Abstract
We calculate E[V 4(C)], the expected volume of a tetrahedron whose vertices are chosen randomly (i.e. independently and uniformly) in the interior of C, a cube of unit volume. We find $$E[V_4 {\rm (cube)}]={3977\over 216000} - {\pi^2 \over 2160}=0.01384277574\ldots$$ The result is in convincing agreement with a simulation of 3000 · 106 trials.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
