where
is the circumradius of
(Danzer et al. 1963).
This gives the special case that every finite set of points in two dimensions with geometric span has an enclosing circle
with radius no greater than (Rademacher and Toeplitz 1957, p. 104).
The Jung constant generalizes the enclosing-radius ratio to other normed spaces. Li (2026) proved for every
positive integer, with equality in dimension five. Here has the taxicab metric;
this is not a replacement for the Euclidean inequality above.
of a compact
set 
in 
satisfies
is the circumradius of 
(Danzer et al. 1963).
has an enclosing circle
with radius no greater than 
(Rademacher and Toeplitz 1957, p. 104).
for every
positive integer 
, with equality in dimension five. Here 
has the taxicab metric;
this is not a replacement for the Euclidean inequality above.
." 6 Oct 2026.