature. The advantage of the notation is that it describes these groups in a way which indicates many of the groups' properties: in particular, it describes the orbifold obtained by taking the quotient of Euclidean space by the group under consideration. Groups representable in this notation include the point groups on the sphere, the frieze groups and wallpaper groups of the Euclidean plane, their analogues on the hyperbolic plane; the following types of Euclidean transformation can occur in a group described by orbifold notation: reflection through a line translation by a vector rotation of finite order around a point infinite rotation around a line in 3-space glide-reflection, i.e. reflection followed by translation. All translations which occur are assumed to form a discrete subgroup of the group symmetries being described.
Each group is denoted in orbifold notation by a finite string made up from the following symbols: positive integers 1, 2, 3, … the infinity symbol, ∞ the asterisk, * the symbol o, called a wonder and a handle because it topologically represents a torus closed surface. Patterns repeat by two translation; the symbol ×, called a miracle and represents a topological crosscap where a pattern repeats as a mirror image without crossing a mirror line. A string written in boldface represents a group of symmetries of Euclidean 3-space. A string not written in boldface represents a group of symmetries of the Euclidean plane, assumed to contain two independent translations; each symbol corresponds to a distinct transformation: an integer n to the left of an asterisk indicates a rotation of order n around a gyration point an integer n to the right of an asterisk indicates a transformation of order 2n which rotates around a kaleidoscopic point and reflects through a line an × indicates a glide reflection the symbol ∞ indicates infinite rotational symmetry around a line.
By abuse of language, we might say that such a group is a subgroup of symmetries of the Euclidean plane with only one independent translation. The frieze groups occur in this way; the exceptional symbol o indicates that there are two linearly independent translations. An orbifold symbol is called good if it is not one of the following: p, pq, *p, *pq, for p,q>=2, p≠q. An object is chiral; the corresponding orbifold is non-orientable otherwise. The Euler characteristic of an orbifold can be read from its Conway symbol; each feature has a value: n without or before an asterisk counts as n − 1 n n after an asterisk counts as n − 1 2 n asterisk and × count as 1 o counts as 2. Subtracting the sum of these values from 2 gives the Euler characteristic. If the sum of the feature values is 2, the order is infinite, i.e. the notation represents a wallpaper group or a frieze group. Indeed, Conway's "Magic Theorem" indicates that the 17 wallpaper groups are those with the sum of the feature values equal to 2.
Otherwise, the order is 2 divided by the Euler characteristic. The following groups are isomorphic: 1* and *11 22 and 221 *22 and *221 2* and 2*1; this is. The symmetry of a 2D object without translational symmetry can be described by the 3D symmetry type by adding a third dimension to the object which does not add or spoil symmetry. For example, for a 2D image we can consider a piece of carton with that image displayed on one side, thus we have n• and *n•. The bullet is added on one- and two-dimensional groups to imply the existence of a fixed point. A 1D image can be drawn horizontally on a piece of carton, with a provision to avoid additional symmetry with respect to the line of the image, e.g. by drawing a horizontal bar under the image. Thus the discrete symmetry groups in one dimension are *•, *1•, ∞• and *∞•. Another way of constructing a 3D object from a 1D or 2D object for describing the symmetry is taking the Cartesian product of the object and an asymmetric 2D or 1D object, respectively.
*Schönflies's point group notation is extended here as infinite cases of the equivalent dihedral points symmetries §The diagram shows one fundamental domain in yellow, with reflection lines in blue, glide reflection lines in dashed green, translation normals in red, 2-fold gyration points as small green squares. A first few hyperbolic groups, ordered by their Euler characteristic are: Mutation of orbifolds Fibrifold notation - an extension of orbifold notation for 3d space groups John H. Conway, Olaf Delgado Friedrichs, Daniel H. Huson, W
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, they play an important role in group theory and chemistry; the notation for the dihedral group differs in abstract algebra. In geometry, Dn or Dihn refers to the symmetries of a group of order 2n. In abstract algebra, D2n refers to this same dihedral group; the geometric convention is used in this article. A regular polygon with n sides has 2 n different symmetries: n rotational symmetries and n reflection symmetries. We take n ≥ 3 here; the associated rotations and reflections make up the dihedral group D n. If n is odd, each axis of symmetry connects the midpoint of one side to the opposite vertex. If n is there are n/2 axes of symmetry connecting the midpoints of opposite sides and n / 2 axes of symmetry connecting opposite vertices. In either case, there are 2 n elements in the symmetry group. Reflecting in one axis of symmetry followed by reflecting in another axis of symmetry produces a rotation through twice the angle between the axes.
The following picture shows the effect of the sixteen elements of D 8 on a stop sign: The first row shows the effect of the eight rotations, the second row shows the effect of the eight reflections, in each case acting on the stop sign with the orientation as shown at the top left. As with any geometric object, the composition of two symmetries of a regular polygon is again a symmetry of this object. With composition of symmetries to produce another as the binary operation, this gives the symmetries of a polygon the algebraic structure of a finite group; the following Cayley table shows the effect of composition in the group D3. R0 denotes the identity. For example, s2s1 = r1, because the reflection s1 followed by the reflection s2 results in a rotation of 120°; the order of elements denoting the composition is right to left, reflecting the convention that the element acts on the expression to its right. The composition operation is not commutative. In general, the group Dn has elements r0, …, rn−1 and s0, …, sn−1, with composition given by the following formulae: r i r j = r i + j, r i s j = s i + j, s i r j = s i − j, s i s j = r i − j.
In all cases and subtraction of subscripts are to be performed using modular arithmetic with modulus n. If we center the regular polygon at the origin elements of the dihedral group act as linear transformations of the plane; this lets us represent elements of Dn with composition being matrix multiplication. This is an example of a group representation. For example, the elements of the group D4 can be represented by the following eight matrices: r 0 =, r 1 =, r 2 =, r 3 =, s 0 =, s 1 =, s 2 =
The Hague is a city on the western coast of the Netherlands and the capital of the province of South Holland. It is the seat of government of the Netherlands. With a metropolitan population of more than 1 million, it is the third-largest city in the Netherlands, after Amsterdam and Rotterdam; the Rotterdam–The Hague metropolitan area, with a population of 2.7 million, is the 13th-largest in the European Union and the most populous in the country. Located in the west of the Netherlands, The Hague is in the centre of the Haaglanden conurbation and lies at the southwest corner of the larger Randstad conurbation; the Hague is the seat of the Cabinet, the States General, the Supreme Court, the Council of State of the Netherlands, but the city is not the constitutional capital of the Netherlands, Amsterdam. King Willem-Alexander lives in Huis ten Bosch and works at the Noordeinde Palace in The Hague, together with Queen Máxima; the Hague is home to the world headquarters of Royal Dutch Shell and other Dutch companies.
Most foreign embassies in the Netherlands and 200 international governmental organisations are located in the city, including the International Court of Justice and the International Criminal Court, which makes The Hague one of the major cities hosting a United Nations institution along with New York City, Vienna and Nairobi. Because of this, The Hague is known as the home of international law and arbitration; the Hague was first mentioned as Die Haghe in 1242. In the 15th century, the name des Graven hage came into use "The Count's Wood", with connotations like "The Count's Hedge, Private Enclosure or Hunting Grounds". "'s Gravenhage" was used for the city from the 17th century onward. Today, this name is only used in some official documents like marriage certificates; the city itself uses "Den Haag" in all its communications. Little is known about the origin of The Hague. There are no contemporary documents describing it, sources are of dubious reliability. What is certain is that The Hague was founded by the last counts of the House of Holland.
Floris IV owned two residences in the area, but purchased a third court situated by the present-day Hofvijver in 1229 owned by a woman called Meilendis. Floris IV intended to rebuild the court into a large castle, but he died in a tournament in 1234, before anything was built, his son and successor William II lived in the court, after he was elected King of the Romans in 1248, he promptly returned to The Hague, had builders turn the court into a "royal palace", which would be called the Binnenhof. He died in 1256 before this palace was completed but parts of it were finished during the reign of his son Floris V, of which the Ridderzaal, still intact, is the most prominent, it is still used for political events, such as the annual speech from the throne by the Dutch monarch. From the 13th century onward, the counts of Holland used The Hague as their administrative center and residence when in Holland; the village that originated around the Binnenhof was first mentioned as Die Haghe in a charter dating from 1242.
It became the primary residence of the Counts of Holland in 1358, thus became the seat of many government institutions. This status allowed the village to grow. In its early years, the village was located in the ambacht, or rural district, of Monster, governed by the Lord of Monster. Seeking to exercise more direct control over the village, the Count split the village off and created a separate ambacht called Haagambacht, governed directly by the Counts of Holland; the territory of Haagambacht was expanded during the reign of Floris V. When the House of Burgundy inherited the counties of Holland and Zeeland in 1432, they appointed a stadtholder to rule in their stead with the States of Holland and West Friesland as an advisory council. Although their seat was located in The Hague, the city became subordinate to more important centres of government such as Brussels and Mechelen, from where the sovereigns ruled over the centralised Burgundian Netherlands. At the beginning of the Eighty Years' War, the absence of city walls proved disastrous, as it allowed Spanish troops to occupy the town.
In 1575, the States of Holland, temporarily based in Delft considered demolishing the city but this proposal was abandoned, after mediation by William the Silent. In 1588, The Hague became the permanent seat of the States of Holland as well as the States General of the Dutch Republic. In order for the administration to maintain control over city matters, The Hague never received official city status, although it did have many of the privileges granted only to cities. In modern administrative law, "city rights" have no place anymore. Only in 1806, when the Kingdom of Holland was a puppet state of the First French Empire, was the settlement granted city rights by Louis Bonaparte. After the Napoleonic Wars, modern-day Belgium and the Netherlands were combined in the United Kingdom of the Netherlands to form a buffer against France; as a compromise and Amsterdam alternated as capital every two years, with the government remaining in The Hague. After the separation of Belgium in 1830, Amsterdam remained the capital of the Netherlands, while the government was situated in The Hague.
When the government started to play a more prominent role in Dutch society after 1850, The Hague expanded. Many streets were built for the large number of civil se
Woodcut is a relief printing technique in printmaking. An artist carves an image into the surface of a block of wood—typically with gouges—leaving the printing parts level with the surface while removing the non-printing parts. Areas that the artist cuts away carry no ink, while characters or images at surface level carry the ink to produce the print; the block is cut along the wood grain. The surface is covered with ink by rolling over the surface with an ink-covered roller, leaving ink upon the flat surface but not in the non-printing areas. Multiple colors can be printed by keying the paper to a frame around the woodblocks; the art of carving the woodcut can be called "xylography", but this is used in English for images alone, although that and "xylographic" are used in connection with block books, which are small books containing text and images in the same block. They became popular in Europe during the latter half of the 15th century. A single-sheet woodcut is a woodcut presented as a single image or print, as opposed to a book illustration.
Since it's origins in China, the practice of woodcut has spread across the world from Europe, to other parts of Asia, to Latin America. In both Europe and the Far East, traditionally the artist only designed the woodcut, the block-carving was left to specialist craftsmen, called block-cutters, or Formschneider in Germany, some of whom became well-known in their own right. Among these, the best-known are the 16th-century Hieronymus Andreae, Hans Lützelburger and Jost de Negker, all of whom ran workshops and operated as printers and publishers; the formschneider in turn handed the block on to specialist printers. There were further specialists; this is why woodcuts are sometimes described by museums or books as "designed by" rather than "by" an artist. The division of labour had the advantage that a trained artist could adapt to the medium easily, without needing to learn the use of woodworking tools. There were various methods of transferring the artist's drawn design onto the block for the cutter to follow.
Either the drawing would be made directly onto the block, or a drawing on paper was glued to the block. Either way, the artist's drawing was destroyed during the cutting process. Other methods were used, including tracing. In both Europe and the Far East in the early 20th century, some artists began to do the whole process themselves. In Japan, this movement was called sōsaku-hanga, as opposed to shin-hanga, a movement that retained traditional methods. In the West, many artists used the easier technique of linocut instead. Compared to intaglio techniques like etching and engraving, only low pressure is required to print; as a relief method, it is only necessary to ink the block and bring it into firm and contact with the paper or cloth to achieve an acceptable print. In Europe, a variety of woods including boxwood and several nut and fruit woods like pear or cherry were used. There are three methods of printing to consider: Stamping: Used for many fabrics and most early European woodcuts; these were printed by putting the paper/fabric on a table or other flat surface with the block on top, pressing or hammering the back of the block.
Rubbing: Apparently the most common method for Far Eastern printing on paper at all times. Used for European woodcuts and block-books in the fifteenth century, widely for cloth. Used for many Western woodcuts from about 1910 to the present; the block goes face up with the paper or fabric on top. The back is rubbed with a "hard pad, a flat piece of wood, a burnisher, or a leather frotton". A traditional Japanese tool used for this is called a baren. In Japan, complex wooden mechanisms were used to help hold the woodblock still and to apply proper pressure in the printing process; this was helpful once multiple colors were introduced and had to be applied with precision atop previous ink layers. Printing in a press: presses only seem to have been used in Asia in recent times. Printing-presses were used from about 1480 for European prints and block-books, before that for woodcut book illustrations. Simple weighted presses may have been used in Europe before the print-press, but firm evidence is lacking.
A deceased Abbess of Mechelen in 1465 had "unum instrumentum ad imprintendum scripturas et ymagines... cum 14 aliis lapideis printis"—"an instrument for printing texts and pictures... with 14 stones for printing". This is too early to be a Gutenberg-type printing press in that location. Main articles Old master print for Europe, Woodblock printing in Japan for Japan, Lubok for Russia Woodcut originated in China in antiquity as a method of printing on textiles and on paper; the earliest woodblock printed fragments to survive are from China, from the Han dynasty, are of silk printed with flowers in three colours. "In the 13th century the Chinese technique of blockprinting was transmitted to Europe." Paper arrived in Europe from China via al-Andalus later, was being manufactured in Italy by the end of the thirteenth century, in Burgundy and Germany by the end of the fourteenth. In Europe, woodcut is the oldest technique used for old master prints, developing about 1400, by using, on paper, existing techniques for printing.
One of the more ancient woodcuts on paper that can be seen today is The Fire Madonna, in the Cat
Escher in the Palace
Escher in Het Paleis is a museum in The Hague, featuring the works of the Dutch graphical artist M. C. Escher, it is housed in the Lange Voorhout Palace since November 2002. In 2015 it was revealed that many of the prints on display at the museum were replicas, scanned from original prints and printed onto the same type of paper used by Escher, rather than original Escher prints as they had been labeled; the museum is housed in the Lange Voorhout Palace, a former royal residence dating back to the eighteenth century. Queen Emma bought the stately house in 1896, she used it as a winter palace from March 1901 till her death in March 1934. It was used by four subsequent Dutch queens for their business offices, until Queen Beatrix moved the office to Paleis Noordeinde; the first and second floors have exhibitions showing the royal period of the palace, highlighting Queen Emma's residence. The museum features a permanent display of a large number of woodcuts and lithographs by M. C. Escher, among them the world-famous prints and Water.
Escher in Het Paleis shows the early lovely Italian landscapes, the many mirror prints and a choice from the tesselation drawings the three versions of the Metamorphosis, from the first small one, to the third, of 7 meters. This one is shown in a circle, it underlines the new vision of the museum on the work of M. C. Escher; the third floor of the museum is dedicated to the Optical Illusion, besides the famous Escher Room in which grownups seem to be smaller than their children, one's eyes will be tricked by multiple interactive displays. In the rooms of the museum are fifteen chandeliers made by the Rotterdam artist, Hans van Bentem; the artist designed these for the museum, with some references to the work of Escher and the Palace. In the ballroom, a star chandelier is endlessly reflected in the two mirrors. In other rooms there are chandeliers such as a shark, a skull, a sea horse; the parquet floor in the Palace was designed in 1991/92 by the American minimal artist Donald Judd on the occasion of the opening of the former Royal palace as an exhibition palace.
Judd applied the principle of different colours and geometric patterns to the parquet floor in the Palace. Escher in het Paleis