Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Transformation (function)In mathematics, a transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
July MonarchyThe July Monarchy (Monarchie de Juillet), officially the Kingdom of France (Royaume de France), was a liberal constitutional monarchy in France under Louis Philippe I, starting on 26 July 1830, with the July Revolution of 1830, and ending 23 February 1848, with the Revolution of 1848. It marks the end of the Bourbon Restoration (1814–1830). It began with the overthrow of the conservative government of Charles X, the last king of the main line House of Bourbon.
Möbius transformationIn geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0. Geometrically, a Möbius transformation can be obtained by first performing stereographic projection from the plane to the unit two-sphere, rotating and moving the sphere to a new location and orientation in space, and then performing stereographic projection (from the new position of the sphere) to the plane.
ParisParis (ˈpærɪs; paʁi) is the capital and most populous city of France, with an official estimated population of 2,102,650 residents as of 1 January 2023 in an area of more than , making it the fourth-most populated city in the European Union as well as the 30th most densely populated city in the world in 2022. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, culture, fashion, gastronomy and many areas.
Air FranceAir France (ɛːʁ fʁɑ̃s; formally Société Air France, S.A.), stylised as AIRFRANCE, is the flag carrier of France headquartered in Tremblay-en-France. It is a subsidiary of the Air France–KLM Group and a founding member of the SkyTeam global airline alliance. , Air France serves 29 destinations in France and operates worldwide scheduled passenger and cargo services to 201 destinations in 78 countries (93 including overseas departments and territories of France) and also carried 46,803,000 passengers in 2019.
DoualaDouala is the largest city in Cameroon and its economic capital. It is also the capital of Cameroon's Littoral Region. Home to Central Africa's largest port and its major international airport, Douala International Airport (DLA), it is the commercial and economic capital of Cameroon and the entire CEMAC region comprising Gabon, Congo, Chad, Equatorial Guinea, Central African Republic and Cameroon. Consequently, it handles most of the country's major exports, such as oil, cocoa and coffee, timber, metals and fruits.
Anglo-Norman languageAnglo-Norman (Anglo-Normaund; anglo-normand), also known as Anglo-Norman French, was a dialect of Old Norman French that was used in England and, to a lesser extent, elsewhere in Great Britain and Ireland during the Anglo-Norman period. When William the Conqueror led the Norman conquest of England in 1066, he, his nobles, and many of his followers from Normandy, but also those from northern and western France, spoke a range of langues d'oïl (northern varieties of Old French).
