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Aspect ratio

From Wikipedia, the free encyclopedia
Attribute of a geometric shape
For other uses, seeAspect ratio (disambiguation).

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Theaspect ratio of ageometric shape is theratio of its sizes in different dimensions. For example, the aspect ratio of arectangle is the ratio of its longer side to its shorter side—the ratio of width to height,[1][2] when the rectangle is oriented as a "landscape".

The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimalfraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1,85 and 1.6 are all ways of representing the same aspect ratio.

In objects of more than two dimensions, such ashyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.

Applications and uses

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The term is most commonly used with reference to:

Aspect ratios of simple shapes

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Rectangles

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Main article:Aspect ratio (image)

For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. Asquare has the smallest possible aspect ratio of 1:1.

Examples:

Ellipses

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For anellipse, the aspect ratio denotes the ratio of themajor axis to theminor axis. An ellipse with an aspect ratio of 1:1 is acircle.

Aspect ratios of general shapes

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Ingeometry, there are several alternative definitions to aspect ratios of generalcompact sets in a d-dimensional space:[3]

  • The diameter-width aspect ratio (DWAR) of a compact set is the ratio of its diameter to its width. A circle has the minimal DWAR which is 1. A square has a DWAR of2{\displaystyle {\sqrt {2}}}.
  • The cube-volume aspect ratio (CVAR) of a compact set is thed-th root of the ratio of thed-volume of the smallest enclosing axes-paralleld-cube, to the set's ownd-volume. A square has the minimal CVAR which is 1. A circle has a CVAR of2{\displaystyle {\sqrt {2}}}. An axis-parallel rectangle of widthW and heightH, whereW>H, has a CVAR ofW2/WH=W/H{\displaystyle {\sqrt {W^{2}/WH}}={\sqrt {W/H}}}.

If the dimensiond is fixed, then all reasonable definitions of aspect ratio are equivalent to within constant factors.

Notations

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Aspect ratios are mathematically expressed asx:y (pronounced "x-to-y").

Cinematographic aspect ratios are usually denoted as a (rounded) decimal multiple of width vs unit height, while photographic and videographic aspect ratios are usually defined and denoted by whole number ratios of width to height. Indigital images there is a subtle distinction between thedisplay aspect ratio (the image as displayed) and thestorage aspect ratio (the ratio of pixel dimensions); seeDistinctions.

See also

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References

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  1. ^Rouse, Margaret (September 2005)."What is aspect ratio?".WhatIs?. TechTarget. Retrieved3 February 2013.
  2. ^Rouse, Margaret (September 2002)."Wide aspect ratio display".display. E3displays. Retrieved18 February 2020.
  3. ^Smith, W. D.; Wormald, N. C. (1998). "Geometric separator theorems and applications".Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280). p. 232.doi:10.1109/sfcs.1998.743449.ISBN 0-8186-9172-7.S2CID 17962961.
Division and ratio
The ratio of width to height of standard-definition television.
Fraction
  • Numerator/Denominator = Quotient
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