The circumradius of planar reduced convex bodies

被引：0

作者：

Chen, Qiuyue ^{[1
]}

Chen, Bing ^{[1
]}

Jin, Hailin ^{[1
]}

机构：

[1] Suzhou Univ Sci & Technol, Dept Math, Suzhou 215009, Peoples R China

来源：

JOURNAL OF GEOMETRY | 2023年 / 114卷 / 01期

关键词：

Reduced convex body; Reduced convex polygon; Reuleaux polygon; Circumradius;

D O I：

10.1007/s00022-023-00667-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we discuss the circumradius of reduced convex polygons and Reuleaux polygons. We prove that from amongst all reduced convex n-gons of a fixed thickness, only the regular n-gon has the minimal circumradius. For Reuleaux polygons, we show that from amongst all n-th Reuleaux polygons, only the regular n-th Reuleaux polygon has the minimal circumradius.

引用

页数：7

共 15 条

[1] ON REDUCED CONVEX-BODIES
DEKSTER, BV
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1986, 56 (02) : 247 - 256
[2] Dekster BV., 1986, J GEOM, V26, P77, DOI [10.1007/BF01221008, DOI 10.1007/BF01221008]
[3] EXTREMAL CONVEX-SETS
GROEMER, H
[J]. MONATSHEFTE FUR MATHEMATIK, 1983, 96 (01): : 29 - 39
[4] Grunbaum B., 1963, P S PURE MATH, V7, P233
[5] On a measure of asymmetry for Reuleaux polygons
Guo Q.
Jin H.L.
[J]. Journal of Geometry, 2011, 102 (1-2) : 73 - 79
[6] Heil E., 1978, PREPRINT
[7] A note on the extremal bodies of constant width for the Minkowski measure
Jin, Hailin
Guo, Qi
[J]. GEOMETRIAE DEDICATA, 2013, 164 (01) : 227 - 229
[8] Asymmetry of Convex Bodies of Constant Width
Jin, HaiLin
Guo, Qi
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 47 (02) : 415 - 423
[9] Jung H., 1901, J REINE ANGEW MATH, V123, P241
[10] Lassak M, 2005, PUBL MATH-DEBRECEN, V67, P349

← 1 2 →