Bibliographic Details
| Title: |
The Number of Configurations of Radii that Can Occur in Compact Packings of the Plane with Discs of n Sizes is Finite. |
| Authors: |
Messerschmidt, Miek1 (AUTHOR) miek.messerschmidt@up.ac.za |
| Source: |
Discrete & Computational Geometry. Mar2024, Vol. 71 Issue 2, p667-682. 16p. |
| Subjects: |
Compact discs |
| Abstract: |
By a compact packing of the plane by discs, P, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc C ∈ P , there exists a sequence of discs D 0 , ... , D m - 1 ∈ P so that each D i is tangent to both C and D i + 1 m o d m . We prove, for every n ∈ N , that there exist only finitely many tuples (r 0 , r 1 , ... , r n - 1) ∈ R n with 0 < r 0 < r 1 < ... < r n - 1 = 1 that can occur as the radii of the discs in any compact packing of the plane with n distinct sizes of disc. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
