Formula (express) – Wikipedia, free encyclopedia

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A formula It is a sequence or chain of characters whose symbols belong to a formal language, in such a way that the expression meets certain rules of good formation and that admits an interpretation consisting in some area of ​​mathematics and in other formal systems. This aims to express a general relationship between the terms expressed in the formula.

In a formal system, a well -formed formula is a character chain or word generated according to a formal grammar from a given alphabet. A formal language is defined as the set of all its well -formed formulas.

In mathematics [ To edit ]

In geometry, statistics and other branches of mathematics, a formula is an equation that relates constant or mathematical variables and is expressed by mathematical equality. [ first ] ​

Mathematical expressions consist of a set of alphabet symbols, which in a mathematical expression includes:

  • Constants and variables, there are several ways to designate this type of entities:
    • Numbers, which are a type of constant.
    • Latin alphabet signs, which is used to name both constants and variables.
    • Signs of the Greek alphabet, used similar to the previous ones.
  • Functions and predicates; Among this set of symbols, some specific ones are used for:
    • Operators, which are usually interpreted as functions, for example the sum + or the product · can be understood as functions of two arguments.
  • Logical symbols
  • Scoring signs, horizontal and vertical separators and divisors.
  • Other symbols of exclusive creation for this language, such as
    ∫ , ∅ , {displaystyle int ,emptyset ,}

    For integral and empty set, among many others.

For example, the problem of determining the volume of geometric bodies, such as Platonic solids, or metric relations of the triangle, or trigonometric reasons. The volume of a sphere requires integral calculation for resolution; According to Archimedes, it can be calculated by the formula that relates the volume to the radio:

IN = 43Pi r 3. {displaystyle V={frac {4}{3}}pi r^{3}.}

In algebra, a formula is an identity that is used to simplify calculations or solve an equation or factor polynomials. For example, for the quadratic equation with real or complex coefficients, there are always two solutions, not necessarily different, called estate , which can be real or complex. It is called Quadratic formula [ 2 ] To the equation that provides the roots of the quadratic equation:

x = −b±b2−4ac2a{displaystyle x={frac {-bpm {sqrt {b^{2}-4ac}}}{2a}}}

where the symbol ± indicates that the values

x1=−b+b2−4ac2a{displaystyle x_{1}={frac {-b+{sqrt {b^{2}-4ac}}}{2a}}}

and  x2=−b−b2−4ac2a{displaystyle x_{2}={frac {-b-{sqrt {b^{2}-4ac}}}{2a}}}

They constitute the two solutions.

The amounts, measurements or unknowns are usually identified or symbolized with capital letters (v = volume), lowercase letters (r = radio), Greek letters (π = pi = 3.1415926…) and other symbols (σ represents the sum of many similar quantities, an arrow on a letter indicates that it is a vector,

a→{displaystyle textstyle {overrightarrow {a}}}

, a point on a letter,

a˙{DisplayStyle Text style {dot {a}}}

, indicates the derivative or differential of that function, etc.). Sometimes it is necessary to use subscripts (x first , x 2 ,…) And superior (x 2 , x 3 , …).

In natural sciences [ To edit ]

In physics, chemistry and other sciences, a formula relates physical magnitudes that can be measured to calculate the value of others very difficult or impossible. In a general context, they provide us with a mathematical solution for a real world problem. A chemical formula expresses the relationship of the elements in a molecule or chemical compound.

The general expression of Newton’s second law, which can also be expressed as F = m a , it is applicable to a very wide range of physical situations and allows us to calculate some variables from other known or predict the behavior of a physical system. The two terms of a physical formula must have the same equation of dimensions, that is, possess the same units of measure, or can become identical. [ 3 ] ​

Often, the formulas are accompanied by the corresponding units because the scientific formulas express relationships between real magnitudes that are the result of measures and that, therefore, have units. In the previous example of the sphere, if r = 2.0 cm, the result for volume will be:

IN = 43Pi ( 2 , 0  cm) 3= 33 , 51  cm3. {Displaystyle V = {Frac {4} {3}} Pi (2.0 {mbox {cm}})^{3} = 33,51 {mbox {cm}}^}^}.}.

In computer science [ To edit ]

In computer science, a formula typically describes a calculation, as a sum, which will be performed on one or more variables. Often the formulas have the implicit format of an instruction or computer command such as:

Celsius degrees = (5/9)*( Grado Fahrenheit -32)

In the terminology of a computer spreadsheet, a formula is usually a text chain that contains cell references, such as = A1+a2 where A1 and A2 describe “cells” (column A, row 1 or 2) within the spreadsheet. The result will appear in the cell containing this formula (for example, in A3, below the above values). The sign = The second term (right) of the formula that indicates the cell in which the data is stored precedes. The left or first member of the formula is omitted in these cases as the result is stored in the place where the formula is located and it would be redundant to say a3 = a1 + a2, if the formula is stored in A3.

Most computer programs, however, cannot handle a symbolic logic and only work with numerical amounts, binary system and Boole’s algebra, and requirements on units in data introduction should be respected.

In social sciences [ To edit ]

Likewise, in economics, [ 4 ] Sociology, psychology and other social sciences, formulas are used that relate the magnitudes of these branches of knowledge.

For example, Okun’s law can be expressed in the following way: (Abel & Bernanke 2005)

(Y¯−Y)Y¯= c ( in – u¯) {displaystyle {frac {({overline {Y}}-Y)}{overline {Y}}}=c(u-{overline {u}})}

, where:

  • Y¯{displaystyle {overline {Y}}}

    It is the GDP of full employment or potential production.
  • And it is the current GDP.

  • u¯{displaystyle {overline {u}}}

    It is the natural unemployment rate.
  • U is the current unemployment rate.
  • C is the factor that relates changes in unemployment to changes in production.

See also [ To edit ]

References [ To edit ]

external links [ To edit ]