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.

Read the rest of this article: http://en.wikipedia.org/wiki/Euclidean_algorithm

_______________________________ Today's selected anniversaries:

618:

Lǐ Yuān became Emperor Gaozu of Tang, initiating three centuries of the Tang Dynasty in China. http://en.wikipedia.org/wiki/Tang_Dynasty

1264:

The Parliament of Ireland met at Castledermot in County Kildare, the first definitively known meeting of this Irish legislature. http://en.wikipedia.org/wiki/Parliament_of_Ireland

1815:

War of the Seventh Coalition: Napoléon Bonaparte fought and lost his final battle, the Battle of Waterloo in Belgium. http://en.wikipedia.org/wiki/Battle_of_Waterloo

1858:

Charles Darwin received a manuscript by fellow naturalist Alfred Russel Wallace on evolution, which prompted Darwin to publish his theory. http://en.wikipedia.org/wiki/Alfred_Russel_Wallace

1940:

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. http://en.wikipedia.org/wiki/Appeal_of_18_June

1979:

The United States and the Soviet Union signed the SALT II treaty, placing specific limits on each side's stock of nuclear weapons. http://en.wikipedia.org/wiki/Strategic_Arms_Limitation_Talks

_____________________________ Wiktionary's word of the day:

colliery (n): 1. (UK) An underground coal mine, together with its surface buildings.

2. (US) A facility that supplies coal http://en.wiktionary.org/wiki/colliery

___________________________ 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 http://en.wikiquote.org/wiki/Arthur_Wellesley%2C_1st_Duke_of_Wellington