View source for Steiner point

The centre of the mass, distributed over the surface of a convex body, with density equal to the Gaussian curvature. For a non-smooth body it is defined by mixed volumes (see [[Mixed-volume theory|Mixed-volume theory]]). The Steiner point is additive with respect to the addition of bodies. The centre of a mass, distributed over a contour of variable curvature in the plane, was first studied by J. Steiner in 1840.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  B. Gruenbaum,   "Measures of symmetry for convex sets"  V.L. Klee (ed.) , ''Convexity'' , ''Proc. Symp. Pure Math.'' , '''7''' , Amer. Math. Soc.  (1963)  pp. 238–270</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  R. Schneider,   "Krümmungsschwerpunkte konvexer Körper (I)"  ''Abh. Math. Sem. Univ. Hamburg'' , '''37''' :  1–4  (1972)  pp. 112–132</TD></TR></table>



====Comments====
Axiomatic characterizations of the Steiner point are treated in [[#References|[a1]]], [[#References|[a2]]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  R. Schneider,   "On Steiner points of convex bodies"  ''Israel J. Math.'' , '''9'''  (1971)  pp. 241–249</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  E.D. Positsel'skii,   "Characterization of Steiner points"  ''Math. Notes'' , '''14'''  (1973)  pp. 698–700  ''Mat. Zametki'' , '''14'''  (1973)  pp. 243–247</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  B. Grünbaum,   "Convex polytopes" , Wiley  (1967)</TD></TR></table>