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Encyclopedia > Proportionality (mathematics)
This article is about proportionality, the mathematical relation. For other uses of the term proportionality, see Proportionality (disambiguation).

In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. Image File history File links Question_book-3. ... The word proportionality may have one of a number of meanings: In mathematics, proportionality is a mathematical relation between two quantities. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Quantity is a kind of property which exists as magnitude or multitude. ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... Multiple is a comic book superhero in the Marvel Comics universe. ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ...

Contents

Definition

More formally, the variable y is said to be proportional (or sometimes directly proportional if the constant is positive) to the variable x, if there exists a non-zero number k such that In computer science and mathematics, a variable (IPA pronunciation: ) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression. ...

The relation is often denoted

and the constant ratio

is called the proportionality constant or constant of proportionality of the proportionality relation. In mathematics, a binary relation (or a dyadic relation) is an arbitrary association of elements of one set with elements of another (perhaps the same) set. ...


Examples

  • If an object travels at a constant speed, then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.
  • On a map drawn to scale, the distance between any two points on the map is proportional to the distance between the two locations the points represent, with the constant of proportionality being the scale of the map.

This article does not cite any references or sources. ... Distance is a numerical description of how far apart objects are at any given moment in time. ... Look up time in Wiktionary, the free dictionary. ... The circumference is the distance around a closed curve. ... Circle illustration This article is about the shape and mathematical concept of circle. ... DIAMETER is a computer networking protocol for AAA (Authentication, Authorization and Accounting). ... When a circles diameter is 1, its circumference is π. Pi or π is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... For other uses, see Map (disambiguation). ... Variable scale to measure distances on maps An important property of a map is the scale. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... Gravity is a force of attraction that acts between bodies that have mass. ... This article is about Earth as a planet. ... This article or section is in need of attention from an expert on the subject. ... In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. ...

Properties

Since

is equivalent to

it follows that if y is proportional to x, with (nonzero) proportionality constant k, then x is also proportional to y with proportionality constant 1/k.


If y is proportional to x, then the graph of y as a function of x will be a straight line passing through the origin with the slope of the line equal to the constant of proportionality. Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... “Line” redirects here. ... In mathematics, the origin of a coordinate system is the point where the axes of the system intersect. ... This article is about the mathematical term. ...


Inverse proportionality

As noted in the definition above, two proportional variables are sometimes said to be directly proportional. This is done so as to contrast proportionality with inverse proportionality.


Two variables are inversely proportional (or varying inversely) if one of the variables is directly proportional with the multiplicative inverse of the other, or equivalently if their product is a constant. It follows, that the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that The reciprocal function: y = 1/x. ...

Basically, the concept of inverse proportion means that as the absolute value or magnitude of one variable gets bigger, the absolute value or magnitude of another gets smaller, such that their product (the constant of proportionality) is always the same. In mathematics, the absolute value (or modulus[1]) of a real number is its numerical value without regard to its sign. ...


For example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.


The graph of two variables varying inversely on the Cartesian coordinate plane is a hyperbola. The product of the X and Y values of each point on the curve will equal the constant of proportionality (k). Since k can never equal zero, the graph will never cross either axis. In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ...


Exponential and logarithmic proportionality

A variable y is exponentially proportional to a variable x, if y is directly proportional to the exponential function of x, that is if there exists a non-zero constant k such that The exponential function is one of the most important functions in mathematics. ...

Likewise, a variable y is logarithmically proportional to a variable x, if y is directly proportional to the logarithm of x, that is if there exists a non-zero constant k such that Logarithms to various bases: is to base e, is to base 10, and is to base 1. ...

Experimental determination

To determine experimentally whether two physical quantities are directly proportional, one performs several measurements and plots the resulting data points in a Cartesian coordinate system. If the points lie on or close to a straight line that passes through the origin (0, 0), then the two variables are probably proportional, with the proportionality constant given by the line's slope. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Fig. ... This article is about the mathematical term. ...


See also


  Results from FactBites:
 
Mathematics - MSN Encarta (1222 words)
The Greeks adopted elements of mathematics from the Babylonians and the Egyptians.
The new element in Greek mathematics was the invention of an abstract mathematics founded on a logical structure of definitions, axioms (propositions accepted as self-evident), and proofs.
The mathematics that had existed before their time was a collection of conclusions based on observation.
Proportionality (mathematics) Summary (1793 words)
In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.
The circumference of a circle is proportional to its diameter, with the constant of proportionality equal to π.
The amount of force acting on a certain object from the gravity of the Earth at sea level is proportional to the object's mass, with the gravitational constant being the constant of proportionality.
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