Results for proportional
On this page:
 
Dictionary:

proportional

  (prə-pôr'shə-nəl, -pōr'-) pronunciation
adj.
  1. Forming a relationship with other parts or quantities; being in proportion.
  2. Properly related in size, degree, or other measurable characteristics; corresponding: Punishment ought to be proportional to the crime.
  3. Mathematics. Having the same or a constant ratio.
n.

One of the quantities in a mathematical proportion.

proportionality pro·por'tion·al'i·ty (-shə-năl'ĭ-tē) n.
proportionally pro·por'tion·al·ly adv.
 
 
Thesaurus: proportional

adjective

  1. Properly or correspondingly related in size, amount, or scale: commensurable, commensurate, proportionate. Idioms: in proportion. See big/small/amount.
  2. Characterized by or displaying symmetry, especially correspondence in scale or measure: balanced, proportionate, regular, symmetric, symmetrical. See same/different/compare.

 
Veterinary Dictionary: proportional

Values expressed as a proportion of the total number of values in a series.

  • p. dwarf — the patient is a miniature without disproportionate reductions or enlargements of body parts.
  • p. morbidity — a percentage estimate of the morbidity of a disease in a group. See also proportional morbidity.
  • p. mortality — the mortality rate due to a specific disease in a group expressed as a proportion of all of the causes of death in the group. See also mortality rate.
 
Wikipedia: 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.

Definition

More formally, the variable y is said to be proportional (or sometimes directly proportional) to the variable x, if there exists a constant non-zero number k such that

y = kx\,

The relation is often denoted

y \propto x

and the constant ratio

k = y/x\,

is called the proportionality constant or constant of proportionality of the proportionality relation.

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.
  • 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 acceleration being the constant of proportionality on the object.

Properties

Since

y = k×x

is equivalent to

x = (1 / k)×y,

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.

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

y = {k \over 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.

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.

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

y = k a^x.\,

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

y = k \log_a (x).\,

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.

See also


This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
Translations: Translations for: Proportional

Dansk (Danish)
adj. - forholdsmæssig
n. - forholdstal

idioms:

  • proportional font    skrifttype, hvor forskellige tegn har forskellig bredde
  • proportional pitch    afstand mellem bogstaver
  • proportional representation    mandatfordeling efter forholdstalsvalg
  • proportional spacing    afstand mellem bogstaver

Nederlands (Dutch)
evenredig, naar verhouding

Français (French)
adj. - proportionnel
n. - (Math) quatrième proportionnelle

idioms:

  • proportional font    (Imprim) fonte proportionnelle
  • proportional pitch    espace proportionnel (des caractères)
  • proportional representation    représentation proportionnelle
  • proportional spacing    espace proportionnel (des caractères)

Deutsch (German)
adj. - proportional, entsprechend
n. - (Math.) Proportionale

idioms:

  • proportional font    Proportionalschriftart
  • proportional pitch    Proportionalabstand
  • proportional representation    Verhältniswahlsystem
  • proportional spacing    Proportionalzwischenraum

Ελληνική (Greek)
adj. - ανάλογος, αναλογικός, σύμμετρος
n. - (μαθημ.) λόγος

idioms:

  • proportional font    (τυπογρ., Η/Υ) αναλογική γραμματοσειρά
  • proportional pitch    (τυπογρ.) αναλογικό βήμα χαρακτήρων
  • proportional representation    αναλογική (εκλογικό σύστημα)
  • proportional spacing    (τυπογρ.) αναλογική απόσταση, αναλογικό διάστημα

Italiano (Italian)
proporzionale

idioms:

  • proportional representation    rappresentazione proporzionale

Português (Portuguese)
adj. - proporcional
n. - proporcional (m)

idioms:

  • proportional representation    representação proporcional

Русский (Russian)
пропорциональный, соразмерный, член пропорции

idioms:

  • proportional representation    пропорциональное представительство

Español (Spanish)
adj. - proporcional
n. - proporcionado a, término de una proporción

idioms:

  • proportional font    fuente proporcional
  • proportional pitch    espaciado variable entre caracteres
  • proportional representation    representación proporcional
  • proportional spacing    espaciado proporcional

Svenska (Swedish)
adj. - proportionell
n. - proportional

中文（简体） (Chinese (Simplified))
比例的, 成比例的, 成常比的, 均衡的, 相称的, 比例项

idioms:

  • proportional font    均衡字体
  • proportional pitch    比例定调
  • proportional representation    比例代表, 人口比例主义, 比例代表制
  • proportional spacing    均匀间距

中文（繁體） (Chinese (Traditional))
adj. - 比例的, 成比例的, 成常比的, 均衡的, 相稱的
n. - 比例項

idioms:

  • proportional font    均衡字體
  • proportional pitch    比例定調
  • proportional representation    比例代表, 人口比例主義, 比例代表制
  • proportional spacing    均勻間距

한국어 (Korean)
adj. - 비례의, 균형이 잡힌
n. - 비례, 균형

日本語 (Japanese)
adj. - 比例の, 比例した

idioms:

  • proportional representation    比例代表制

العربيه (Arabic)
‏(صفه) نسبي, تناسبي, متناسب مع (الاسم) احدى قيم التناسب‏

עברית (Hebrew)
adj. - ‮יחסי, מתכונתי, פרופורציונלי‬
n. - ‮כל אחד מהאיברים המקיימים ביניהם יחס מסוים (מתמטיקה)‬

If you are unable to view some languages clearly, click here.

To select your translation preferences click here.


 
Best of the Web: proportional

Some good "proportional" pages on the web:


Math
mathworld.wolfram.com
 
 
 

Join the WikiAnswers Q&A community. Post a question or answer questions about "proportional" at WikiAnswers.

 

Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.  Read more
Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.  Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Proportionality (mathematics)".  Read more
Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved.  Read more

Search for answers directly from your browser with the FREE Answers.com Toolbar!  
Click here to download now. 

Get Answers your way! Check out all our free tools and products.

On this page:   E-mail   print Print  Link  

 

Keep Reading

Mentioned In:

 |  More >More >
 

Do you have the answers?