3
$\begingroup$

Determine the tetrahedron $ABCD$ so that $\frac{L}{R}$ has the maximum value, where $L=AB+AC+AD+BC+BD+CD$, and $R$ is the radius of the circumsphere of $ABCD$. sorry about my bad English ^-^

  • 0
    Can you find a formula for $R$ in terms of side lengths and angles?2012-04-03
  • 1
    It seems "obvious" that the tetrahedron you want is regular. If so, formulas for the radius of the sphere are available on the web.2012-04-04
  • 1
    The regular tetrahedron has $L/R\doteq 9.8$, a flat square degenerate tetrahedron has $L/R\doteq9.65$.2013-02-08
  • 0
    @RossMillikan It is natural to think that the tetrahedron maximizing the given isoperimeter is probably regular. But do you have any clue how to prove it?2015-02-14

0 Answers 0