A Pair in a Crowd of Unit Balls

✍ Scribed by K. Hosono; H. Maehara; K. Matsuda

• Book ID: 102570917
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 130 KB
• Volume: 22
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2001.0547

✦ Synopsis

Let F be a family of mutually nonoverlapping unit balls in the n-dimensional Euclidean space R n . The distance between the centres of A, B ∈ F is denoted by d(A, B). We prove, among others, that if d(A, B) < 4 and n ≥ 5, then A and B are always visible from each other, that is, a light ray emanating from the surface of A reaches B without being blocked by other unit balls. Furthermore, if d(A, B) < √ 2 n/2 , then any small "shake' of F can make A, B visible from each other.