Editing Aspect ratio (section)

==Aspect ratios of general shapes==
In [[geometry]], there are several alternative definitions to aspect ratios of general [[compact set]]s in a d-dimensional space:<ref name=SmithWormald1998>{{Cite book
| last1 = Smith | first1 = W. D.
| last2 = Wormald | first2 = N. C.
| doi = 10.1109/sfcs.1998.743449
| chapter = Geometric separator theorems and applications
| title = Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
| pages = 232
| year = 1998
| isbn = 0-8186-9172-7
| s2cid = 17962961
| url = http://users.monash.edu.au/~nwormald/papers/geomsep.ps.gz
}}</ref>
* 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 of <math>\sqrt{2}</math>.
* The cube-volume aspect ratio (CVAR) of a compact set is the ''d''-th root of the ratio of the ''d''-volume of the smallest enclosing axes-parallel ''d''-cube, to the set's own ''d''-volume. A square has the minimal CVAR which is 1. A circle has a CVAR of <math>\sqrt{2}</math>. An axis-parallel rectangle of width ''W'' and height ''H'', where ''W''&gt;''H'', has a CVAR of <math>\sqrt{W^2/WH} = \sqrt{W/H}</math>.

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