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109-488: Only the western part of the sanctuary has been excavated, which consists of an upper area and three terraces, centring on a small temple for the hero Triptolemus , an outer propylon (gateway) and a South Stoa. A circular building in the southernmost part of the sanctuary might be a banqueting hall dedicated to Plouton and a precinct at the northernmost edge of the area might have belonged to Hecate . Sculptural fragments have been discovered from an inner propylon which led to

218-409: A closed polygonal chain . The segments of a closed polygonal chain are called its edges or sides . The points where two edges meet are the polygon's vertices or corners . An n -gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. More precisely, the only allowed intersections among the line segments that make up

327-500: A 1.5 metre wide cutting runs the whole length of the stoa. Conglomerate blocks sat in this cutting supported the front steps and columns. The short western exterior wall had bases for mounting inscriptions, which could be read by passers-by on the Panathenaic Way. Destruct debris shows that the stoa went out of use in the late fourth century. By the 6th century, parts of its structure had been incorporated into new buildings and

436-466: A ball for the head that was pinched to make the nose. Sometimes breasts were added. They differ from the figurines found in contemporary deposits elesewhere in the Agora, which are mostly horses and shields. A pottery vessel called a plemochoe ( Ancient Greek : πλημοχόη ) is a common votive find in the sanctuary from the beginning of the 4th century BC until the end of the 2nd century BC. They consist of

545-403: A city, which Eumelus named Aroe from the tilling of soil or fertile land. The son of Eumelus, Antheias, attempted to sow the seed of agriculture himself by using the dragon drawn chariot while Triptolemus slept, but Antheias fell from the car and was killed. Eumelus and Triptolemus then founded another nearby city and named it Antheia for his lost son. Triptolemus is credited with teaching

654-417: A diameter of 7.75-8.00 metres, but the blocks of the wall come from an Archaic or Classical structure which was also circular, but larger, with a diameter of about 19 metres. This earlier structure must have been located somewhere else. The floor was packed clay and at the exact centre of the room, a 1.35 metre wide millstone was set in the floor. There are no internal supports for a roof, so it may have been

763-514: A female deity at this time. The absence of signs of habitation in the area may indicate that it was already a sacred site before this. The upper terrace was enclosed by the Archaic peribolos wall ca. 575-550 BC. This may have been the work of the tyrant Peisistratus , but this is not certain; it may pre-date him. No literary sources refer to a connection between him and the Eleusinian cult. At

872-494: A given perimeter, the one with the largest area is regular (and therefore cyclic). Many specialized formulas apply to the areas of regular polygons . The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by This radius is also termed its apothem and is often represented as a . The area of a regular n -gon in terms of the radius R of its circumscribed circle can be expressed trigonometrically as: The area of

981-427: A high foot supporting a wide bowl, ranging in diameter from 0,024 metres to 0.26 metres, with a handle on either side. Originally they had peaked lids with holes in them. They are rarely decorated and are made of soft or coarse clay, suggesting that they were only intended to be used once. They are depicted on the relief from the inner propylon and a similar relief from Eleusis. A large marble plemochoe (0.62 metres high)

1090-509: A marsh, was created at the end of the 6th century BC with the rubble from clearing the middle terrace of houses. It was outside the peribolos wall of the Eleusinion and it is unclear whether it was part of the sanctuary. A 6-meter-long east–west wall at the western end of this terrace, just north of the retaining wall, was built in the fourth century BC, it may have been the peribolos for a small adjunct shrine, of which no trace now remains. In

1199-522: A ramp had been built through the back wall to allow access to the east–west road behind it. A circular building was constructed 17.2 metres south of the South Stoa in Section II. It is known from a circular cutting in the bedrock and part of a poros wall, preserved to a height of 0.52 metres. The bedrock around the structure was smoothed down to create a flat area. The cutting indicates that it had

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1308-401: A regular n -gon inscribed in a unit-radius circle, with side s and interior angle α , {\displaystyle \alpha ,} can also be expressed trigonometrically as: The area of a self-intersecting polygon can be defined in two different ways, giving different answers: Using the same convention for vertex coordinates as in the previous section, the coordinates of

1417-623: A second-story balustrade or from the western and eastern walls. At the east end, the back wall is preserved to a height of 2.75 metres. The interior floor was a layer of beaten earth, which slowly wore away until visitors were walking directly on the bedrock. Three phases of construction are attested in the back (south) wall. In the first, preserved for the western 18.5 metres, the foundation was built from regular yellow poros orthostates (0.65 metres high, 1.15 metres long, 0.42 metres thick), connected together with wooden clamps, and topped by dressed masonry. A second-century BC date for this initial phase

1526-470: A simple flat structure of timber. Remains of at least five altars were found nearby, confirming that the building served a religious function. Margaret Miles suggests that it was used for ritual dining. This is supported by the discovery of large amounts of cooking ware in the area. A well on the east side of the building may have been connected with this function. In particular, the circular building may have been linked with meals held in honour of Plouton, who

1635-399: A simple formula for the polygon's area based on the numbers of interior and boundary grid points: the former number plus one-half the latter number, minus 1. In every polygon with perimeter p and area A , the isoperimetric inequality p 2 > 4 π A {\displaystyle p^{2}>4\pi A} holds. For any two simple polygons of equal area,

1744-564: A solid polygon. A polygonal chain may cross over itself, creating star polygons and other self-intersecting polygons . Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon ), even when the chain does not lie in a single plane. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. There are many more generalizations of polygons defined for different purposes. The word polygon derives from

1853-491: A source of purifying water, a shrine called the Tomb of Immaradus , and a Ploutonion. The sanctuary consists of an upper area and three terraces, descending down the slope from south to north. The original sanctuary consisted of only section II and the upper terrace, but it was later expanded to incorporate the middle terrace. It is unclear whether the lower terrace was actually part of the sanctuary. The upper (southernmost) area

1962-510: A stele on the outer west side of the sanctuary. The section of the Panatheniac Way running along the west side of the sanctuary was lowered and paved in two stages in the first and second centuries AD. A branch from the aqueduct of Hadrian was built behind the sanctuary in the mid-second century AD. In the same period, the inner propylon seems to have been built and the circular building was renovated. The sanctuary's continued importance

2071-413: Is "Section II", a steep slope, located outside the peribolos wall, but apparently part of the original sanctuary area, since archaeological evidence reveals votive deposits. There is also a circular building of Hellenistic date. A vaulted branch of the aqueduct of Hadrian , built in the mid-2nd century AD, runs along the north side of the section, ultimately feeding into the nymphaeum in the southeast of

2180-427: Is 25.40 metres long, but the stoa continued further east into the unexcavated area. Fragments from the superstructure indicate that the steps were made of Hymettan marble, while the columns and entablature were Pentelic marble . The columns were roughly three metres apart and were probably Doric . It was probably only one story high, but this is not certain. A set of diamond and oval lattice window frames might come from

2289-408: Is asked to nurse their only son Demophon. Rather than nurse Demophon, Demeter anoints him with ambrosia , the food of the gods, breathes on him gently while holding him to her chest, and places him within the flames of fire during the night, all in an effort to make him immortal. Demeter is foiled in her plan in this retelling as well. Triptolemus was equally associated with the bestowal of hope for

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2398-747: Is both isogonal and isotoxal, or equivalently it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon . Euclidean geometry is assumed throughout. Any polygon has as many corners as it has sides. Each corner has several angles. The two most important ones are: In this section, the vertices of the polygon under consideration are taken to be ( x 0 , y 0 ) , ( x 1 , y 1 ) , … , ( x n − 1 , y n − 1 ) {\displaystyle (x_{0},y_{0}),(x_{1},y_{1}),\ldots ,(x_{n-1},y_{n-1})} in order. For convenience in some formulas,

2507-439: Is commonly called the shoelace formula or surveyor's formula . The area A of a simple polygon can also be computed if the lengths of the sides, a 1 , a 2 , ..., a n and the exterior angles , θ 1 , θ 2 , ..., θ n are known, from: 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

2616-421: Is enclosed by a polygonal limestone wall ("the Archaic peribolos "), built around 575-550 BC. It varied between 0.9 and 1.15 metres in thickness at the base; the whole 22 metre-long stretch is preserved on the western side; the foundation trench and shorter stretches are preserved on the northern and southern sides for 26 and 28 metres respectively. The eastern wall has not been uncovered. The original entrance to

2725-461: Is indicated by pottery in the fill of the foundations and by the absence of mortar . In the second stage, in the late Roman period, the orthostates were patched using irregular limestone blocks topped brick and mortar (preserved in the eastern portion). Finally, in Byzantine times, the wall was patched again with brick and stone, serving as a wall for later structures. At the north side of the stoa,

2834-535: Is known to have had a shrine in the City Eleusinion. It may also have been connected with the Thesmophoria. The structure was built in the 2nd century BC, as shown by pottery from the fill of the foundations. Fills from the northwestern and eastern sections show it was dismantled and rebuilt with the same plan but a new floor around AD 100, probably in connection with a new drainage system, which closed

2943-451: Is large, this approaches one half. Or, each vertex inside the square mesh connects four edges (lines). The imaging system calls up the structure of polygons needed for the scene to be created from the database. This is transferred to active memory and finally, to the display system (screen, TV monitors etc.) so that the scene can be viewed. During this process, the imaging system renders polygons in correct perspective ready for transmission of

3052-486: Is shown by the fact that they are rarely found in any context aside from the Eleusinion and the sanctuary of Demeter and Kore at Eleusis. In many cases they were buried in holes specifically cut for them in the bedrock, a chthonian setting, which corroborates the association with Plouton. From the fifth century BC through the 4th century AD, various individuals dedicated monuments in the sanctuary, mostly statues. Twenty-six inscribed bases from these statues are known, of which

3161-593: Is shown by the fact that, after the Herulian Sack in 267 AD, it was placed inside the Post-Herulian wall (much of the city, including most of the Agora was left outside this new circuit wall). That the sanctuary continued in use is shown by the fact that, unlike many other structures, it was not spoliated to provide building material for the wall. The Eleusinian cult remained active until at least 375 AD, but

3270-616: Is unlikely to have survived the Anti-pagan legislation of Theodosius I . The South Stoa and perhaps the Temple of Triptolemus were demolished at the end of the fourth century, probably as a result of Alaric the Goth 's sack of Athens in AD 396. The area was then covered over with houses and a laundry complex was built on the western end of the south stoa in the 7th century AD, taking advantage of

3379-461: The Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. However, if the polygon is simple and cyclic then the sides do determine the area. Of all n -gons with given side lengths, the one with the largest area is cyclic. Of all n -gons with

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3488-635: The Giant's Causeway in Northern Ireland , or at the Devil's Postpile in California . In biology , the surface of the wax honeycomb made by bees is an array of hexagons , and the sides and base of each cell are also polygons. In computer graphics , a polygon is a primitive used in modelling and rendering. They are defined in a database, containing arrays of vertices (the coordinates of

3597-456: The Greek adjective πολύς ( polús ) 'much', 'many' and γωνία ( gōnía ) 'corner' or 'angle'. It has been suggested that γόνυ ( gónu ) 'knee' may be the origin of gon . Polygons are primarily classified by the number of sides. Polygons may be characterized by their convexity or type of non-convexity: The property of regularity may be defined in other ways: a polygon is regular if and only if it

3706-558: The Thesmophoria festival. Two inscriptions from the late fourth century BC and one from the first century BC honour wealthy Athenian men for preparing ritual meals in honour of Plouton. From the late Hellenistic period, these meals may have been held in the circular building in section II. During the games at the Great Panathenaea festival, several cavalry races were held on the Panathenaic Way, with their end point at

3815-552: The clans of the Eumolpidae and Kerykes. The highest-ranking officials were the priestess of Demeter and Kore and the hierophant , both of whom came from the Eumolpid clan and held office for life. Andocides says that regulations for the Eleusinion were included in the mid-sixth century BC laws of Solon . Literary sources and inscriptions make regular references to regulations and ritual norms. These regulations tend to treat

3924-456: The geometrical vertices , as well as other attributes of the polygon, such as color, shading and texture), connectivity information, and materials . Any surface is modelled as a tessellation called polygon mesh . If a square mesh has n + 1 points (vertices) per side, there are n squared squares in the mesh, or 2 n squared triangles since there are two triangles in a square. There are ( n + 1) / 2( n ) vertices per triangle. Where n

4033-488: The regular star pentagon is also known as the pentagram . To construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows. The "kai" term applies to 13-gons and higher and was used by Kepler , and advocated by John H. Conway for clarity of concatenated prefix numbers in the naming of quasiregular polyhedra , though not all sources use it. Polygons have been known since ancient times. The regular polygons were known to

4142-399: The "Attic Stelae", which listed all the property, sales prices, and purchasers, were erected in the Eleusinion, where most of the 77 known fragments have been found. All the Eleusinian officials uttered curses against the convicts, except for the priestess of Demeter and Kore, Theano, who declared that she was "a praying priestess not a cursing priestess." A series of inscribed accounts describe

4251-400: The 1st century AD, the area was flattened and a complex was built on the western edge of the terrace, consisting of four rooms, three bases for monuments or altars, and an offering table. This complex may have been a workshop, a separate sanctuary, or - most likely - a set of storerooms for the Eleusinion's grain supply. The northern edge of the lower terrace was bound by an east–west street from

4360-507: The 3rd century to the early 1st century BC is also the time when most of the honorific decrees were erected in the sanctuary - seventeen are known, mostly honouring epimeletai (organisers) of the Eleusinian Mysteries. The Panhellenion , established by Emperor Hadrian in 131/2 AD, seems to have had a role in the administration of the Eleusinion and the Eleusinian cult. They had a letter from an Imperial official inscribed on

4469-473: The 4th century BC. Three depict Triptolemus; others show the Eleusinian heroes Iacchus, Eubouleus, and Ploutus; and two show Hecate . There are also fragments from two marble torches. By the second century BC, the priestesses of Demeter and Kore had the right to erect a painted portrait of themselves in the temple of Demeter and Kore. The administration of the Eleusinion was regulated by the Athenian state and

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4578-481: The 6th century BC until the Ottoman period. Abutting this street and the Panathenaic Way, in the northwest corner of the sanctuary, was a small precinct, probably for Hecate . The temple faces north–south and is 17.813 m long and 11.065 metres wide. The entrance was at the south end (i.e. opening onto the upper terrace). Traces of the foundation and roof have been found; nothing from the superstructure survives, but it

4687-469: The Acropolis were also used in the walls. Because of the steepness of the slope, the south end of the temple sits directly on the bedrock, while the north end required ten courses of masonry. The cuttings in the bedrock for the temple's foundations are still visible on the western side. The foundations were built of high-quality polygonal masonry, without clamps or dowels. The foundation blocks survive for

4796-472: The Agora. To the south of that was a narrow Roman road, which led to a gate in the Post-Herulian wall. The upper terrace, formed by a flat section of bedrock was the original core of the sanctuary. It contains a "rocky outcrop" at the western edge, which is 2 metres wide, 3 metres long and rises above the surrounding area. Such outcrops were often important in cults of Demeter throughout the Greek world. The area

4905-487: The City Eleusinion, a smaller Eleusinion at Phalerum , and the sanctuary at of Demeter and Kore at Eleusis as a single unit. The surviving inscribed regulations from the City Eleusinion are: Numerous decrees whose topics touched in Eleusinian matters were also erected in the sanctuary. Thirty such decrees have been found, of which between 17 and 21 are honorific. Most of these belong to the Hellenistic period and honour

5014-415: The Eleusinian cult are found throughout the Agora, but they cluster mainly in the area of the Eleusinion. Three inscriptions found in the area specifically state that they were to be set up in the Eleusinion. These factors confirm the identification of the site as the Eleusinion. Pausanias describes the sanctuary in the 2nd century AD, as containing two temples, one for Demeter and Kore ( Persephone ) and

5123-572: The Eleusinion by the ephebes . They were stored there for the first five days of the festival. During this time people who wished to be initiated into the Eleusinian mysteries gathered in the Eluesinion to undergo the "pre-initiation" ( myesis ) under the guidance of members of the two Eleusinian clans , the Eumolpidae and the Kerykes . Aside from this, non-initiates were not allowed to enter

5232-401: The Eleusinion. In the second century BC, these included a chariot race and the apobates . Seventh century BC votive deposits consist of terracotta figurines, miniature vessels, pottery, spindles, loomweights, and disks. The figurines are called "columnar females" because the body is formed from a long column that flares out at the bottom to represent a skirt. There are two outstretched arms and

5341-567: The National Museum, Athens ( illustration ), which probably came from his temple, the boy Triptolemus stands between the two Goddesses, Demeter and the Kore , and receives from Demeter a golden ear of grain (now lost). Triptolemus was given three commandments to living a simple and pious life: "Honor your parents", "Honor the gods with fruits"—for the Greeks, this includes grains—and "Spare

5450-578: The Post-Herulian Wall was built in the late third century AD. The southern limit is the perimeter road running around the upper slopes of the Acropolis. The northern boundary was the northern branch of the Street of the Tripods . The distance from north to south is about 200 metres. The eastern border is unknown, but may have been up to 200 metres from the western edge. The general location of

5559-750: The Post-Herulian wall was uncovered (which was largely constructed of classical sculpture, masonry, and inscriptions), as well as the retaining wall above the temple of Triptolemus. Pittakis believed the site was part of the grounds of the Bouleuterion (town council). A minor excavation was undertaken by Konstantinos Kourouniotis  [ de ] in 1910. Triptolemus Triptolemus / ˌ t r ɪ p ˈ t ɒ l ɪ m ə s / ( Greek : Τριπτόλεμος , romanized :  Triptólemos , lit.   'Tripartite warrior'), also known as Buzyges ( Greek : Βουζύγης , romanized :  Buzyges , lit.   'Bull-hitcher'),

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5668-459: The Rharium plane near Eleusis was the first place to be sown for crops. Triptolemus is depicted as a young man with a branch or diadem placed in his hair, usually sitting on his chariot, adorned with serpents . His attributes include a plate of grain, a pair of wheat or barley ears and a scepter . Triptolemus' first introduction to Demeter is during Demeter's search for her daughter following

5777-452: The abduction of Persephone . While Demeter , in the guise of an old woman named Doso, was searching for her daughter Persephone (Kore), who had been abducted by Hades (Pluto), she received a hospitable welcome from Celeus , the King of Eleusis. He asked her to nurse Demophon —"killer of men", a counterpart to Triptolemus— and Triptolemus, his sons by Metanira . Demeter saw Triptolemus

5886-603: The actual Temple of Demeter and Kore in the unexcavated area to the east and literary sources mention further structures. Many inscriptions, sculptures, pottery vessels, and other offerings from the sanctuary have been recovered. The sanctuary is located on the lower part of the northern slope of the Acropolis , just to the south of the Athenian Agora . The western boundary was the Panathenaic Way , along which

5995-523: The afterlife associated with the expansion of the Eleusinian Mysteries. Triptolemus traveled to Scythia on his dragon drawn chariot to teach King Lyncus and the Scythians the art of agriculture. Bearing the gifts of Demeter, he scattered seeds across Scythia so the realm may yelid a large harvest of good food. Lyncus grew envious of Triptolemus and his gift of agriculture, so he planned to murder Triptolemus while he slept, hoping that he could receive

6104-539: The ancient Greeks, with the pentagram , a non-convex regular polygon ( star polygon ), appearing as early as the 7th century B.C. on a krater by Aristophanes , found at Caere and now in the Capitoline Museum . The first known systematic study of non-convex polygons in general was made by Thomas Bradwardine in the 14th century. In 1952, Geoffrey Colin Shephard generalized the idea of polygons to

6213-455: The animals". Socrates names Triptolemus as one of the judges in the afterlife along with three sons of Zeus , Minos , Rhadamanthus , and Aeacus . Each of the judges had their own roles in the afterlife: Aeacus was the doorkeeper and judged the deceased of Europe, Rhadamanthus was the Lord of Elysium and judged the deceased of Asia, and Minos was to be the deal breaker if any indeceasion

6322-407: The archaic Homeric Hymn to Demeter , Triptolemus is briefly mentioned as one of the original priests of Demeter, one of the first men to learn the secret rites and mysteries of Eleusinian Mysteries : Diocles driver of horses, the mighty Eumolpos , Celeus leader of peoples, and Polyxeinus were the others mentioned as some of the first priests. According to Xenophon , Triptolemus first shares

6431-509: The archaic peribolos. The northern and western parts of the peribolos were covered over by a massive retaining wall in the 4th century BC. It may have supported a platform for viewing the Panathenaic procession. There were steps on the outer west face of this retaining wall for inscribed stelae. A 0.8 metre-wide dividing wall runs north–south to the east of the temple, diving the it off from the inner sanctuary. The lower terrace, originally

6540-429: The bedrock. In the centre, the foundations were covered over by Hymettan marble pavers, some of which survive. The date of construction is indicated by pottery sherds found in the packing of the foundations and by parallels with other Athenian structures of similar date. It precedes cuttings made into the bedrock to the west in order to lower and pave the Panathenaic Way in the first and second centuries AD. The propylon

6649-453: The centroid of a solid simple polygon are In these formulas, the signed value of area A {\displaystyle A} must be used. For triangles ( n = 3 ), the centroids of the vertices and of the solid shape are the same, but, in general, this is not true for n > 3 . The centroid of the vertex set of a polygon with n vertices has the coordinates The idea of a polygon has been generalized in various ways. Some of

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6758-532: The chariot dragons to be killed keep Triptolemus from escaping. Again Demeter came to Triptolemus' rescue, returning the chariot to him and replacing the lost dragon. Traveling from Attica , Triptolemus went to the city of Patrae located near the river Peirus and the river Glaucus . The land was ruled by Eumelus , who was said to be indigenous to the land, and he was king over few subjects. Triptolemus shared with him cultivated corn and taught him how to found

6867-522: The city of Athens are typical of those constructed under Hadrian, part of "an imperial Athenianisation of Eleusis." The site was occupied in the Neolithic period and in the Middle Bronze Age , because of the nearby Klepsydra spring . The middle terrace contained housing from ca. 850 BC, while the terracotta figurines found in the upper terrace indicate that it was a religious sanctuary for

6976-429: The comparative table. Triptolemus was said to be the ancestor to a royal priestly caste of the Eleusinian Mysteries, who claimed to be Buzygae (Βουζύγαι), that taught agriculture and performed secret rites and rituals, of which Pericles was its most famous descendant. Polygonal In geometry , a polygon ( / ˈ p ɒ l ɪ ɡ ɒ n / ) is a plane figure made up of line segments connected to form

7085-426: The complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons . Polygons appear in rock formations, most commonly as the flat facets of crystals , where the angles between the sides depend on the type of mineral from which the crystal is made. Regular hexagons can occur when the cooling of lava forms areas of tightly packed columns of basalt , which may be seen at

7194-412: The contents of the sanctuary in 408/7 BC, including many gold votives, as well as construction materials. A financial account from 329/8 BC describes extensive repairs to the Eleusinion in that year, as part of the wider revitalisation of Athens and its cults spearheaded by Lycurgus . This was also the period when most votive relief plaques were dedicated. In the second century BC, a major renovation to

7303-636: The cultivation of crops to the Pelasgian later known as the Arcadians. He taught Arcas , the son of Callisto and the King of Pelasgia (later Arcadia ) following the death of Nyctimus . The Eleusinian Mysteries were initiations held every year for the cult of Demeter and Persephone based at the Panhellenic Sanctuary of Eleusis in ancient Greece. They are considered the "most famous of the secret religious rites of ancient Greece". In

7412-512: The earliest is a dedication of two crowns by the priestess Lysistrate around 450 BC. Of the rest, eleven were dedicated in the 4th century BC, one in the 3rd century BC, five in the 2nd century BC, four in the 1st century BC (including a herm of Phaedrus the Epicurean ), and one each in the first four centuries AD. Nineteen pieces of sculpture have been recovered, including thirteen votive reliefs. Most of these depict Demeter and Kore and belong to

7521-467: The eastern well. A final set of fills show that it was partially dismantled in the late 2nd or 3rd centuries AD. The inner propylon, built in the mid-second century AD, was a monumental gateway leading from the outer sanctuary (the excavated area, centring on the Temple of Triptolemus) to the inner sanctuary centring on the Temple of Demeter and Kore, which was closed to non-initiates. The foundations of this structure have not been excavated, but fragments of

7630-403: The end of the sixth century or the beginning of the fifth century, the middle terrace was cleared of housing and added to the sanctuary, more than doubling its size. The first evidence specifically identifying the site as the Eleusinion are a pair of altars associated with the new temple, which are inscribed with the regulations of the Eleusinian Mysteries and date to ca. 510-500 BC. Construction of

7739-453: The first human to receive the gifts of farming and initiation into the Eleusinian Mysteries from Demeter. He then rode around the world in a winged chariot, informing all people of these gifts. Pausanias states that there was a statue of Triptolemus inside the temple. This has not been discovered archaeologically, but is probably one of the symbols depicted on fourth-century BC Panathenaic amphorae . There are examples from 364/3 onwards showing

7848-485: The inner part of the sanctuary, which was demarcated by the inner propylon. On the sixth day of the festival, a great procession took them back to Eleusis, where they were revealed to the initiates at the culmination of the mysteries. After the mysteries, the Council of Five Hundred met in the Eleusinion in order to review the conduct of the festival. The Eleusinion was probably also one of the sites where women celebrated

7957-480: The land on his chariot wafting the wheat through the air to sow crops across the inhabitied earth. Demeter and Persephone, once restored to her mother, cared for him, and helped him complete his mission of educating the whole world in the art of agriculture. In the Homeric Hymn to Demeter , Triptolemus is not a son of Celeus and Metanira but rather known as a king of Eleusis who served justice, and Demeter

8066-640: The masonry and sculpture have been found in the excavations and reused in the Little Metropolis . The fragments closely parallel those from the inner propylon of the sanctuary at Eleusis, which provides the basis for a reconstruction. The main sculptural fragments are two caryatids, which would have stood on the inner side of the gate, supporting a porch. A Doric frieze on the outside of the gate consisted of metopes and triglyphs with Eleusinian symbols ( poppies , myrtle , plemochoae , phialae , bucrania ). Parallels between structures at Eleusis and in

8175-833: The more important include: The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , 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. Beyond decagons (10-sided) and dodecagons (12-sided), mathematicians generally use numerical notation, for example 17-gon and 257-gon. Exceptions exist for side counts that are easily expressed in verbal form (e.g. 20 and 30), or are used by non-mathematicians. Some special polygons also have their own names; for example

8284-552: The notation ( x n , y n ) = ( x 0 , y 0 ) will also be used. If the polygon is non-self-intersecting (that is, simple ), the signed area is or, using determinants where Q i , j {\displaystyle Q_{i,j}} is the squared distance between ( x i , y i ) {\displaystyle (x_{i},y_{i})} and ( x j , y j ) . {\displaystyle (x_{j},y_{j}).} The signed area depends on

8393-423: The ordering of the vertices and of the orientation of the plane. Commonly, the positive orientation is defined by the (counterclockwise) rotation that maps the positive x -axis to the positive y -axis. If the vertices are ordered counterclockwise (that is, according to positive orientation), the signed area is positive; otherwise, it is negative. In either case, the area formula is correct in absolute value . This

8502-530: The organisers of the Eleusinian Mysteries. In the late fifth and fourth centuries BC, inscribed inventories listing all the cult's assets were erected annually by a board of epistatai , who were responsible for the finances of the Eleusinian cult. Following the chance discovery of some masonry blocks on 22 June 1848, Kyriakos Pittakis pushed for excavations, eventually undertaking exploratory excavations from 11 to 15 April 1851, which led to larger-scale excavations from 1851 to 1852. Houses were removed and part of

8611-500: The other for Triptolemus . There was a bronze statue of a bull in front of the latter. Pausanias says that he was forbidden from discussing the contents of the sanctuary in detail by a dream and says nothing about the temple of Demeter and Kore, but does describe the temple of Triptolemus. This seems to indicate that the sanctuary consisted of an inner, holier section containing the former temple and an outer, less holy section containing Triptolemus' temple. Other sources refer to an altar,

8720-408: The polygon are the shared endpoints of consecutive segments in the polygonal chain. A simple polygon is the boundary of a region of the plane that is called a solid polygon . The interior of a solid polygon is its body , also known as a polygonal region or polygonal area . In contexts where one is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to

8829-469: The praise for the harvest instead. Before Lyncus could enact his plan he was thwarted by Demeter who turned him into a lynx as punishment and sent Triptolemus back into the sky in her chariot. Triptolemus also traveled to the kingdom of Getae where he intended to continue to spread the art of agriculture and share grain with the people. The king of Getae, Charnabon (also spelt Carnabon ) made an attempt at Triptolemus' life, seized him and ordering one of

8938-451: The precinct was on the south side, 3 metres from the western end, opening onto "Section II". A second entrance was built on the same wall, 20 metres to the east, in the period 350-325 BC, possibly part of the construction work of 329/8 BC. In the Hellenistic period, the south peribolos wall was demolished and the South Stoa was built over the top of it, separating the upper terrace from "Section II" and sealing both entrances.A propylon (gateway)

9047-426: The processed data to the display system. Although polygons are two-dimensional, through the system computer they are placed in a visual scene in the correct three-dimensional orientation. In computer graphics and computational geometry , it is often necessary to determine whether a given point P = ( x 0 , y 0 ) {\displaystyle P=(x_{0},y_{0})} lies inside

9156-566: The rites of Demeter and Persephone with Heracles, the traditional ancestor of the Spartan kings, and the Dioscuri , twin deities Castor and Pollux . Celeus or the peasant Dysaules may be substituted for Triptolemus as the primordial Eleusinian recipient of the first gifts of the Mysteries. Triptolemus' role at Eleusis is unique as he was one of the first men to learn the mystic rites and

9265-423: The ritual because she was discovered burying the babe in the fire. Instead, Demeter gifted Triptolemus a chariot drawn by winged dragons or serpents and wheat, representative of the gift of agriculture. Demeter taught Triptolemus the art of agriculture and shared with him how to conduct her rites and taught him her mysteries. From Triptolemus, the rest of Greece learned to plant and reap crops as he flew across

9374-399: The roofs of the treasuries in the sanctuary of Apollo at Delos (478-450 BC). The archaeological remains are identified as the temple of Triptolemus mentioned by Pausanias because his account indicates that it was in the outer part of the sanctuary and archaeology shows that the entrance to the Eleusinion in his time was through the propylon next to this temple. In mythology, Triptolemus was

9483-534: The sanctuary took place, involving the construction of the South Stoa, the Hellenistic Propylon, and the circular building. Two inscriptions honour individuals for undertaking construction in the sanctuary at this time. One is fragmentary; the other honours Satyra priestess of the Thesmophori for repairing all the temples, the sanctuary of Plouton, and paying for annual sacrifices. The period from

9592-877: The sanctuary was known from references in Xenophon , Philostratus , scholia to Aristophanes , and especially Pausanias , who places it above the Enneakrounos (nine jets) fountain, which he locates in the south central Agora. The site was excavated as part of the American excavations of the Athenian Agora, in 1936-1939 and 1959–1960. Only a strip from the western edge of the sanctuary has been excavated, varying in width from 18 to 40 metres. Many structures known from literary sources have not been found and are presumed to be located further east, under modern housing. Inscriptions, sculpture, and votive vessels relating to

9701-413: The size of the sanctuary. The temple of Triptolemus stood here, with its entrance facing onto the edge of the upper stoa. The area was surrounded by the "early 5th-century peribolos wall," which is preserved in small stretches on the west and north. It is made of limestone and was 1.10 metres wide. The northern wall has been revealed for a length of 28 metres. The western wall was 21 metres long and continues

9810-430: The southern end, in the 2nd century BC, opening onto the Panathenaic Way. It served as the main entrance to the Eleusinion thereafter. It was a porch, with an H-shaped ground plan, i.e. two walls perpendicular to the peribolos wall which supported a roof, and a cross-wall between them, containing the actual doors. The foundations are consist of poros, conglomerate, and marble blocks - many of them reused - set directly into

9919-401: The statue standing in a winged chariot holding a branch, with a snake next to the chariots wheels. Pausanias also mentions statues of the semi-legendary seer Epimenides and of a bull in front of this temple. The latter probably depicted the bull with gilded horns which was the standard sacrificial offering for Triptolemus according to the late fifth-century First-Fruits decree . To the east of

10028-436: The temple between 500 and 490 BC, as shown by pottery evidence from the foundations. The remnants of the roof seem to date to 475-450 BC. This date coincides with the proliferation of images of Triptolemus in Athenian art. The chief of works may have been Coroebus , who also oversaw the construction of the 5th century Telesterion at Eleusis. The foundations are made of gray kara limestone , but yellow poros and limestone from

10137-527: The temple of Triptolemus began around 500, was interrupted by the Persian Wars , and was completed between 475 and 450 BC. Three deposits indicate that the sanctuary was damaged during the Persian sack of Athens in 479 BC. It is likely that a new temple of Demeter and Kore was built at this time as well, although there is no archaeological evidence for this, since it has not been excavated. The sanctuary

10246-403: The temple, there are the limestone foundations of altar (1.10 x 2.70 metres), probably built in ca. 500 BC. East of this is a 2.20 metre long monument base of yellow poros, running east–west, which was built in the period 450-425 BC; it seems to have been intended to support a set of inscribed stelae (no longer present). A propylon (gateway) was built into the peribolos wall on the west side, near

10355-467: The water supply still provided by the aqueduct of Hadrian. There was a large fire in the area in the reign of Constans II (641-668), which destroyed the laundry and would have seriously damaged any Classical structures that were still standing. Spoliation of masonry and sculpture from the area took place throughout the Byzantine and Ottoman periods, but especially in the 9th-10th centuries, when there

10464-405: The whole north side and parts of the western and eastern sides. The foundations of the cross-wall that separated the pronaos from the cella are partially preserved. An extension was added to the east side of the temple during construction, which measures 2.20-2.355 m wide and is composed of red crystalline blocks originally cut for use in some other context. The addition may have been made so that

10573-437: The width:length ratio of the temple would be closer to the golden ratio , which became popular in temple construction at this time. The remains of the roof consist of 88 fragments from marble tiles (30 cover tiles, 58 pan tiles, 1 end ridge tile) and 4 marble antefixes . The workmanship is of a very high standard. The palmettes of the antefixes resemble the archaic Telesterion at Eleusis (510-500 BC), and especially those from

10682-499: Was a hero of Eleusis in Greek mythology , central to the Eleusinian Mysteries and is worshipped as the inventor and patron of agriculture. Triptolemus is credited with being the first to sow seed for cultivation after being taught by Demeter and is credited for the use of oxen and the plough. Xenophon claims that Peloponnesus was the first place Triptolemus shared Demeter's agricultural gift while Pausanias claims

10791-479: Was a pupil of Demeter who was charged with bringing agriculture to humankind. Separate from the Mysteries, Triptolemus was thought to have a cult of his own as he had a temples dedicated to him in Athens and Eleusis. It is said that temples and alters were erected in his honor because he gave the people food by cultivation and shared with them the way to not only live but to live well. In the 5th-century bas-relief in

10900-424: Was a quarry on the lower terrace. The churches of Hypapanti and of Christ were built at the south and north ends of the area respectively, in the 17th century, incorporating the gates of the Post-Herulian wall and parts of the sanctuary into their foundations. The Church of Christ had fallen into ruin by the 1850s, but its northern wall is still in situ and its wall paintings are faintly visible. The Church of Hypapanti

11009-467: Was built into the peribolos wall on the west side, near the southern end, at the same time as the South Stoa was built, and served as the main entrance to the Eleusinion thereafter. The north edge was of the upper terrace was formed by a retaining wall 6.8 metres north of the Stoa, which was demolished in the 4th century AD. The middle terrace was added to the sanctuary at the end of the 6th century, doubling

11118-433: Was deconsecrated and demolished in 1936 to allow the excavations to take place. At the beginning of the nineteenth century, the area had a reputation as a good source of marble for use as building material. Marbles from the Eleusinion have been found in old buildings throughout the old centre of Athens, notably in the Little Metropolis . It remained a residential area until excavated in the twentieth century. The Eleusinion

11227-418: Was found in Section II of the Eleusinion, suggesting an association specifically with the shrine of Plouton. In processions, women carried them on top of their heads. According to Athenaeus , on the last day of the Eleusinian Mysteries two plemochoae were filled with liquid and then tipped over, one to the west and one to the east, while a magic formula was recited. Their close connection with the Eleusinian cult

11336-399: Was incorporated into the Post-Herulian Wall in the late third century AD. The South Stoa was added on the south side of the upper terrace in the second century BC, replacing the archaic peribolos. This stoa provided a sheltered area facing the temple of Triptolemus, which was used for dedications and for visitors to the sanctuary. It measures 8.90 metres from north–south. The excavated portion

11445-542: Was one of the few sites in Athens not to be occupied by refugees from the countryside at the outbreak of the Peloponnesian War , according to Thucydides , because its walls and gates allowed it to be locked. In 414 BC, following the conviction of Alcibiades and others for the profanation of the mysteries and mutilation of the Herms , their property was seized and auctioned off. A set of ten inscriptions known as

11554-401: Was probably made of marble, like the roof. Margaret Miles proposes that the dimensions and materials indicate that it was an Ionic tetrastyle amphiprostyle temple, i.e. with four Ionic columns at the north and south ends. This is the same design used for the later Temple of Athena Nike on the Acropolis. The columns would have been about 1.10 m in diameter at the base. Construction began on

11663-533: Was reached. Triptolemus was said to have rule over the deceased who were initiated into the mysteries. Triptolemus' parentage is highly debated across sources: He was either a mortal prince and the eldest son of King Celeus of Eleusis and Metanira or according to Pseudo-Apollodorus , Panyasis believed he was the son of Eleusis, while Pherecydes believed he was the son of the divine son of Gaia and Oceanus (Ocean and Earth). Multiple other parentage combinations have been mentioned by other authors as seen in

11772-402: Was sick and fed him her breast milk and placed him under the hot coals of a fire. Not only did this recover his strength but he grew instantly into manhood. As a gift to Celeus, in gratitude for his hospitality, Demeter secretly planned to make Demophon immortal by placing him in the flames of the hearth to strip him of his mortal flesh. With each day Demophon grew but she was unable to complete

11881-434: Was the Athenian base of the cult of Demeter and Kore at Eleusis in western Attica. It was one of several sanctuaries in the city of Athens that linked the city to a cult in an outlying area of Attica, alongside the sanctuary of Artemis of Brauron atop the Acropolis and that of Dionysius of Eleutherae on the south slopes of the Acropolis. At the start of the Eleusinian Mysteries, sacred objects were brought from Eleusis to

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