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...
Euclid's method for finding the greatest common divisor (GCD) of two starting lengths BA and DC, both defined to be multiples of a common "unit" length. The length DC being shorter, it is used to "measure" BA, but only once because the remainder EA is less than DC. EA now measures (twice) the shorter length DC, with remainder FC shorter than EA. Then FC measures (three times) length EA. Because there is no remainder, the process ends with FC being the GCD. On the right Nicomachus's example with numbers 49 and 21 resulting in their GCD of 7 (derived from Heath 1908:300).
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematicianEuclid, who first described it in his Elements (c. 300 BC).
It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules,
and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations.
The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 252 − 105 = 147. Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal. When that occurs, they are the GCD of the original two numbers. By reversing the steps or using the extended Euclidean algorithm, the GCD can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each multiplied by an integer (for example, 21 = 5 × 105 + (−2) × 252). The fact that the GCD can always be expressed in this way is known as Bézout's identity. (Full article...)
Image 3Shards 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 11The 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 12Traditional flag used from 1769 to the War of Independence (from Culture of Greece)
Image 20The 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)
Image 38Alexander 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 50The ancient theatre of Epidaurus continues to be used for staging ancient Greek plays. (from Culture of Greece)
Image 51A page from a 16th-century edition of the 10th century Byzantine encyclopaedia of the ancient Mediterranean world, the Suda. (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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