Relative distance of boundary points of a convex body and touching by homothetical copies

• Autorzy: Lángi Z.
• Języki publikacji: EN

Abstrakty

EN

The relative distance of points p and g of a convex body C is the ratio of the length of the segment pq to the half of the length of a longest chord of C parallel to pq. In this paper we find a connection between pairwise relative distances of k points in the boundary of a convex body and the rafio of k homothetical copies of a convex body touching it.

Słowa kluczowe

EN

Minkowski sum; homothetical copy; relative distance

PL

suma Minkowskiego; kopia podobna; odległość względna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 4
• Strony: 439--444
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Lángi Z.

• Department of Geometry, Faculty of Natural Sciences, Eötvös Loránd University, Pázmány Péter s. 1/C, 1117 Budapest, Hungary

Bibliografia

• [1] K. Doliwka, On five points in the boundary of a plane convex body pairwise in at least unit relative distances, J. Geom., 53 (1995) 76-78.
• [2] K. Doliwka, M. Lassak, On relatively short and long sides of convex pentagons, Geom. Dedicata, 56 (1995) 221-224.
• [3] P. G. Doyle, J. C. Lagarias, D. Randall, Self-packing of centrally symmetric convex bodies in R2, Discrete Comput. Geom., 8 (1992) 171-189.
• [4] I. Fáry, E. Makai, Jr., Isoperimetry in variable metric, Stud. Scient. Math. Hung., 17 (1982) 143-158.
• [5] S. Gołąb, Some metric problems of the geometry of Minkowski, Trav. Acad. Mines Cracovie, 6 (1932).
• [6] B. Grünbaum, On a conjecture of H. Hadwiger, Pacific J. Math., 11 (1961) 215-219.
• [7] H. Hadwiger, Über Treffanzahlen bei translationsgeichen Eikörpern, Archiv der Mathematik, 8 (1957) 212-213.
• [8] Z. Lángi, On seven points in the boundary of a plane convex body in large relative distances, Beiträge Algebra Geom., to be published.
• [9] Z. Lángi, M. Lassak, Relative distance and packing a body by homothetical copies, Geombinatorics, (2003) to be published.
• [10] M. Lassak, On five points in a plane convex body pairwise in at least unit relative distances, Coll. Math. Soc. János Bolyai, 63 (1991) 245-247.
• [11] M. Lassak, On relatively equilateral polygons inscribed in a convex body, Publicationes Math., to be published.
• [12] H. Minkowski, Dichteste gitterformige Lagerung kongruenter Körper, Nachr. der K. ges. der Wiss. zu Göttingen, Math.-Phys. Kl., (1904) 311-355 (=Gesam. Abh., Vol. 2, Leipzig und Berlin, (1911) 3-42).