caa a22 4500 445813415 CHVBK 20180317145218.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00022-011-0096-9 doi (NATIONALLICENCE)springer-10.1007/s00022-011-0096-9 On a measure of asymmetry for Reuleaux polygons [Elektronische Daten] [Qi Guo, HaiLin Jin] In a previous paper, we showed that for regular Reuleaux polygons R n the equality $${{\rm as}_\infty(R_n) = 1/(2\cos \frac\pi{2n} -1)}$$ holds, where $${{\rm as}_\infty(\cdot)}$$ denotes the Minkowski measure of asymmetry for convex bodies, and $${{\rm as}_\infty(K)\leq \frac 12(\sqrt{3}+1)}$$ for all convex domains K of constant width, with equality holds iff K is a Reuleaux triangle. In this paper, we investigate the Minkowski measures of asymmetry among all Reuleaux polygons of order n and show that regular Reuleaux polygons of order n (n ≥ 3 and odd) have the minimal Minkowski measure of asymmetry. Springer Basel AG, 2011 Asymmetry measures nationallicence constant width nationallicence Reuleaux polygons nationallicence Guo Qi Department of Mathematics, Suzhou University of Science and Technology, Suzhou, China aut Jin HaiLin Department of Mathematics, Shanghai University, Shanghai, China aut Journal of Geometry SP Birkhäuser Verlag Basel 102/1-2(2011-12-01), 73-79 0047-2468 102:1-2<73 2011 102 22 https://doi.org/10.1007/s00022-011-0096-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00022-011-0096-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Guo Qi Department of Mathematics, Suzhou University of Science and Technology, Suzhou, China aut NATIONALLICENCE 700 1- Jin HaiLin Department of Mathematics, Shanghai University, Shanghai, China aut NATIONALLICENCE 773 0- Journal of Geometry SP Birkhäuser Verlag Basel 102/1-2(2011-12-01), 73-79 0047-2468 102:1-2<73 2011 102 22 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer