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Convex Bodies Instead of Needless in Buffon's Experiment (1997)

Aleman, A. ; Stoka, M. ; Zamfirescu, T.

Springer

Geometriae dedicata 67 (1997), S. 301-308

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ISSN: 1572-9168

Keywords: random convex sets ; hitting probability ; independent hitting events.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In this paper we consider the two events that a random congruent copy of a convex body meets each one of two given families of equidistant lines in the plane. The probabilities are easily calculated. Then it is discovered that there always exists a value for the angle α between the nonparallel lines, such that the two events be independent. For convex bodies of constant width, and only for them, the two events are independent for any α.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1004949008834

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