Vector (mathematics and physics)In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number (a scalar), or to elements of some vector spaces. Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities that have both a magnitude and a direction, such as displacements, forces and velocity. Such quantities are represented by geometric vectors in the same way as distances, masses and time are represented by real numbers.
Terence TaoTerence Chi-Shen Tao (; born 17 July 1975) is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to ethnic Chinese immigrant parents and raised in Adelaide.
Pythagorean theoremIn mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
Vector calculusVector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations.
TrapezoidIn geometry, a trapezoid (ˈtɹæpəzɔɪd) in USA and Canadian English, or trapezium (trəˈpiːziəm) in British and other forms of English, is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast with the special cases below.
Vector fieldIn vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space . A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point.
March 9141 BC – Liu Che, posthumously known as Emperor Wu of Han, assumes the throne over the Han dynasty of China. 1009 – First known mention of Lithuania, in the annals of the monastery of Quedlinburg. 1226 – Khwarazmian sultan Jalal ad-Din conquers the Georgian capital of Tbilisi. 1230 – Bulgarian Tsar Ivan Asen II defeats Theodore of Epirus in the Battle of Klokotnitsa. 1500 – The fleet of Pedro Álvares Cabral leaves Lisbon for the Indies. The fleet will discover Brazil which lies within boundaries granted to Portugal in the Treaty of Tordesillas in 1494.
Hotel Casa del MarThe Hotel Casa del Mar is a historic luxury hotel located on the beach in Santa Monica, California. It is owned and operated by the Edward Thomas Collection of Hotels (ETC Hotels). The building was constructed by brothers E.A. "Jack" Harter and T.D. "Til" Harter, doing business as the H & H Holding Company, at a cost of $2 million. It opened as Club Casa del Mar, a private beach club, on May 1, 1926. Designed by Los Angeles architect Charles F.
OpenGLOpenGL (Open Graphics Library) is a cross-language, cross-platform application programming interface (API) for rendering 2D and 3D vector graphics. The API is typically used to interact with a graphics processing unit (GPU), to achieve hardware-accelerated rendering. Silicon Graphics, Inc. (SGI) began developing OpenGL in 1991 and released it on June 30, 1992; applications use it extensively in the fields of computer-aided design (CAD), virtual reality, scientific visualization, information visualization, flight simulation, and video games.
Mar del PlataMar del Plata is a city on the coast of the Atlantic Ocean, in Buenos Aires Province, Argentina. It is the seat of General Pueyrredón district. Mar del Plata is the second largest city in Buenos Aires Province. The name "Mar del Plata" is a shortening of "Mar del Rio de la Plata," and has the meaning of "sea of the Rio de la Plata basin" or "adjoining sea to the (River) Plate region". Mar del Plata is one of the major fishing ports and the biggest seaside beach resort in Argentina. With a population of 682.
