Great circleIn mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space. For any pair of distinct non-antipodal points on the sphere, there is a unique great circle passing through both. (Every great circle through any point also passes through its antipodal point, so there are infinitely many great circles through two antipodal points.
Ruled surfaceIn geometry, a surface S is ruled (also called a scroll) if through every point of S there is a straight line that lies on S. Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle.
Cartesian closed categoryIn , a is Cartesian closed if, roughly speaking, any morphism defined on a of two can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming, in that their internal language is the simply typed lambda calculus. They are generalized by , whose internal language, linear type systems, are suitable for both quantum and classical computation.
Marginal costIn economics, the marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as output is increased by an infinitesimal amount. As Figure 1 shows, the marginal cost is measured in dollars per unit, whereas total cost is in dollars, and the marginal cost is the slope of the total cost, the rate at which it increases with output.
Cost curveIn economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible level of production, and the result is a cost curve. Profit-maximizing firms use cost curves to decide output quantities. There are various types of cost curves, all related to each other, including total and average cost curves; marginal ("for each additional unit") cost curves, which are equal to the differential of the total cost curves; and variable cost curves.
Unit circleIn mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S1 because it is a one-dimensional unit n-sphere. If (x, y) is a point on the unit circle's circumference, then and are the lengths of the legs of a right triangle whose hypotenuse has length 1.
Minimal surfaceIn mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame.
Squaring the circleSquaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi () is a transcendental number.
Curve fittingCurve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors.
Opportunity costIn microeconomic theory, the opportunity cost of a choice is the value of the best alternative forgone where, given limited resources, a choice needs to be made between several mutually exclusive alternatives. Assuming the best choice is made, it is the "cost" incurred by not enjoying the benefit that would have been had by taking the second best available choice. The New Oxford American Dictionary defines it as "the loss of potential gain from other alternatives when one alternative is chosen.
Implicit stereotypeAn implicit bias or implicit stereotype is the pre-reflective attribution of particular qualities by an individual to a member of some social out group. Implicit stereotypes are thought to be shaped by experience and based on learned associations between particular qualities and social categories, including race and/or gender. Individuals' perceptions and behaviors can be influenced by the implicit stereotypes they hold, even if they are sometimes unaware they hold such stereotypes.
Implicit functionIn mathematics, an implicit equation is a relation of the form where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. For example, the equation of the unit circle defines y as an implicit function of x if −1 ≤ x ≤ 1, and y is restricted to nonnegative values.
