Characterizing circles by a convex combinatorial property
Let K0 be a compact convex subset of the plane R 2 , and assume that K1 ⊆ R 2 is similar to K0, that is, K1 is the image of K0 with respect to a similarity transformation R 2 → R 2 . Kira Adaricheva and Madina Bolat have recently proved that if K0 is a disk and both K0 and K1 are contained in a tria...
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| További közreműködők: | |
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2017
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| Sorozat: | Acta scientiarum mathematicarum
83 No. 3-4 |
| Kulcsszavak: | Kombinatorika, Geometria - konvex, Hálóelmélet, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-016-570-x |
| Online Access: | http://acta.bibl.u-szeged.hu/50057 |
| Tartalmi kivonat: | Let K0 be a compact convex subset of the plane R 2 , and assume that K1 ⊆ R 2 is similar to K0, that is, K1 is the image of K0 with respect to a similarity transformation R 2 → R 2 . Kira Adaricheva and Madina Bolat have recently proved that if K0 is a disk and both K0 and K1 are contained in a triangle with vertices A0, A1, and A2, then there exist a j ∈ {0, 1, 2} and a k ∈ {0, 1} such that K1−k is contained in the convex hull of Kk∪({A0, A1, A2}\ {Aj}). Here we prove that this property characterizes disks among compact convex subsets of the plane. In fact, we prove even more since we replace “similar” by “isometric” (also called “congruent”). Circles are the boundaries of disks, so our result also gives a characterization of circles. |
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| Terjedelem/Fizikai jellemzők: | 683-701 |
| ISSN: | 0001-6969 |