On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman

  title={On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman},
  author={Arseniy V. Akopyan and Alexey Balitskiy and M. M. Grigorev},
  journal={Discrete \& Computational Geometry},
In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii $$r_1$$r1, $$\ldots $$…, $$r_n$$rn in the plane, it is always possible to cover them by a disk of radius $$R = \sum r_i$$R=∑ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove… 
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Problems from St. Petersburg School Olympiad on Mathematics 2000-2002
  • Nevskiy Dialekt, St. Petersburg
  • 2006
Problems from St
  • Petersburg School Olympiad on Mathematics 2000–2002. Nevskiy Dialekt, St. Petersburg
  • 2006