View source for Self-perimeter

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The length $2\pi_S$ of a centrally-symmetric closed convex curve $S$ on a plane, measured in the Minkowski metric for which $S$ plays the role of unit circle. Always $3\leq\pi_S\leq4$ (see [[#References|[1]]]). In the generalization to the non-symmetric case, a self-perimeter is the length of a directed curve $S$, and depends on the choice of the origin inside $S$ (see [[#References|[2]]], [[#References|[3]]]). The case of a star $S$ has been considered (see [[#References|[4]]]). There are various generalizations of a self-perimeter for the unit sphere $S$ in a normed space of dimension greater than two (see [[#References|[5]]], [[#References|[6]]]).

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  Yu.G. Reshetnyak,   "An extremal problem in the theory of surfaces"  ''Uspekhi Mat. Nauk'' , '''8''' :  6  (1953)  pp. 125–126  (In Russian)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  V.A. Sorokin,   "Minkowski geometry with asymmetric indicatrix"  ''Uchebn. Zap. Moskov. Gos. Ped. Inst.'' , '''243'''  (1965)  pp. 160–185  (In Russian)</TD></TR>
<TR><TD valign="top">[3]</TD> <TD valign="top">  G.D. Chakerian,   W.K. Talley,   "Some properties of the self-circumference of convex sets"  ''Arch. Math.'' , '''20''' :  4  (1969)  pp. 431–443</TD></TR>
<TR><TD valign="top">[4]</TD> <TD valign="top">  S. Gołab,   "Sur la longueur d'indicatrice dans la géométrie plane de Minkowski"  ''Colloq. Math.'' , '''15''' :  1  (1966)  pp. 141–144</TD></TR>
<TR><TD valign="top">[5]</TD> <TD valign="top">  J.J. Schäffer,   "Spheres with maximum inner diameter"  ''Math. Ann.'' , '''190''' :  3  (1971)  pp. 242–247</TD></TR>
<TR><TD valign="top">[6]</TD> <TD valign="top">  C.M. Petty,   "Geominimal surface area"  ''Geom. Dedic.'' , '''3''' :  1  (1974)  pp. 77–97</TD></TR>
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