The History of the Decline and Fall of the Roman Empire (sometimes shortened to Decline and Fall of the Roman Empire) is a book of history written by the English historian Edward Gibbon, which traces the trajectory of Western civilization (as well as the Islamic and Mongolian conquests) from the height of the Roman Empire to the fall of Byzantium. It was published in six volumes. Volume I was published in 1776 and went through six printings. Volumes II and III were published in 1781; volumes IV, V, and VI in 1788–89. The original volumes were published in quarto sections, a common publishing practice...

In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression f(x) dx from one-variable calculus is called a 1-form, and can be integrated over an interval [a,b] in the domain of f: and...

Der Ring des Nibelungen (The Ring of the Nibelung), WWV 86, is a cycle of four epic operas by the German composer Richard Wagner (1813–1883). The works are based loosely on characters from the Norse sagas and the Nibelungenlied. The composer termed the cycle a "Bühnenfestspiel" (stage festival play), structured in three days preceded by a Vorabend ("ante-evening"). It is often referred to as the Ring Cycle, Wagner's Ring, or simply the Ring. Wagner wrote the libretto and music over the course of about twenty-six years, from 1848 to 1874. The four operas that constitute the Ring cycle are, in sequence...

The Nibelungenlied, translated as The Song of the Nibelungs, is an epic poem in Middle High German. The story tells of dragon-slayer Siegfried at the court of the Burgundians, how he was murdered, and of his wife Kriemhild's revenge. The Nibelungenlied is based on pre-Christian Germanic heroic motifs (the "Nibelungensaga"), which include oral traditions and reports based on historic events and individuals of the 5th and 6th centuries. Old Norse parallels of the legend survive in the Völsunga saga, the Prose Edda, the Poetic Edda, the Legend of Norna-Gest, and the Þiðrekssaga. In 2009, the three...