Euler's formulaEuler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x: where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine").
Urban areaAn urban area, built-up area or urban agglomeration is a human settlement with a high population-density and an infrastructure of built environment. This is the core of a metropolitan statistical area in the United States, if it contains a population of more than 50,000. Urban areas originate through urbanization, and researchers categorize them as cities, towns, conurbations or suburbs. In urbanism, the term "urban area" contrasts to rural areas such as villages and hamlets; in urban sociology or urban anthropology it contrasts with natural environment.
Law of cosinesIn trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite respective angles and (see Fig. 1), the law of cosines states: The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then and the law of cosines reduces to The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.
2017 St. Louis Cardinals seasonThe 2017 St. Louis Cardinals season was the 136th for the St. Louis Cardinals of Major League Baseball (MLB), a franchise in St. Louis, Missouri. It was the 126th season for the Cardinals in the National League (NL), and their 12th at Busch Stadium III. The Cardinals missed the playoffs for a second consecutive season, having last done that between the 2007 and 2008 seasons. Major League Baseball and the Players' Association reached a new, tentative CBA contract to reduce the 15-day disabled list timetable to 10-days.
Virasoro algebraIn mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. The Virasoro algebra is spanned by generators Ln for n ∈ Z and the central charge c. These generators satisfy and The factor of is merely a matter of convention. For a derivation of the algebra as the unique central extension of the Witt algebra, see derivation of the Virasoro algebra.
Metropolitan areaA metropolitan area or metro is a region consisting of a densely populated urban agglomeration and its surrounding territories sharing industries, commercial areas, transport network, infrastructures and housing. A metro area usually comprises multiple principal cities, jurisdictions and municipalities: neighborhoods, townships, boroughs, cities, towns, exurbs, suburbs, counties, districts, as well as even states and nations like the euro districts.
SpinorIn geometry and physics, spinors spɪnɚ are elements of a complex number-based vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, but unlike geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state.
ExerciseExercise is a body activity that enhances or maintains physical fitness and overall health and wellness. It is performed for various reasons, including weight loss or maintenance, to aid growth and improve strength, develop muscles and the cardiovascular system, hone athletic skills, improve health, or simply for enjoyment. Many individuals choose to exercise outdoors where they can congregate in groups, socialize, and improve well-being as well as mental health.
Chicago metropolitan areaThe Chicago metropolitan area, also colloquially referred to as Chicagoland, is the metropolitan area containing the City of Chicago, which includes its surrounding suburbs and satellite cities. Encompassing 10,286 square mi (28,120 km2), the metropolitan area includes the city of Chicago, its suburbs and hinterland, that span 14 counties across northeast Illinois, northwest Indiana, and southeast Wisconsin. The MSA had a 2020 census population of 9,618,502 and the combined statistical area which spans up to 19 counties had a population of nearly 10 million people.
Laplace operatorIn mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols , (where is the nabla operator), or . In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form.
Differential operatorIn mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist, such as the Schwarzian derivative.
UnicodeUnicode, formally The Unicode Standard, is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic scripts, as well as symbols, thousands of emoji (including in colours), and non-visual control and formatting codes.
