Covering the sphere with equal circles. (English) Zbl 1370.52036
Given \(n\), how can a 2-sphere be covered by \(n\) congruent circles with a radius as small as possible? The author proves that an arrangement of eight circles found by Schütte is optimal and provides the solution for \(n=8\) [K. Schütte, Math. Ann. 129, 181–186 (1955; Zbl 0066.14403)]. Also determined is the combinatorial type of a solution for \(n=9\).
Reviewer: Egon Schulte (Boston)
MSC:
| 52C15 | Packing and covering in \(2\) dimensions (aspects of discrete geometry) |
| 52C17 | Packing and covering in \(n\) dimensions (aspects of discrete geometry) |
| 51M16 | Inequalities and extremum problems in real or complex geometry |
Citations:
Zbl 0066.14403Software:
plantriReferences:
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