Kepler's Conjecture/Mistake

Source Work

 * Thème et variations
 * $0,77963 55700 \ldots$
 * $0,77963 55700 \ldots$

Mistake

 * $\sqrt {18} \paren {\operatorname {Arcos} 1/3 - \pi / 3}$
 * ''Le meilleur majorant connu pour la densité d'un empilement de sphères dans $R^3$.

That is, in English:


 * $\sqrt {18} \paren {\arccos 1/3 - \pi / 3}$
 * The best known upper bound for the density of a stack of spheres in $\R^3$.

Correction
This constant is in fact the packing density of a regular tetrahedron.

That is:


 * Let $S$ be a regular tetrahedron of edge length $2$.


 * Let $B$ be the part of $S$ that lies within distance $1$ of some vertex.


 * Then this constant is the ratio of the volume of $B$ to the volume of $S$.

Also see

 * Packing Density of Regular Tetrahedron