Greece/ˈɡriːs/ⓘ (Greek: Ελλάδα, Ellada), officially the Hellenic Republic (Ελληνική Δημοκρατία, Elliniki Dimokratia), and historically Hellas (Ancient Greek: Ἑλλάς, Hellas; Modern Greek: Ελλάς, Ellas), is a country in the southeast of Europe on the southern tip of the Balkan peninsula. Bounded on land by Bulgaria, North Macedonia, and Albania to the north, to the east by Turkey and the waters of the Aegean Sea and to the west and south by the Ionian and Mediterranean Seas. Regarded by many as the cradle of Western civilisation, Greece has a long and rich history during which it spread its influence over three continents. Read more...
Figure 1: A solution (in purple) to Apollonius's problem. The given circles are shown in black.
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 BC – c. 190 BC) posed and solved this famous problem in his work Ἐπαφαί (Epaphaí, "Tangencies"); this work has been lost, but a 4th-century AD report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2), a pair of solutions for each way to divide the three given circles in two subsets (there are 4 ways to divide a set of cardinality 3 in 2 parts).
In the 16th century, Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution does not use only straightedge and compass constructions. François Viète found such a solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius (a point) or expanded to infinite radius (a line). Viète's approach, which uses simpler limiting cases to solve more complicated ones, is considered a plausible reconstruction of Apollonius' method. The method of van Roomen was simplified by Isaac Newton, who showed that Apollonius' problem is equivalent to finding a position from the differences of its distances to three known points. This has applications in navigation and positioning systems such as LORAN. (Full article...)
Image 22The I Battalion of the Army of National Defence marches on its way to the front, 1916. Greece joined united with the Allies side in summer 1917. (from History of Greece)
Image 23Alexander the Great also known as Alexander III, king of Macedon, was one of the most successful military commanders in history. (from Culture of Greece)
Image 28Protest against the junta by Greek political exiles in Germany, 1967 (from History of Greece)
Image 29Map of earthquakes in Greece and adjacent countries 1900–2017 (from Geography of Greece)
Image 30A page from a 16th-century edition of the 10th century Byzantine encyclopaedia of the ancient Mediterranean world, the Suda. (from Culture of Greece)
Image 34Shards of pottery vases on the street, after being thrown from the windows of nearby houses. A Holy Saturday tradition in Corfu. (from Culture of Greece)
Image 71The most famous artist born in Greece was probably Doménikos Theotokópoulos, better known as El Greco (The Greek) in Spain. He did most of his painting there during the late 1500s and early 1600s. (from Culture of Greece)
...that the Greco-Buddhist art is an artistic manifestation of Greco-Buddhism, a cultural syncretism between the Greek culture and Buddhism, which developed in Central Asia after the conquests of Alexander the Great?
...that the country's highest mountain, Mount Olympus was said to be the home of the Greek Gods in ancient Greek religion?
...that the Olympic Games, originated in Greece 3000 years ago, and that the 1st games of the modern Olympics were held in Greece in 1896, as a revival of the Games?
...that the Greek state comprises only the centre of the ancient Greek world, which comprised also Southern Italy, the coastal areas of modern Turkey and the Black Sea, as well as some colonies in North Africa, Southern France and Spain?
...that even though the modern Greek state was established in 1832, some areas of Greece were not liberated until after the Balkan Wars and WW2?
In Greece, from ancient times down to the present, has been produced countless world-famous poetry in addition to philosophers like Socrates, Plato and Aristotle and historians like Herodotus and Thucydides. Notable figures of modern Greek literature include Odysseas Elytis and Constantine Cavafy.
Sing, O goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Zeus fulfilled from the day on which the son of Atreus, king of men, and great Achilles, first fell out with one another.
Greek art began in the Cycladic and Minoan prehistorical civilization. The art of ancient Greece has exercised an enormous influence on the culture of many countries from ancient times until the present, particularly in the areas of sculpture and architecture. In the West, the art of the Roman Empire was largely derived from Greek models. In the East, Alexander the Great's conquests initiated several centuries of exchange between Greek, Central Asian and Indian cultures. During the Renaissance , the humanist aesthetic and the high technical standards of Greek art inspired generations of European artists.Read more...
A short video of the main sites at the ancient sanctuary of Delphi in Central Greece. Delphi was considered to be the center of the world by the Greeks and the most important oracle in the Greek world.
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