In geometry, the mean width is a measure of the "size" of a body; see Hadwiger's theorem for more about the available measures of bodies. In dimensions, one has to consider -dimensional hyperplanes perpendicular to a given direction in , where is the n-sphere (the surface of a -dimensional sphere).
The "width" of a body in a given direction is the distance between the closest pair of such planes, such that the body is entirely in between the two hyper planes (the planes only intersect
with the boundary of the body). The mean width is the average of this "width" over all in .
More formally, define a compact body B as being equivalent to set of points in its interior plus the points on the boundary (here, points denote elements of ). The support function of body B is defined as
where is a direction and denotes the usual inner product on . The mean width is then
where is the -dimensional volume of .
Note, that the mean width can be defined for any body (that is compact), but it is most
useful for convex bodies (that is bodies, whose corresponding set is a convex set).
In geometry, the meanwidth is a measure of the "size" of a body; see Hadwiger's theorem for more about the available measures of bodies. In n {\displaystyle...
dimensions, based on MRI scans of 28 women: Mean length from cervix to introitus: 6.3 cm (2.5 in). Meanwidth: at the proximal vagina: 3.3 cm (1.3 in);...
Red blood cell distribution width (RDW), as well as various types thereof (RDW-CV or RCDW and RDW-SD), is a measure of the range of variation of red blood...
has a complex shape. Another method of specifying spectral width is a special case of root-mean-square deviation where the independent variable is wavelength...
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same...
of 350 m. The about-2-km-deep cave has a main passage with a meanwidth of 50 m and a mean height of 20 m. Sunlight reaches about 200 m from the entrance...
with a fixed width. Although there is also a history of half-width characters, many Japanese, Korean and Chinese fonts include full-width forms for the...
equalization are to permit greater recording times (by decreasing the meanwidth of each groove), to improve sound quality, and to reduce the groove damage...
2{\text{ × Area}}(r)} . The meanwidth of a convex polygon is equal to its perimeter divided by π {\displaystyle \pi } . So its width is the diameter of a circle...
the hub Meanwidth ratio = (Area of one blade outside the hub/length of the blade outside the hub)/Diameter Blade width ratio = Maximum width of a blade/Diameter...
{\bar {m}}} and v {\displaystyle \textstyle v} are mean and biased variance of a histogram with bin-width h {\displaystyle \textstyle h} , m ¯ = 1 k ∑ i =...
commonly found variations are the variable width box plots and the notched box plots shown in Figure 4. Variable width box plots illustrate the size of each...
which its width is abnormally reduced (upper and lower face width less than 2 SD below the mean subjectively, or apparent reduction of the width of the upper...
where the size 0 (or 1) is positioned. Some systems also indicate the shoe width, sometimes also as a number, but in many cases by one or more letters. Some...
lake is pear-shaped and has a maximum length of 64.3 km (40.0 mi) with a meanwidth of 20.1 km (12.5 mi). Another lake in India called Vembanad Lake is the...
reports largely list meanwidth whereas contemporary years list maximum width. Values provided by Grazulis are the average width, with estimates being...
In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one...
The mean corpuscular volume, or mean cell volume (MCV), is a measure of the average volume of a red blood corpuscle (or red blood cell). The measure is...
Abnormal values indicate the presence of anemia and which type of anemia it is. Mean corpuscular volume (MCV) is the average volume of a red blood cell and is...
River and Xiuguluan River and their branches. Subtropical plains, with a meanwidth around 3–6 km (1.9–3.7 mi), dominate the valleys between both mountain...
wide spores have a meanwidth ranging from 7.5 to 10μm, respectively, while the subspherical ones range from 5.3-8μm in meanwidth. The subspherical forms...
The wide spores have a meanwidth ranging from 7.5-10μm, respectively, while the subspherical ones range from 5.3-8μm in meanwidth. The subspherical forms...
would mean that the nominal width of the tire is approximately 195 mm at the widest point, the height of the side-wall of the tire is 55% of the width (107 mm...