Friday, January 11, 2008

Lunate bone
The lunate bone (semilunar bone) is a bone in the human hand that may be distinguished by its deep concavity and crescentic outline. It is situated in the center of the proximal row of the carpus, or wrist, between the scaphoid and triangular bone.
The etymology derives from the Latin luna which means "moon."

See also

Bone terminology
Terms for anatomical location

Thursday, January 10, 2008


In geometry a polygon (IPA: [ˈpɒlɪˌɡɒn ~ ˈpɒliˌɡɒn]) is a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. The interior of the polygon is called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.
In the computer graphics (image generation) field, the term polygon has taken on a slightly altered meaning, more related to the way the shape is stored and manipulated within the computer.

Classification
Polygons are primarily classified by the number of sides, see naming polygons below.

Number of sides
Polygons may be characterised by their degree of convexity:

Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
Non-convex: a line may be found which meets its boundary more than twice.
Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
Concave: Non-convex and simple.
Star-shaped: the whole interior is visible from a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
Self-intersecting: the boundary of the polygon crosses itself. Branko Grünbaum calls these coptic, though this term does not seem to be widely used. The term complex is sometimes used in contrast to simple, but this is mistaken: a complex polygon is one which exists in the unitary plane, which comprises two complex dimensions.
Star polygon: a polygon which self-intersects in a regular way. Convexity

Equiangular: all its corner angles are equal.
Cyclic: all corners lie on a single circle.
Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular.
Equilateral: all edges are of the same length. (A polygon with 5 or more sides can be equilateral without being convex.) (Williams 1979, pp. 31-32)
Isotoxal or edge-transitive: all sides lie within the same symmetry orbit. The polygon is also equilateral.
Regular. A polygon is regular if it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon. Polygonal Miscellaneous
We will assume Euclidean geometry throughout.

Properties
The reasoning also applies if some interior angles are more than 180°: going clockwise around, it means that one sometime turns left instead of right, which is counted as turning a negative amount. (Thus we consider something like the winding number of the orientation of the sides, where at every vertex the contribution is between -½ and ½ winding.)
The measure of any interior angle of a convex regular n-gon is (n−2)π/n radians or (n−2)180/n degrees. The interior angles of regular star polygons were first studied by Poinsot, in the same paper in which he describes the four regular star polyhedra.
Moving around an n-gon in general, the sum of the exterior angles (the total amount one "turns" at the vertices) can be any integer times 360°, e.g. 720°For a pentagram and 0°For an angular "eight". See also orbit (dynamics).

Any polygon, regular or irregular, complex or simple, has as many corners as it has sides.
Each corner has several angles. The two most important ones are:

  • Interior angle - The sum of the interior angles of a simple n-gon is (n−2)π radians or (n−2)180 degrees. This is because any simple n-gon can be considered to be made up of (n−2) triangles, each of which has an angle sum of π radians or 180 degrees. In topology and analysis,
    Exterior angle - Imagine walking around a simple n-gon marked on the floor. The amount you "turn" at a corner is the exterior or external angle. Walking all the way round the polygon, you make one full turn, so the sum of the exterior angles must be 360°. The exterior angle is the supplementary angle to the interior angle, and from this the sum of the interior angles can be easily confirmed. Angles
    The area of a polygon is the measurement of the 2-dimensional region enclosed by the polygon.

    Area
    The area A of a simple polygon can be computed if the cartesian coordinates (x1, y1), (x2, y2), ..., (xn, yn) of its vertices, listed in order as the area is circulated in counter-clockwise fashion, are known. The formula is
    A = frac{ (x_1 y_2 - x_2 y_1) + (x_2 y_3 - x_3 y_2) + ... + (x_n y_1 - x_1 y_n) }{2} ,

    = frac{ x_1 (y_2 - y_n) + x_2 (y_3 - y_1) + x_3 (y_4 - y_2) + ... + x_n (y_1 - y_{n-1}) }{2}.
    The formula was described by Meister in 1769 and by Gauss in 1795. It can be verified by dividing the polygon into triangles, but it can also be seen as a special case of Green's theorem.
    The area A of a simple polygon can also be computed if the lengths of the sides, a1,a2, ..., an and the exterior angles, θ12, ..., θn are known. The formula is
    begin{align}A = frac12 ( a_1[a_2 sin(theta_1) + a_3 sin(theta_1 + theta_2) + ... + a_{n-1} sin(theta_1 + theta_2 + ... + theta_{n-2}> <br /> + a_2[a_3 sin(theta_2) + a_4 sin(theta_2 + theta_3) + ... + a_{n-1} sin(theta_2 + ... + theta_{n-2})] <br /> + ; ... ;;;;;;;;;;;;;;;;;;;;;;;;;;;; <br /> + a_{n-2}[a_{n-1} sin(theta_{n-2})] ) end{align} The formula was described by Lopshits in 1963.
    If the polygon can be drawn on an equally-spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.
    If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon. This is the Bolyai-Gerwien theorem.
    For a regular polygon with n sides of length s, the area is given by:
    A = frac{n}{4} s^2 cot{cfrac{pi}{n}}.

    Simple polygons
    The area of a self-intersecting polygon can be defined in two different ways, each of which gives a different answer:

    Using the above methods for simple polygons, we discover that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region. For example the central convex pentagon in the centre of a pentagram has density = 2. The two triangular regions of a cross-quadrilateral (like a figure 8) have opposite-signed densities, and adding their areas together can give a total area of zero for the whole figure.
    Considering the enclosed regions as point sets, we can find the area of the enclosed point set. This corresponds to the area of the plane covered by the polygon, or to the area of a simple polygon having the same outline as the self-intersecting one (or, in the case of the cross-quadrilateral, the two simple triangles). Self-intersecting polygons
    An n-gon has 2n degrees of freedom, including 2 for position and 1 for rotational orientation, and 1 for over-all size, so 2n-4 for shape. In the case of a line of symmetry the latter reduces to n-2.
    Let k≥2. For an nk-gon with k-fold rotational symmetry (Ck), there are 2n-2 degrees of freedom for the shape. With additional mirror-image symmetry (Dk) there are n-1 degrees of freedom.

    Degrees of freedom
    In a broad sense, a polygon is an unbounded sequence or circuit of alternating segments (sides) and angles (corners). The modern mathematical understanding is to describe this structural sequence in terms of an 'abstract' polygon which is a partially-ordered set (poset) of elements. The interior (body) of the polygon is another element, and (for technical reasons) so is the null polytope or nullitope.
    Generally, a geometric polygon is a 'realization' of this abstract polygon; this involves some 'mapping' of elements from the abstract to the geometric. Such a polygon does not have to lie in a plane, or have straight sides, or enclose an area, and individual elements can overlap or even coincide. For example a spherical polygon is drawn on the surface of a sphere, and its sides are arcs of great circles. As another example, most polygons are unbounded because they close back on themselves, while apeirogons (infinite polygons) are unbounded because they go on for ever so you can never reach any bounding end point. So when we talk about "polygons" we must be careful to explain what kind we are talking about.
    A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc of a different great circle and you have a digon. Tile the sphere with digons and you have a polyhedron called a hosohedron. Take just one great circle instead, run it all the way round, and add just one "corner" point, and you have a monogon or henagon.
    Other realizations of these polygons are possible on other surfaces - but in the Euclidean (flat) plane, their bodies cannot be sensibly realized and we think of them as degenerate.
    The idea of a polygon has been generalised in various ways. Here is a short list of some degenerate cases (or special cases, depending on your point of view):

    Digon. Angle of 0° in the Euclidean plane. See remarks above re. on the sphere.
    Angle of 180°: In the plane this gives an apeirogon), on the sphere a dihedron
    A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions. The Petrie polygons of the regular polyhedra are classic examples.
    A spherical polygon is a circuit of sides and corners on the surface of a sphere.
    An apeirogon is an infinite sequence of sides and angles, which is not closed but it has no ends because it extends infinitely.
    A complex polygon is a figure analogous to an ordinary polygon, which exists in the unitary plane. Generalizations of polygons
    The word 'polygon' comes from Late Latin polygōnum (a noun), from Greek polygōnon/polugōnon πολύγωνον, noun use of neuter of polygōnos/polugōnos πολύγωνος (the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral, and nonagon are exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. A variable can even be used, usually n-gon. This is useful if the number of sides is used in a formula.
    Some special polygons also have their own names; for example, the regular star pentagon is also known as the pentagram.
    "hectogon" is the Greek name (see hectometre), "centagon" is a Latin-Greek hybrid; neither is widely attested.
    To construct the name of a polygon with more than 20 and less than 100 edges, combine the prefixes as follows
    The 'kai' is not always used. Opinions differ on exactly when it should, or need not, be used (see also examples above).
    That is, a 42-sided figure would be named as follows:
    and a 50-sided figure
    But beyond enneagons and decagons, professional mathematicians prefer the aforementioned numeral notation (for example, MathWorld has articles on 17-gons and 257-gons).

    Naming polygons
    Numerous regular polygons may be seen in nature. In the world of minerals, crystals often have faces which are triangular, square or hexagonal. Quasicrystals can even have regular pentagons as faces. Another fascinating example of regular polygons occurs when the cooling of lava forms areas of tightly packed hexagonal columns of basalt, which may be seen at the Giant's Causeway in Ireland, or at the Devil's Postpile in California.
    The most famous hexagons in nature are found in the animal kingdom. The wax honeycomb made by bees is an array of hexagons used to store honey and pollen, and as a secure place for the larvae to grow. There also exist animals who themselves take the approximate form of regular polygons, or at least have the same symmetry. For example, starfish display the symmetry of a pentagon or, less frequently, the heptagon or other polygons. Other echinoderms, such as sea urchins, sometimes display similar symmetries. Though echinoderms do not exhibit exact radial symmetry, jellyfish and comb jellies do, usually fourfold or eightfold.
    Radial symmetry (and other symmetry) is also widely observed in the plant kingdom, particularly amongst flowers, and (to a lesser extent) seeds and fruit, the most common form of such symmetry being pentagonal. A particularly striking example is the Starfruit, a slightly tangy fruit popular in Southeast Asia, whose cross-section is shaped like a pentagonal star.
    Moving off the earth into space, early mathematicians doing calculations using Newton's law of gravitation discovered that if two bodies (such as the sun and the earth) are orbiting one another, there exist certain points in space, called Lagrangian points, where a smaller body (such as an asteroid or a space station) will remain in a stable orbit. The sun-earth system has five Lagrangian points. The two most stable are exactly 60 degrees ahead and behind the earth in its orbit; that is, joining the centre of the sun and the earth and one of these stable Lagrangian points forms an equilateral triangle. Astronomers have already found asteroids at these points. It is still debated whether it is practical to keep a space station at the Lagrangian point — although it would never need course corrections, it would have to frequently dodge the asteroids that are already present there. There are already satellites and space observatories at the less stable Lagrangian points.

    Polygons in nature

    Cut up a piece of paper into polygons, and put them back together as a tangram.
    Join many edge-to-edge as a tiling or tessellation.
    Join several edge-to-edge and fold them all up so there are no gaps, to make a three-dimensional polyhedron.
    Join many edge-to-edge, folding them into a crinkly thing called an infinite polyhedron.
    Use computer-generated polygons to build up a three-dimensional world full of monsters, theme parks, aeroplanes or anything - see Polygons in computer graphics below.. Polygons in computer graphics

    Polygon name generator: type in the number of sides and see the polygon's name!
    Eric W. Weisstein, Polygon at MathWorld.
    What Are Polyhedra? (with Greek Numerical Prefixes)
    Polygons, types of polygons, and polygon properties With interactive animation
    How to draw monochrome orthogonal polygons on screens, by Herbert Glarner

Wednesday, January 9, 2008

Guernsey cricket team
The Guernsey cricket team is the team that represents the Crown dependency of Guernsey in international cricket matches. They became an affiliate member of the International Cricket Council in 2005. [1]

International Competition
Guernsey has a long rivalry with fellow Channel Island Jersey playing an annual encounter against each other known as the inter-insular match. The most recent encounter in 2006 saw a 15 run victory for Guernsey, who have now won the encounter five consecutive times, although have a long way to go to match Jersey's run of ten consecutive victories from 1992 to 2001. [2] They made their debut at the European Championship in 2006, and finished in 5th place in Division Two, the tournament being won by Norway. They will remain in Division Two in 2008.
International matches are being played by Guernsey outside the above two events also, with matches against Bermuda and Namibia in 2005, and more matches against Bermuda in 2006. Games against France and a tour of Canada are being planned for 2007. [3]

Tuesday, January 8, 2008


George Jacob Jung (born August 6, 1942) was a major player in cocaine importation in the United States in the 1970s and early 80s. Jung was a part of the Medellín Cartel. His life story was portrayed in the 2001 movie Blow, starring Johnny Depp.

George JungGeorge Jung Biography

The Yogurt Connection
The Wonderland Gang

Monday, January 7, 2008

Delta (letter)
Delta (upside down A, uppercase Δ, lowercase δ) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. It was derived from the Phoenician letter Dalet Dalet. Letters that arose from Delta include the Latin D and the equivalent in the Cyrillic alphabet Д.
In Modern Greek it represents a voiced dental fricative /ð/, (like the th in the English word this) but in the Ancient Greek language, it represented a voiced dental plosive [d].
A river delta is named after the letter delta because it has roughly the triangular shape of the upper-case delta.
The upper-case letter Δ can be used to denote:
{y_2-y_1over x_2-x_1} = {Delta y over Delta x} = the average change of y per unit x commonly known as the change of y over the change of x.
Delta f = sum_{i=1}^n {frac{partial^2}{partial x_i^2}}
Delta = b^2 - 4ac,!
The lower-case letter δ can be used to denote:

The difference operator, effecting a change or difference between mathematical values:
By extension of the above, change generally, a use which shows up frequently in medical charts.
The Laplace operator:
The discriminant of the quadratic equation:
A macroscopic change in the value of a variable in mathematics or science.
Any of the delta particles in particle physics.
That an associated locant number represents the location of a covalent bond in an organic compound, the position of which is variant between isomeric forms.
In legal shorthand, it represents a defendant.
In genetics, it can stand for a gene deletion, e.g. the CCR5-Δ32 a deletion of the CCR5 at the 32nd bp segment.
In medical shorthand, it can stand for change of any type.
An infinitesimal change in the value of a variable in mathematics or science.
An auxiliary function in Calculus used to rigorously define the limit or continuity of a given function.
The Kronecker delta in mathematics.
The Dirac delta function in mathematics.
Deflection in engineering mechanics
Text requiring deletion in proofreading. The usage is said to date back to classical times.
The relative electronegativity of different atoms in a molecule, δ

Wednesday, January 2, 2008


Thanks to its hardy nature, pottery bulks large in the archaeological record of Ancient Greece, and because we have so much of it (some 100,000 vases are recorded in the Corpus vasorum antiquorum) it has exerted a disproportionately large influence on our understanding of Greek society. Little survives, for example, of ancient Greek painting except for what is found on the earthenware in everyday use, so we must trace the development of Greek art through its vestiges on a derivative art form. Nevertheless the shards of pots discarded or buried in the first millennium BCE are still the best guide we have to the customary life and mind of the ancient Greeks.

Development of Vase Painting
Vases of protogeometrical period (c. 1050-900 BCE.) represent the return of craft production after the collapse of the Mycenaean Palace culture and the ensuing Greek dark ages. Indeed, it is one of the few modes of artistic expression besides jewellery in this period since the sculpture, monumental architecture and mural painting of this era are unknown to us. Yet by 1050 BC life in the Greek peninsula seems to have become sufficiently settled to allow a marked improvement in the production of earthenware. The style is confined to the rendering of circles, triangle, wavy lines and arcs, but placed with evident consideration and notable dexterity, probably aided by compass and multiple brush. The site of Lefkandi is our chief source of ceramics from this period where a cache of grave goods has been found giving evidence of a distinctive Euboian protogeometric. Attic production was the first to resume and influence the rest of Greece, especially Boeotia, Corinth, the Cyclades (in particular Naxos) and the Ionian colonies in the east Aegean.

Protogeometric Style
Geometrical art flowered in the 9th and 8th centuries BC. It was characterized by new motifs, breaking with the iconography of the Minoan and Mycenean periods: meanders, triangles and other geometrical decoration (from whence the name of the style) as distinct from the predominantly circular figures of the previous style. The best examples we have were grave goods, which often allows us to differentiate Attic, other mainland and island styles since we may assume they were produced in a batch for the sole purpose of burial. However our chronology comes from exported wares found in datable contexts overseas.
With the Early geometrical style (approximately 900-850 BCE) one finds only abstract motifs, in what is called the "Black Dipylon" style, which is characterized by an extensive use of black varnish, with the Middle Geometrical (approx. 850-770 BCE), figurative decoration makes its appearance: they are initially identical bands of animals (horses, stags, goats, geese, etc) which alternate with the geometrical bands. In parallel, the decoration becomes complicated and becomes increasingly ornate; the painter feels reluctant to leave empty spaces and fills them with meanders or swatiskas. This phase is named horror vacui and will not cease until the end of geometrical period.
In the middle of the century there begin to appear human figures. The best known representations of which are those of the vases found in Dipylon, one of the cemeteries of Athens. The fragments of these large funerary vases show mainly processions of chariots or warriors or of the funerary scenes: πρόθεσις / prothesis (exposure and lamentation of dead) or ἐκφορά / ekphora (transport of the coffin to the cemetery). The bodies are represented in a geometrical way except for the calves, which are rather protuberant. In the case of soldiers, a shield in form of a Diabolo, called "Dipylon shield" because of its characteristic drawing, covers the central part of the body. The legs and the necks of the horses, the wheels of the chariots are represented one beside the other without perspective. The hand of this painter, so called in the absence of signature, is the Dipylon Master, could be identified on several pieces, in particular monumental amphorae.
At the end of the period there appear representations of mythology, probably at the moment when Homer codifies the traditions of Trojan cycle in the Iliad and the Odyssey. Here however, the interpretation constitutes a risk for the modern observer: a confrontation between two warriors can be as well a Homeric duel as a simple combat; a failed boat can represent the shipwreck of Odysseus or any hapless sailor.
Lastly, we have the local schools that appear in Greece. Production of vases was largely the prerogative of Athens - it is well attested that as in the proto-geometrical period, in Corinth, Boeotia, Argos, Crete and Cyclades, the painters and potters were satisfied to follow the Attic style. From about the 8th century BC on, they created their own styles, Argos specializing in the figurative scenes, Crete remaining attached to a more strict abstraction.

Geometric Style
see also Orientalizing Period
The orientalizing style was the product of cultural ferment in the Aegean and Eastern Mediterranean of the 7th century BC and 8th century BC. Fostered by trade links with the city-states of Asian Minor the artifacts of the East influenced a highly stylized yet recognizable representational art. Ivories, pottery and metalwork from the Neo-Hittite principalities of northern Syria and Phoenicia found their way to Greece, as did goods from Anatolian Urartu and Phrygia, yet there was little contact with the cultural centers of Egypt or Assyria. The new idiom developed initially in Corinth and later in Athens between circa 725 BC to 625 BC. It was characterized by an expanded vocabulary of motifs: sphinx, griffin, lions, etc, as well as a repertory of non-mythological animals arranged in friezes across the belly of the vase. In these friezes the painter also from now on applies lotuses or palmettes. Depictions of humans were relatively rare; of these we most commonly find figures in silhouette with some incised detail, this was perhaps the origin of the incised silhouette figures of the black-figure period. There is sufficient detail on these figures to allow us to discern a number of different artist's hands. Geometrical features remained in the style called proto-Corinthian that embraced these orientalizing experiments, yet which co-existed with a conservative sub-geometric style.
The ceramics of Corinth were exported all over Greece, and their technique arrived in Athens, prompting the development of a less markedly eastern idiom there. During this time described as protoattic, the orientalizing motifs appear but the features remain not very realistic. The painters show a preference for the typical scenes of the Geometrical Period, like the procession of chariots. However, they adopt the principle of line drawing to replace the silhouette. In the middle of 7th century BC there appears the black and white style: black figures on a white zone, accompanied by polychromy to render the color of the flesh or clothing. Clay used in Athens was much more orange than that of Corinth, and so did not lend itself as easily to the representation of flesh.
Crete, and especially the islands of the Cyclades, are characterized by their attraction to the vases known as "plastic", i.e. whose paunch or collar is moulded in the shape of head of an animal or a man. At Aegina, the most popular form of the plastic vase is the head of the griffin. The Melanesian amphoras, manufactured at Paros, exhibit little knowledge of Corinthian developments. They present a marked taste for the epic composition and a horror vacui, which is expressed in an abundance of swastikas and meanders.
Finally one can identify the last major style of the period, that of Wild Goat Style, allotted traditionally to Rhodes because of an important discovery within the necropolis of Camiros. In fact, it is widespread over all of Asia Minor, with centers of production at Miletos and Chios. Two forms prevail: oenochoes, which copied bronze models, and dishes, with or without feet. The decoration is organized in superimposed registers in which stylized animals, in particular of feral goats (from whence the name) pursue each other in friezes. Many decorative motifs (floral triangles, swastikas, etc.) fill the empty spaces.

Orientalizing Style
see also Black-figure pottery
The black-figure period coincides approximately with the era designated by Winkelmann as the middle to late Archaic, from c. 620 to 480 BCE. The technique of incising silhouetted figures with enlivening detail which we now call the black-figure method was, as we saw, a Corinthian invention of the 7th century and spread from there to other city states and regions including Sparta, Boeotia, Euboea, the east Greek islands and most importantly Athens.
The Corinthian fabric, extensively studied by HGG Payne and Darrell Amyx, can be traced though the parallel treatment of animal and human figures. The Animal motifs have greater prominence on the vase and show the greatest experimentation in the early phase of Corinthian black-figure. As Corinthian artists gained in confidence in their rendering of the human figure the animal frieze declined in size relative to the human scene during the middle to late phase. By the mid 6th century BC the quality of Corinthian ware had fallen away significantly to the extent that some Corinthian potters would disguise their pots with a red slip in imitation of superior Athenian ware.
It was to be at Athens that black-figure would reach its full potential. It is at Athens we first find the phenomenon of vase painters signing their work, the first known being a Dinos by Sophilos (illus. below, BM c. 580), this perhaps indicative of their increasing ambition as artists in producing the monumental work demanded as grave markers, as for example with Kleitias's François Vase. The finest work in the style belongs to Exekias and the Amasis Painter whose feeling for composition and narrative mark them out from the jobbing artisans of their contemporaries.
Circa 520 BC the red-figure technique was developed and was gradually introduced in the form of the bilingual vase by those trailblazers the Andokides Painter, Oltos and Psiax. Red-figure quickly eclipsed black-figure yet in the unique form of the Panathanaic Amphora black-figure continued to be utilised well into the 4th century BCE.

Black Figure
see also Red-figure pottery
The innovation of the red-figure technique was an Athenian invention of the late 6th century, the ability to render detail by direct painting rather than incision offered new expressive possibilities to artists such as three-quarter profiles, greater anatomical detail and the representation of perspective. The first generation of red-figure painters worked in both red and black-figure as well as other methods including Six's technique and white ground; the latter was developed at the same time as red-figure. However within 20 years experimentation had given way to specialization as seen in the vases of the Pioneer Group whose figural work was exclusively in red-figure, though they retained the use of black-figure for some early floral ornamentation. The Pioneers deserve particular note not just because they are significant artists in their own right (Euphronios and Euthymides especially) but because their shared values and goals signal that they were something approaching a self-conscious movement though they left behind no testament other than their own work. John Boardman said of them "the reconstruction of their careers, common purpose, even rivalries, can be taken as an archaeological triumph"
The next generation of late Archaic vase painters (ca. 500 to 480 BCE.) brought an increasing naturalism to the style as seen in the gradual change of the profile eye. This phase also sees the specialization of painters into pot and cup painters, with the Berlin and Kleophrades Painters notable in the former category and Douris and Onesimos in the latter.
By the early to high classical era of red-figure painting (c. 480 to 425 BCE) a number of distinct schools had evolved. The mannerists associated with the workshop of Myson and exemplified by the Pan Painter hold to the archaic features of stiff drapery and awkward poses and combine that with exaggerated gestures. By contrast the school of the Berlin Painter in the form of the Achilles Painter and his peers (who may have been the Berlin Painter's pupils) favoured a naturalistic pose usually of a single figure against a solid black background or of restrained white-ground lekythoi. With the school of the Niobid Painter we can include Polygnotos and the Kleophon Painter whose work indicates something of the influence of the Parthenon sculptures both in theme (i.e Polygnotos's centauromachy, Brussels, Musées Royaux A. & Hist., A 134) and in feeling for composition.
Towards the end of the century the so-called Rich style of Attic sculpture as seen in the Nike Balustrade is reflected in contemporary vase painting with an ever greater attention to incidental detail (hair, jewelery, etc). The Meidias Painter is usually most closely identified with this style.
Vase production in Athens stopped around 330-320 BCE possibly due to Alexander's control of the city, and had been in slow decline over the 4th century along with the political fortunes of Athens herself. However vase production continued in the 4th and 3rd centuries in the Greek colonies of southern Italy where five regional styles may be distinguished. These are the Apulian, Lucanian, Sicilian, Campanian and Paestan. Red-figure work flourished there with the distinctive addition of polychromatic painting and in the case of the Black Sea colony of Panticapeum the gilded work of the Kerch Style.

Red Figure
see also Hellenistic art
The Hellenistic period (which we take to be roughly the late 4th century to the 1st century BC) is one of cultural decline in the traditional centres of Greek pottery production. Red-figure painting had died out in Athens by the end of the 4th century BC to be replaced by what is known as West Slope ware, so named after the finds on the west slope of the Athenian Acropolis. This latter style consisted of painting in a tan coloured slip and white paint on a black glaze background with some incised detailing, representations of people diminished with this idiom to be replaced with simpler motifs such as wreaths, dolphins, rosettes, etc. Variations of this style spread throughout the Greek world with notable centres in Crete and Apulia, where figural scenes continued to be in demand, indeed leadership in vase production of this time passed to the Greek colonies of southern Italy as witnessed by both the quantity and quality of the work done there. Several noteworthy artists' work comes down to us including the Darius Painter and the Underworld Painter, both active in the late 4th century, whose crowded polychromatic scenes often essay a complexity of emotion not attempted by earlier painters. Their work represents a late mannerist phase to the achievement of Greek vase painting.

Hellenistic Period

Manufacture
Greece enjoys ample deposits of fine clay, in particular large quantities of good quality secondary clay. The clay around Athens is distinctive for its infusion with iron oxide (Fe2O3) which when fired gives a reddish-orange colour. This marks it out from the clays of other regions such as Corinth where the pottery has a lighter, creamy-white appearance. Indeed spectroscopy and other methods has revealed unexpected connections amongst vases distributed around the Mediterranean basin, as in the case of the hydriai from Hadra near Alexandria. Previously thought to be Egyptian in origin analysis of their chemical composition has shown them to have been imported from a workshop in Rhodes.
Primary clay was rarer and used sparingly mostly as an accessory colour in decoration, for example on white ground vases where it was applied in a thin uniform layer while the pot was on the wheel. All clay was purified through sedimentation in order to remove such impurities as quartz and limestone as would cause spalling or cracking during firing, and to increase the malleability of the clay in the potter's hands.

Material
Wheelmade pottery dates back to roughly 2500 BCE where before the coil method of building the walls of the pot was employed. Most Greek vases were wheelmade, though as with the Rhyton mould-made pieces (so-called "plastic" pieces) are also found and decorative elements either hand formed or by mould were added to thrown pots (the handles on a volute crater for instance). More complex pieces were made in parts then assembled when it was leather hard by means of joining with a slip, whereupon the potter returned to the wheel for the final shaping, or turning. It was then glazed and incised ready for the kiln.

Construction
The striking black metallic glaze (strictly speaking it is a gloss not a glaze) so characteristic of Greek pottery was a fine suspension of the same clay that was used for the rest of the vase with no added colouration, only levigated in alkaline water. The effect was achieved by of means changing the amount of oxygen present during firing. This was done in a single cycle, first the kiln was heated to around 800° C when a vent is opened bringing oxygen into the firing chamber and turning pot and glaze a reddish-brown. Then as the temperature increased to about 950° C the vent was closed and green wood introduced creating carbon monoxide which formed black ferrous oxide or magnetic oxide of iron with the ferric oxide in the clay. In the final reoxidizing phase the kiln was gradually cooled to around 900° C and a little oxygen reintroduced causing the unglazed reserved clay to go back to orange-red, the glazed surface was sintered and could no longer be oxidized and remained black.

Firing
Inscriptions on Greek pottery are of two kinds; the incised (graffito) the earliest of which are contemporary with the beginnings of the Greek alphabet in the 8th century BC, and the painted (dipinto), which only begin to appear a century later. Both forms are relatively common on painted vases until the Hellenistic period when the practice of inscribing pots seems to die out. They are by far most frequently found on Attic pottery where approximately one in ten (some 8,000 to 10,000) bears a legend.
A number of sub-classes of inscription can be distinguished. Potters and painters occasionally signed their works with epoiesen and egraphsen respectively. Trademarks are found from the start of the 6th century on Corinthian pieces; these may have belonged to an exporting merchant rather than the pottery workshop (as with much of the rest of the study in this field this remains a matter of conjecture.) Patron's names are also sometimes recorded, as are the names of characters and objects depicted. At times we may find a snatch of dialogue to accompany a scene, as in 'Dysniketos's horse has won', announces a herald on a Panathenaic amphora (BM, B 144). More puzzling, however, are the kalos and kalee inscriptions, which might have formed part of courtship ritual in Athenian high society, yet are found on a wide variety of vases not necessarily associated with a social setting. Finally there are abecedaria and nonsense inscriptions, though these are largely confined to black-figure pots.
Some of the leading vase painters of Athens, such as the Pioneer Group, seem to have revelled in adding text to their vases and it is a testament to their literacy and cultural daring that they did so. Undoubtedly it places them in a class apart from other ancient Greek artisans.

Inscriptions
Interest in Greek art lagged behind the revival of classical scholarship during the Renaissance and revived in the academic circle round Nicholas Poussin in Rome in the 1630s. Though modest collections of vases recovered from ancient tombs in Italy were made in the 15th and 16th centuries these were regarded as Etruscan. It is possible that Lorenzo de Medici bought several Attic vases directly from Greece; however the connection between them and the examples excavated in central Italy was not made until much later. Winckelmann's 'Geschichte der Kunst des Alterthums of 1764 first refuted the Etruscan origin of what we now know to be Greek pottery, yet Sir William Hamilton's two collections, one lost at sea the other now in the British Museum, were still published as "Etruscan vases"; it would take until 1837 with Stackelberg's Gräber der Hellenen to conclusively end the controversy.
Much of the early study of Greek vases took the form of production of albums of the images they depict, however neither D'Hancarville's nor Tischbein's folios record the shapes or attempt to supply a date and are therefore unreliable as an archaeological record. Serious attempts at scholary study made steady progress over the 19th century starting with the founding of the Instituto di Corrispondenza in Rome in 1828(later the German Archaeological Institute), followed by Eduard Gerhard's pioneering study Auserlesene Griechische Vasenbilder (1840 to 1858), the establishment of the journal Archaeologische Zeitung in 1843 and the Ecole d'Athens 1846. It was Gerhard who first outlined the chronology we now use, namely: Orientalizing (Geometric, Archaic), Black Figure, Red Figure, Polychromatic (Hellenistic). Finally it was Otto Jahn's 1854 catalogue Vasensammlung of the Pinakothek, Munich, that set the standard for the scientific description of Greek pottery, recording the shapes and inscriptions with a previously unseen fastidousness. Jahn's study was the standard textbook on the history and chronology of Greek pottery for many years, yet in common with Gerhard he dated the introduction of the red figure technique to a century later than was in fact the case. This error was corrected when the Aρχαιολογικη 'Εταιρεια undertook the excavation of the Acropolis in 1885 and discovered the so-called "Persian debris" of red figure pots destroyed by Persian invaders in 480 BC. With a more soundly established chronology it was possible for Adolf Furtwängler and his students in the 1880s and 90s to date the strata of his archaeological digs by the nature of the pottery found within them, a method of seriation Flinders Petrie was later to apply to unpainted Egyptian pottery.
Where the 19th century was a period of discovery and the laying out of first principles the 20th century has been one of consolidation and intellectual industry. Efforts to record and publish the totality of public collections of vases began with the creation of the Corpus vasorum antiquorum under Edmond Pottier and the Beazley archive. It is to John Beazley's comprehensive studies Attic Red-Figure Vase Painters 1942 and Attic Black-Figure Vase Painters 1956 we owe the naming of dozens of previously forgotten artists by Morellian stylistic analysis. Similarly Arthur Dale Trendall and Humfrey Payne along with Darrell A. Amyx supplied the chronology to the otherwise neglected Apulian and Corinthian schools.

Uses and Types of Ancient Greek pottery

Typology of Greek Vase Shapes
Minoan pottery
Black-figure pottery
Red-figure pottery
List of Greek Vase Painters
Greek Terracotta Figurines
Tanagra figurine Pottery of ancient Greece Notes

John Beazley, Attic Black-Figure Vase Painters, Oxford University Press, Oxford, 1956.
John Beazley, Attic Red-Figure Vase Painters, Oxford University Press, Oxford, 1942.
John Beazley, The Development of Attic Black-Figure, University of California, 1951.
John Beazley, Paralipomena, Oxford University Press, Oxford, 1971.
John Boardman, Athenian Black figure Vases, London, 1974.
John Boardman, Athenian Red Figure Vases, London, 1975.
Coldstream, J.N., Geometric Greece 900-700 BC, London 2003 (Second Edition).
Martin Robinson, The Art of Vase-Painting in Classical Athens, Cambridge, 1992.
Arthur Dale Trendall, Red figure Vases of South Italy and Sicily, London, 1989.

Tuesday, January 1, 2008


Data in everyday language is a synonym for information. In the exact sciences there is a clear distinction between data and information, where data is a measurement that can be disorganized and when the data becomes organized it becomes information. Data may relate to reality, or to fiction as in a fictional movie. Data about reality consists of propositions. A large class of practically important propositions are measurements or observations of a variable. Such propositions may comprise numbers, words or images.

Data Etymology
In English, the word datum is still used in the general sense of "something given", and more specifically in cartography, geography, geology, NMR and drafting to mean a reference point, reference line, or reference surface. The Latin plural data is also used as a plural in English, but it is perhaps more commonly treated as a mass noun and used in the singular, at least in day-to-day usage. For example, "This is all the data from the experiment". This usage is inconsistent with the rules of Latin grammar, which would suggest, "These are all the data from the experiment" instead; each measurement or result is a single datum. Many (perhaps most) academic, scientific, and professional style guides (e.g., see page 43 of the World Health Organization Style Guide) request that authors treat data as a plural noun.

Usage in English

Main article: Data (computing)