Asphericity

Asphericity is defined as (Eq.5):

$\langle A\rangle ={\frac {\langle \mathrm {Tr} ^{2}-3M\rangle }{\langle \mathrm {Tr} ^{2}\rangle }}$

where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \mathrm {Tr} } is the trace of the moment of inertia tensor, given by (Eq. 3)

$\mathrm {Tr} =R_{1}^{2}+R_{2}^{2}+R_{3}^{2}$

and $M$ is the sum of the three minors, given by

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle M=R_{1}^{2}R_{2}^{2}+R_{1}^{2}R_{3}^{2}+R_{2}^{2}R_{3}^{2}}

where $R_{1}^{2}$, $R_{2}^{2}$ and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_3^2} are the three eigenvalues of the tensor.

See also

• Random walk