ENCYCLOPEDIA OF DISTANCES

• Preliminary version: Dictionary of Distances, Elsevier, 2006; its online ScienceDirect version

• Russian updated translation: Encyclopedic Dictionary of Distances, Naouka, 2008

• Encyclopedia of Distances (1st edition), Springer, 2009;

• 2nd edition, Springer, 2012; its online SpringerLink version

• 3rd edition, Springer, 2014; its online SpringerLink version

• 4th edition, Springer, 2016; its online SpringerLink version

Nice distances (as a perspective) images: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

• CHAPTER 9: Add in Section 9.1 after the end of item "Demyanov distance", i,e, on page 188 after line 13, from \newline:

\item{\index{\bf Minkowski length of lattice polytope}}

Let $P$ be a convex $d$-dimensional {\em lattice polytope} in $\mathbb {R}^d$, i.e., a convex hull of finitely many points in the integer lattice $\mathbb{Z}^d \subset \mathbb{R}^d$. The {\em lattice diameter} $l((P)$ is defined as one less than the largest number of collinear lattice points in $P$.

For any $1\le n\le d$, the {\em $n$-th Minkowski length} $L_n(P)$ is defined (Soprunov--Soprunova, 2009) as the largest number of lattice polytopes of positive dimension whose Minkowski sum is contained in $P$, i.e., the largest number of lattice segments whose Minkowski sum is at most $n$-dimensional and is contained in $P$; so, $L_1(P)=l(P)$. The {\bf Minkowski length} of $P$ is $L_d(P)$.

• CHAPTER :

• CHAPTER 23: Add in Section 23.3 (in"Collective motion") on page 471 line 17 from below, from \newline:

The largest synchronized movement of biomass on Earth is diel vertical migration of zooplankton in the ocean and lakes.

• CHAPTER 25:: Add on page 547 line 6 from below:

$50-300$ km: unexplored slice of atmosphere, where the air is too thin to support research balloons, but it is too thick for satellites to survive the drag forces for more than a few months.

REFERENCES, add within their place in alphabetic order:

FURTHER COMMENTS should be sent to Michel Deza at this address: Michel.Deza@ens.fr