Portal:Greece

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Introduction

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Greece /ˈɡrs/ (About this soundlisten) (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...

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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 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 mathematician Euclid, 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...)

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Recognized content

Featured article star.svg 1896 Summer Olympics, Alcibiades, Archimedes, Aspasia, Attalus I, Basiliscus, Battle of Dyrrhachium (1081), Battle of Greece, Byzantine Empire, Byzantine navy, Cleomenean War, Corinthian War, Cretan War (205–200 BC), Demosthenes, Diocletian, El Greco, Epaminondas, Euclidean algorithm, George I of Greece, Greece runestones, Greek mythology, Hippocrates, Manuel I Komnenos, Macedonia (terminology), Orion (mythology), Pericles, Philitas of Cos, Problem of Apollonius, Stamata Revithi, Rhodes blood libel, Slavery in ancient Greece, The Battle of Alexander at Issus, The Penelopiad, Theramenes, Thrasybulus
Symbol a class.svg Battle of Artemisium, Battle of Thermopylae, Battle of Kalavrye, Battle of Marathon, Battle of Salamis, Byzantine civil war of 1341–47, Byzantine–Sasanian War of 602–628, First Macedonian War, John Kourkouas, Yannis Makriyannis, Sviatoslav's invasion of Bulgaria, Vikos–Aoös National Park

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Greece

Literature and philosophy

Homer

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.

— Homer, Iliad

Art

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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...

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Ancient Greek wikipedia

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Pontic Greek wikipedia

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Notable Greeks

Music

Maria Callas

Cinema

Angelopoulos

Architecture

Phidias

Sculpture

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Painting

El Greco

Science

Caratheodory

Philosophy

Aristotle

Literature

Cavafy

Politics

Eleftherios Venizelos

Featured video

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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