Christopher Columbus was an Italian explorer and colonizer who completed four voyages across the Atlantic Ocean that opened the New World for conquest and permanent European colonization of the Americas. His expeditions, sponsored by the Catholic Monarchs of Spain, were the first European contact with the Caribbean, Central America, South America. Columbus's early life is somewhat obscure, but scholars agree that he was born in the Republic of Genoa and spoke a dialect of Ligurian as his first language, he went to sea at a young age and travelled as far north as the British Isles and as far south as what is now Ghana. He married Portuguese noblewoman Filipa Moniz Perestrelo and was based in Lisbon for several years, but took a Castilian mistress. Though self-educated, Columbus was read in geography and history, he formulated a plan to seek a western sea passage to the East Indies, hoping to profit from the lucrative spice trade. Following persistent lobbying, Queen Isabella I and King Ferdinand II agreed to sponsor a journey west, in the name of the Crown of Castile.

Columbus left Castile in August 1492 with three ships, after a stopover in the Canary Islands made landfall in the Americas on 12 October. His landing place was an island in the Bahamas, known by its native inhabitants as Guanahani. Columbus subsequently visited the islands now known as Cuba and Hispaniola, establishing a colony in what is now Haiti—the first European settlement in the Americas since the Norse colonies nearly 500 years earlier, he arrived back in Castile in early 1493. Word of his voyages soon spread throughout Europe. Columbus made three further voyages to the New World, exploring the Lesser Antilles in 1493, Trinidad and the northern coast of South America in 1498, the eastern coast of Central America in 1502. Many of the names he gave to geographical features—particularly islands—are still in use, he continued to seek a passage to the East Indies, the extent to which he was aware that the Americas were a wholly separate landmass is uncertain. He never renounced his belief that he had reached the Far East and gave the name indios to the indigenous peoples he encountered.

Columbus's strained relationship with the Spanish crown and its appointed colonial administrators in America led to his arrest and removal from Hispaniola in 1500, to protracted litigation over the benefits that he and his heirs claimed were owed to them by the crown. Columbus's expeditions inaugurated a period of exploration and colonization that lasted for centuries, helping create the modern Western world; the transfers between the Old World and New World that followed his first voyage are known as the Columbian exchange, the period of human habitation in the Americas prior to his arrival is referred to as the Pre-Columbian era. Columbus's legacy continues to be debated, he was venerated in the centuries after his death, but public perceptions have changed as recent scholars have given greater attention to negative aspects of his life, such as his enslavement of the indigenous population in his quest for gold and his brutal subjugation of the Taíno people, leading to their near-extinction, as well as allegations of tyranny towards Spanish colonists.

Many landmarks and institutions in the Western Hemisphere bear his name, including the country of Colombia and the name Columbia, used as a personification for the United States, appears in many place names there. The name Christopher Columbus is the Anglicisation of the Latin Christophorus Columbus, his name in Ligurian is Cristoffa Corombo, in Italian Cristoforo Colombo, in Spanish Cristóbal Colón, in Portuguese, Cristóvão Colombo. He was born before 31 October 1451 in the territory of the Republic of Genoa, though the exact location remains disputed, his father was Domenico Colombo, a wool weaver who worked both in Genoa and Savona and who owned a cheese stand at which young Christopher worked as a helper. His mother was Susanna Fontanarossa, he had three brothers, Giovanni Pellegrino, Giacomo. He had a sister named Bianchinetta, his brother Bartolomeo worked in a cartography workshop in Lisbon for at least part of his adulthood. Columbus never wrote in his native language, presumed to have been a Genoese variety of Ligurian: his name in the 16th-century Genoese language would have been Cristoffa Corombo.

In one of his writings, he says he went to sea at the age of 10. In 1470, the Columbus family moved to Savona. In the same year, Christopher was on a Genoese ship hired in the service of René of Anjou to support his attempt to conquer the Kingdom of Naples; some modern authors have argued that he was not from Genoa but, from the Aragon region of Spain or from Portugal. These competing hypotheses have been discounted by mainstream scholars. In 1473, Columbus began his apprenticeship as business agent for the important Centurione, Di Negro and Spinola families of Genoa, he made a trip to Chios, an Aegean island ruled by Genoa. In May 1476, he took part in an armed convoy sent by Genoa to carry valuable cargo to northern Europe, he docked in Bristol and Galway, Ireland. A few writers speculate, it is known that in the autumn of 1477, he sailed on a Portuguese ship from Galway to Lisbon, where he found his brother Bartolomeo, they continued trading for the Centurione family. Columbus based himself in Lisbon from 1477 to 14

In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. More the term motion is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry. In the latter case, hyperbolic motions provide an approach to the subject for beginners. Motions can be divided into indirect motions. Direct, proper or rigid motions are motions like translations and rotations that preserve the orientation of a chiral shape. Indirect, or inproper motions are motions like reflections, glide reflections and Improper rotations that invert the orientation of a chiral shape; some geometers define motion in such a way. In differential geometry, a diffeomorphism is called a motion if it induces an isometry between the tangent space at a manifold point and the tangent space at the image of that point. Given a geometry, the set of motions forms a group under composition of mappings.

This group of motions is noted for its properties. For example, the Euclidean group is noted for the normal subgroup of translations. In the plane, a direct Euclidean motion is either a translation or a rotation, while in space every direct Euclidean motion may be expressed as a screw displacement according to Chasles' theorem; when the underlying space is a Riemannian manifold, the group of motions is a Lie group. Furthermore, the manifold has constant curvature if and only if, for every pair of points and every isometry, there is a motion taking one point to the other for which the motion induces the isometry; the idea of a group of motions for special relativity has been advanced as Lorentzian motions. For example, fundamental ideas were laid out for a plane characterized by the quadratic form x 2 − y 2 in American Mathematical Monthly; the motions of Minkowski space were described by Sergei Novikov in 2006: The physical principle of constant velocity of light is expressed by the requirement that the change from one inertial frame to another is determined by a motion of Minkowski space, i.e. by a transformation ϕ: R 1, 3 ↦ R 1, 3 preserving space-time intervals.

This means that ⟨ ϕ − ϕ, ϕ − ϕ ⟩ = ⟨ x − y, x − y ⟩ for each pair of points x and y in R1,3. An early appreciation of the role of motion in geometry was given by Alhazen, his work "Space and its Nature" uses comparisons of the dimensions of a mobile body to quantify the vacuum of imaginary space. In the 19th century Felix Klein became a proponent of group theory as a means to classify geometries according to their "groups of motions", he proposed using symmetry groups in his Erlangen program, a suggestion, adopted. He noted that every Euclidean congruence is an affine mapping, each of these is a projective transformation; the term motion, shorter than transformation, puts more emphasis on the adjectives: projective, Euclidean. The context was thus expanded, so much that "In topology, the allowed movements are continuous invertible deformations that might be called elastic motions."The science of kinematics is dedicated to rendering physical motion into expression as mathematical transformation.

The transformation can be written using vector algebra and linear mapping. A simple example is a turn written as a complex number multiplication: z ↦ ω z where ω = cos ⁡ θ + i sin ⁡ θ, i 2 = − 1. Rotation in space is achieved by use of quaternions, Lorentz transformations of spacetime by use of biquaternions. Early in the 20th century, hypercomplex number systems were examined, their automorphism groups led to exceptional groups such as G2. In the 1890s logicians were reducing the primitive notions of synthetic geometry to an absolute minimum. Giuseppe Peano and Mario Pieri used the expression motion for the congruence of point pairs. Alessandro Padoa celebrated the reduction of primitive notions to point and motion in his report to the 1900 International Congress of Philosophy, it was at this congress. In his book Principles of Mathematics, Russell considered a motion to be a Euclidean isometry that preserves orientation. In 1914 D. M. Y. Sommerville used the idea of a geometric motion to establish the idea of distance in hyperbolic geometry when he wrote Elements of Non-Euclidean Geometry.

He explains: By a motion or displacement in the general sense is not meant a change of position of a single point or any bounded figure, but a displacement of the whole space, or, if we are dealing with only two dimensions, of the whole plane. A motion is a transformation which changes each point P into another point P ′ in such a way that distances and angles are unchanged. Lasz

Lapérouse, sometimes spelled La Pérouse, is a hydrographic survey vessel, meaning a scientific ship that explores the sea floor in order to obtain a precise cartography, of the Lapérouse class of the French Navy. The vessel is deployed on the French coast, or in foreign waters within the framework of international cooperation, it is fitted with electric propulsion and a hydrographic winch that allows it to perform oceanographic work. Laid down on June 11, 1985 and launched on November 15, 1986, the hydrographic vessel Lapérouse entered into service on April 20, 1988, it is the first vessel of this type. Based in Brest, Lapérouse performs hydrographic work for the Naval Hydrographic and Oceanographic Service, although since June 2, 2000 it is hierarchically attached to the Naval Action Force; the principal mission of hydrographic vessels is scientific. During their deployment they may confront sensitive situations: encounter pirates, respond to terrorist threats, evacuate citizens, or rescue seamen in distress.

These ships may from time to time, participate in action of the French State at sea by performing border patrol missions. The patron city of Lapérouse is Albi since Octobre 7, 1988. Displacement: 850 t. Dimensions: 59 × 10,9 × 3.63. Range: 6,000 nautical miles at 12 knots. Propulsion: 2 SACM Wärtsilä UD30 RVR V12 M6 diesel motors, 2 controllable pitch propeller, 1 bow thruster. Power: 2500 hp. Radar: Navigational radar DECCA 1226. Electric plant: 620 kW. Complement: 4 officers, 18 petty officers, 15 crew members, 11 hydrographers. Armament: Two AANF1 7.5 mm machine guns and two Browning M2 12.7 mm machine gunsThe hull and the superstructures are painted white, as is the case for all scientific ships of the French Navy. List of active French Navy ships "Lapérouse". Marine nationale