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A Pair in a Crowd of Unit Balls

โœ 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

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โœฆ 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 โˆˆ F is denoted by d(A, B). We prove, among others, that if d(A, B) < 4 and n โ‰ฅ 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) < โˆš 2 n/2 , then any small "shake' of F can make A, B visible from each other.


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How Small Is a Unit Ball?
โœ David J. Smith and Mavina K. Vamanamurthy ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Mathematical Association of America ๐ŸŒ English โš– 383 KB