View source for Jung theorem

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Every set of diameter $d$ in a Euclidean space $E_n$ is contained in a ball in $E_n$ of radius $r=d(n/2(n+1))^{1/2}$. There are analogues and generalizations of Jung's theorem (e.g. replacing the Euclidean distance by other metrics) (cf. [[#References|[2]]]).

The theorem was proved by H.W.E. Jung [[#References|[1]]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  H.W.E. Jung,   "Ueber den kleinsten Kreis, der eine ebene Figur einschliesst"  ''J. Reine Angew. Math.'' , '''130'''  (1901)  pp. 310–313</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  L. Danzer,   B. Grünbaum,   V.L. Klee,   "Helly's theorem and its relatives"  V.L. Klee (ed.) , ''Convexity'' , ''Proc. Symp. Pure Math.'' , '''7''' , Amer. Math. Soc.  (1963)  pp. 101–180</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  H. Hadwiger,   H. Debrunner,   "Combinatorial geometry in the plane" , Holt, Rinehart &amp; Winston  (1964)  (Translated from German)</TD></TR></table>



====Comments====
The counterpart for inscribed balls is Steinhagen's theorem (cf. [[#References|[a1]]]).

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  T. Bonnesen,   W. Fenchel,   "Theorie der konvexen Körper" , Springer  (1974)</TD></TR></table>