An article from Science News Jan 2020

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Article

## Algebra

The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a specified system (Fig. 1). The origins of algebra were based on the need to develop equations that…

Article

## Cardioid

A heart-shaped curve generated by a point of a circle that rolls (without slipping) on a fixed circle of the same diameter. In point-wise construction of the curve, let O be a fixed point of a circle C of diameter a, and Q a variable point of C. Lay…

Article

## Differentiation

A mathematical operation performed on a function to determine the effect of a change in the value of the independent variable. Functions of one variable are considered in this article. For differentiation of functions of several variablesPartial…

Article

## Discriminant

For a polynomial f(x) = an xn + an−1 xn−1 + + a1 x + a0, the discriminant is given by the expression where x1, x2, …, xn are the roots of the equation f(x) = 0. There are n(n − 1)/2 terms (xi − xj)2 in the product corresponding to all possible…

Article

## Dyadic

A mathematical abstraction corresponding to an expression of the type βγ + δ∊ + · · · , in which the elements (dyad symbols) consist of two vector symbols in juxtaposition without the intervention of either the dot (·) or cross (×). Essentially a…

Article

## Finite element method

A numerical analysis technique for obtaining approximate solutions to many types of engineering problems. The need for numerical methods arises from the fact that for most engineering problems analytical solutions do not exist. While the governing…

Article

## Matrix theory

The study of matrices and their properties, and of linear transformations on vector spaces, which can be represented by matrices. A matrix is a rectangular array of numbers, with the numbers that appear in the matrix being called entries. For…

An article from Science News May 2019

## The kilogram just got a revamp. A unit of time might be next

Article

## Addition

One of the four fundamental operations of arithmetic and algebra. The symbol + of addition is thought to be a ligature for “et,” used in a German manuscript of 1456 to denote addition. Its first printed appearance is in Johann Widman's Behennede und…

Article

## Algebraic geometry

The study of zero sets of polynomial equations. Examples are the parabola y − x2 = 0, thought of as sitting in the (x, y)-plane, and the locus of all points (t, t2, t3, t4), which is defined by Eqs. (1), 1 in the coordinate space with coordinates w,…

Article

## Analysis of variance

Total variation in experimental data is partitioned into components assignable to specific sources by the analysis of variance. This statistical technique is applicable to data for which (1) effects of sources are additive, (2) uncontrolled or…

Article

## Analytic geometry

A branch of mathematics in which algebra is applied to the study of geometry. Because algebraic methods were first systematically applied to geometry in 1637 by the French philosopher-mathematician René Descartes, the subject is also called…

Article

## Analytic hierarchy

A framework for solving a problem. The analytic hierarchy process is a systematic procedure for representing the elements of any problem. It organizes the basic rationality by breaking down a problem into its smaller constituents and then calls for…

Article

## Area

The superficial contents of a geometrical figure of two dimensions. The area of any rectangle or square is the product of two adjacent sides, one of which may be called the base and the other the altitude. In general, any line segment that partially…

Article

## Arithmetic

A branch of mathematics dealing with numbers, operations on numbers, and computation. Arithmetic is useful in solving many practical problems, such as buying, selling, budgets, sports statistics, and measurement. The usual numbers of arithmetic are…

Article

## Asymptote

If the graph of a function y = f (x) goes out to infinity, each “end” of the graph may get closer and closer to a straight line, which is then called an asymptote. In other words, some straight line may well approximate the graph as the function…

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## Barycentric calculus

The application of the properties of the centroid of a set of weighted points to geometry. For certain new operations such as the addition of point and point or of point and vector, it is possible to give their vector equivalents and work within the…

Article

## Bayesian statistics

An approach to statistics in which estimates are based on a synthesis of a prior distribution and current sample data. Bayesian statistics is not a branch of statistics in the way that, say, nonparametric statistics is. It is, in fact, a…

Article

## Bessel functions

By definition the solutions of Bessel's differential equation, Eq. (1). 1Bessel functions, also called cylinder functions, are examples of special functions which are introduced by a differential equation. Bessel functions are of great interest in…

Article

## Binomial theorem

One of the most important algebraic identities, with many applications in a variety of fields. The binomial theorem, discovered by Isaac Newton, expresses the result of multiplying a binomial by itself any number of times, as given in Eq. (1),…

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## Biometrics

The application of mathematical and statistical methods to describe and analyze data concerning the variation of biological characteristics obtained from either observation or experiment. The concept of a population and the samples derived from it…

Article

## Calculus

The branch of mathematics dealing with two fundamental operations, differentiation and integration, which are carried out on functions. The subject, as traditionally developed in college textbooks, is partly an elementary development of the purely…

Article

## Catenary

The curve formed by an ideal heavy uniform string hanging freely from two points of support. The lowest point A (Fig. 1) is the vertex. The portion AP is an equilibrium under the horizontal tension H at A, the tension F directed along the tangent at…

Article

## Circle

The curve that is the locus of points in a plane with equal distance from a fixed point. One of the most basic geometric figures, a circle is perfectly round. In elementary mathematics, "circle" often refers to the finite portion of the plane…