This is another name for the Battle of the Bulge (16 December, 1944 - 25 January 1945), a German offensive through the Ardennes Mountains region of Belgium. Its official name was the Ardennes-Alsace campaign, and the German army referred to it as Unternehmen Wacht am Rhein (Operation Watch on the Rhine, a reference to the German hymn).
The German goal was to split the British-American line and capture the city of Antwerp, before encircling and isolating the Allied armies, forcing them to negotiate an armistice in Germany's favour, and enabling Germany to devote more resources to the battle on the eastern front.
The operation was planned and coordinated in secret, and it took the Allies by surprise. Allied air forces were grounded by the heavy winter conditions. However, fierce resistance, especially around the town of Bastogne, disadvantageous terrain, the arrival of reinforcements in the form of General Patton's legendary Third Army, and a change in weather conditions that allowed the Allies to mobilise their superior air force rendered the German offensive a failure.
Both sides suffered heavy casualties, and the Battle of the Bulge represented the most damaging battle of the war for American forces.
The Poisson Distribution describes the probability of a particular number of discrete events occurring within a fixed period of time if these events occur with a known average rate, independently of the time since the last event.
P(x; μ) = (e^-μ) (μ^x) / x!
where the average rate is μ and the actual number of events is x.
The distribution was first introduced by Simeon Denis Poisson in 1838.
This is the informal name for the book A Course of Modern Analysis by E.T. Whittaker and G.N. Watson, published in 1902.
It was a standard reference text for a generation of mathematicians, such as John Edensor Littlewood, G.H. Hardy and Jean Delsarte. Today it is still a useful reference for modern mathematicians, and represents a high point for the Mathematical Tripos at Cambridge University.
Moxie is a carbonated drink that was the first of its kind sold in the United States.
It originated as a patent medicine in 1876, designed by Dr. Augustin Thompson. He claimed that it utilised a rare South American plant discovered by his friend Lieutenant Moxie, and was useful in treating paralysis, "softening of the brain," anxiety and insomnia.
Later, he added soda water to the medicine and sold it in bottles as a sweet drink. The product enjoyed great success, and even President Coolidge was said to enjoy it. However, the company made the decision in the 1930s to spend money expanding its sugar reserves, rather than maintaining its advertising campaigns. As a result, demand slumped.
The rise of Coca-Cola and similar products also had a detrimental impact on Moxie's sales, but the product is still available in certain areas of the US, such as Pennsylvania and New England.
This is a cameo appearance by a young Malcolm X.
Malcolm X (1925-1965) was an American Muslim minister, speaker and activist. He was a deeply controversial figure, admired by some as a courageous advocate of the rights of African-Americans, whilst feared by others as a preacher of racism, black supremacy and violence.
The son of a broken home, he got involved in crime at an early age and turned to the Nation of Islam whilst in prison. He became one of its most high-profile members, but eventually left the group as a result of a rivalry with Elijah Muhammed, another high-profile figure in the organisation. Malcolm then became a Sunni Muslim, made a pilgrimage to Mecca, and renounced racism. He continued to travel extensively throughout the world, and founded a number of religious and secular organisations. He was assassinated by the Nation of Islam in 1965.
In 1941, Malcolm had moved to Boston to live with his older half-sister. He held a number of jobs both legitimate and illegitimate, including as a shoeshine. His nickname at the time was "Red" due to his dark cinnamon-brown hair.
Palladian architecture is a European design style based on the work of Venetian architect Andrea Palladio.
Palladio's work was inspired by the symmetry and perspective of ancient Greek and Roman architecture. It achieved a great deal of popularity in Britain during the mid-17th century. It became popular again throughout Europe in the early 18th century. As this surge in popularity waned, British colonies in North America began making use of the style. Examples can be found in Drayton Hall, South Carolina; the Redwood Library, Newport, Rhode Island; the Morris-Jurnel Mansion in New York; and Thomas Jefferson's Monticello and Poplar Forest, Virginia.
The style was popular in Europe during the 19th and 20th centuries, but saw competition from the revival in Gothic architecture and opposition from those who deemed it too pagan given its roots in ancient Greek and Roman culture. However, it continues to have an influence on modern architecture today.