Take the 2-minute tour ×
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.

I have read a book called "Proofs From The Book", but it defined many terms and contains much terminology, so I couldn't understand how to obtain a proof by using Bricard's condition. However, I couldn't understand the proof of Bricard's condition either, so I have no hope to understand the formal proof, hope you could give me the intuition behind the proof.

Thanks in advance!

P.S. And how do we define split of tetrahedra?

share|improve this question
3  
I imagine if there was intuition behind any of Hilbert's problems, they wouldn't be as infamous as they are! –  Adam Dec 31 '11 at 19:47

1 Answer 1

up vote 3 down vote accepted

Bricard proved a special case of scissors congruence: Any two polyhedra that are mirror images of one another are scissors congruent. And along the way, he discovered a precursor to the Dehn invariant. There is intuition behind the Dehn invariant, essentially relying on a distinction between dihedral angles that are rational multiples of $\pi$ and those that are not. The cube is not scissors congruent to the regular tetraheron basically because the latter has irrational (multiples of $\pi$) dihedral angles while the cube has rational dihedral angles, $\frac{1}{2}\pi$. Of course, there is much more, but this is somehow the essence.

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.