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 n {\displaystyle n} dimensions, one has to consider ( n − 1 ) {\displaystyle (n-1)} -dimensional hyperplanes perpendicular to a given direction n ^ {\displaystyle {\hat {n}}} in S n − 1 {\displaystyle S^{n-1}} , where S n {\displaystyle S^{n}} is the n-sphere (the surface of a ( n + 1 ) {\displaystyle (n+1)} -dimensional sphere).
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 n {\displaystyle n} dimensions, one has to consider ( n − 1 ) {\displaystyle (n-1)} -dimensional hyperplanes perpendicular to a given direction n ^ {\displaystyle {\hat {n}}} in S n − 1 {\displaystyle S^{n-1}} , where S n {\displaystyle S^{n}} is the n-sphere (the surface of a ( n + 1 ) {\displaystyle (n+1)} -dimensional sphere).
Source: Wikipedia "Mean width" · CC BY-SA 4.0
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