Geodesic
A Property of Plane Sets of Constant Width
Canadian mathematical bulletin, Tome 6 (1963) no. 3, pp. 409-415

Voir la notice de l'article provenant de la source Cambridge

DOI

It is well known that sets of constant width share several properties with spheres. In this note we consider a simple property of the circle and we show that it is shared by every plane set of constant width. As an application we derive a stronger form of the following theorem of D. Gale, [1]: every plane set of diameter 1 is a union of three sets of diameters not exceeding √3/2, and this constant is best possible. We shall make free use of the more elementary properties of convex sets and of sets of constant width; for these properties and for the terminology see the standard reference [2], or [3]. 
Melzak, Z.A. A Property of Plane Sets of Constant Width. Canadian mathematical bulletin, Tome 6 (1963) no. 3, pp. 409-415. doi: 10.4153/CMB-1963-036-6
@article{10_4153_CMB_1963_036_6,
     author = {Melzak, Z.A.},
     title = {A {Property} of {Plane} {Sets} of {Constant} {Width}},
     journal = {Canadian mathematical bulletin},
     pages = {409--415},
     year = {1963},
     volume = {6},
     number = {3},
     doi = {10.4153/CMB-1963-036-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-036-6/}
}
TY  - JOUR
AU  - Melzak, Z.A.
TI  - A Property of Plane Sets of Constant Width
JO  - Canadian mathematical bulletin
PY  - 1963
SP  - 409
EP  - 415
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-036-6/
DO  - 10.4153/CMB-1963-036-6
ID  - 10_4153_CMB_1963_036_6
ER  - 
%0 Journal Article
%A Melzak, Z.A.
%T A Property of Plane Sets of Constant Width
%J Canadian mathematical bulletin
%D 1963
%P 409-415
%V 6
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-036-6/
%R 10.4153/CMB-1963-036-6
%F 10_4153_CMB_1963_036_6

Cité par Sources :