The Euclidean algorithm is an efficient method for computing the
greatest common divisor. It is named for the ancient Greek
mathematician Euclid, who first described it. The GCD of two numbers is
the largest number that divides both of them without leaving a
remainder. The Euclidean algorithm is based on the principle that the
greatest common divisor of two numbers does not change if the smaller
number is subtracted from the larger number. Euclid's algorithm was
first described in Euclid's Elements (c. 300 BC), making it one of the
oldest numerical algorithms still in common use. The original algorithm
was described only for natural numbers and geometric lengths (real
numbers), but the algorithm was generalized in the 19th century to
other types of numbers, such as Gaussian integers and polynomials of
one variable. This led to modern abstract algebraic notions such as
Euclidean domains. The Euclidean algorithm has been generalized further
to other mathematical structures, such as knots and multivariate
polynomials. The Euclidean algorithm has many theoretical and practical
applications. It is a key element of the RSA algorithm, a public-key
encryption method widely used in electronic commerce.
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Today's selected anniversaries:
Lǐ Yuān became Emperor Gaozu of Tang, initiating three centuries of the
Tang Dynasty in China.
The Parliament of Ireland met at Castledermot in County Kildare, the
first definitively known meeting of this Irish legislature.
War of the Seventh Coalition: Napoléon Bonaparte fought and lost his
final battle, the Battle of Waterloo in Belgium.
Charles Darwin received a manuscript by fellow naturalist Alfred Russel
Wallace on evolution, which prompted Darwin to publish his theory.
World War II: Charles de Gaulle , leader of the Free French Forces,
made an appeal to the French people following the fall of France to
Nazi Germany, rallying them to support the Resistance.
The United States and the Soviet Union signed the SALT II treaty,
placing specific limits on each side's stock of nuclear weapons.
Wiktionary's word of the day:
1. (UK) An underground coal mine, together with its surface buildings.
2. (US) A facility that supplies coal
Wikiquote quote of the day:
Nothing except a battle lost can be half so melancholy as a battle won.
--Arthur Wellesley, 1st Duke of Wellington