4
votes
Accepted
Proof verification: A cube and a tetrahedron are not scissors congruent?
Yes, there is a flaw. If you cut an edge in half, you get another copy of that edge's dihedral angle, which can affect your sum arbitrarily.
You can observe that $A'(\mathcal{P})\neq A'(\mathcal{Q})$ ...
- 17.7k
1
vote
Accepted
Chvatal-Gomory integer rounding method to find facets of $\operatorname{conv}(S)$
Here's a systematic approach that uses LP duality. First write your constraints as \begin{align}
4x_1 + x_2 &\le 28 \tag1\label1\\
x_1 + 4x_2 &\le 27 \tag2\label2\\
x_1 - x_2 &\le 1 \...
- 47.4k
1
vote
Do the second differences of the fifth powers count the sphere packing of a polyhedron?
Those second differences are all multiples of $30$. Proof:
$(n+1)^5-2n^5+(n-1)^5=20n^3+10n=20n(n+1)(n-1)+30n$
and $n(n+1)(n-1)$ must have a factor divisible by $3$. Divide out this factor of $30$ and ...
- 41.4k
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