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Academia - Collins - Pocket Scientific Dictionaries - Mathematics - English - French - Arabic Letter 3_ E

equal
égal

Equal. Quantities that are similar in certain aspects are said to be equal in these aspects. The symbol = is used to indicate equality.

The equality relationship is an example of an equivalence relationship.

equation
équation f

An equation is a statement of an equality relationship between two quantities or expressions. A large part of mathematics is concerned with studying methods for solving different types of equations. For example:

(x+1)2=x²+2x+1

This is an equation that expresses a neutral relationship that holds for any numerical value of x. As for:

3x+1=10

It is a simple linear equation conditional on the value of x. The solution to this equation is: x3

Other examples of common types of simple equations include: quadratic simultaneous equations and simultaneous equations.

equator
équateur m

Equator. A line of latitude representing a great circle.

The equator is a circle drawn on the Earth's surface by taking a section that passes through its center perpendicular to its axis. The equator is a reference line for the locations of latitudes on the Earth's surface. For example, a line of latitude of 60° north means 60° north of the equator.

equilateral
équilatéral

Equilateral polygon with all sides equal in length.

Equilateral triangle
Equilateral pentagon

The interior angles of an equilateral triangle are necessarily equal, but this is not generally true of all equilateral polygons.

equilibrium
équilibre m

Equilibrium When the forces acting on a body in a system are equal and have a resultant equal to zero, the body is in a state of equilibrium.

This marble balanced on the base of an inverted cup is in unstable equilibrium. When the marble is displaced, it will move away from its equilibrium position.

This marble at rest on the bottom of the cup is in stable equilibrium. If it is displaced from its position, it returns to its equilibrium position.

equivalence
équivalence f

The equivalence relation R between members of a set has three properties:

a) It is a reflexive relation cRc: reflexive for all c elements in the set.

b) It is a symmetric relation if aRb is true then bRa is true

c) It is a transitive relation: if dRe and eRf are true then dRf is true.

For example: The relation is similar to defined on a set of flat shapes equivalence relation.

The equivalence relation divides the set into subsets called equivalence classes.

equivalent
éequivalent m

Equivalent Two fractions are said to be equivalent if they represent the same rational number, that is, they can be cancelled to produce a common fraction.

The fractions a/b and cd are equivalent if ad=bc.

For example: 3/4, 6/8, 9/12, 21/28, and 315/420 are equivalent fractions.

euclidean
euclidien

Euclidean. Named after the famous Greek mathematician Euclid. A term often used to describe the regular geometry of space in two or three dimensions.