Editing Mean width (section)

===Three dimensions===
For convex bodies ''K'' in three dimensions, the mean width of ''K'' is related to the average of the [[mean curvature]], ''H'', over the whole surface of ''K''. In fact,

: <math>\int_{\delta K} \frac{H}{2\pi} dS = b(K)</math>

where <math>\delta K</math> is the boundary of the convex body <math>K</math> and <math>dS</math>
a surface integral element, <math>H</math> is the [[mean curvature]] at the corresponding position
on <math>\delta K</math>. Similar relations can be given between the other measures  
and the generalizations of the mean curvature, also for other dimensions 
.<ref>
{{citation
|last1=Jiazu
|first1=Zhou 
|first2=Jiang
|last2=Deshuo
|title=On mean curvatures of a parallel convex body

|journal=Acta Mathematica Scientia 
|volume=28
|issue=3
|pages=489–494 
|year=2008 
|doi=10.1016/S0252-9602(08)60050-8
}}</ref>
As the integral over the mean curvature is typically much easier to calculate
than the mean width, this is a very useful result.