Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 ^-^

share|cite|improve this question
Can you find a formula for $R$ in terms of side lengths and angles? – Alex Becker Apr 3 '12 at 23:32
It seems "obvious" that the tetrahedron you want is regular. If so, formulas for the radius of the sphere are available on the web. – Ross Millikan Apr 4 '12 at 13:05
The regular tetrahedron has $L/R\doteq 9.8$, a flat square degenerate tetrahedron has $L/R\doteq9.65$. – Christian Blatter Feb 8 '13 at 10:37
@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? – Gilles Bonnet Feb 14 '15 at 12:56

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.