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Convex bodies instead of needles in Buffon's experiment

Aleman, Alexandru LU ; Stoka, M. and Zamfirescu, Tudor (1997) In Geometriae Dedicata 67(3). p.301-308
Abstract
An arbitrary fixed convex set in ${\bf R}^2$ is considered as are two families of equally spaced parallel lines making angle $\alpha$ with each other. It is assumed that the inter-line distance in each family of parallel lines is greater than the maximum width of the convex set. A congruent copy of the convex set is placed randomly (centroid uniform in one particular parallelogram cell and orientation uniform on $[0,2\pi))$. A simple formula for the probability that the randomly placed set intersects at least one of the lines is obtained. A consequence of the formula is that there exists at least one angle $\alpha$ (depending on the convex set) such that the event of intersecting some line in one of the two families of parallel lines is... (More)
An arbitrary fixed convex set in ${\bf R}^2$ is considered as are two families of equally spaced parallel lines making angle $\alpha$ with each other. It is assumed that the inter-line distance in each family of parallel lines is greater than the maximum width of the convex set. A congruent copy of the convex set is placed randomly (centroid uniform in one particular parallelogram cell and orientation uniform on $[0,2\pi))$. A simple formula for the probability that the randomly placed set intersects at least one of the lines is obtained. A consequence of the formula is that there exists at least one angle $\alpha$ (depending on the convex set) such that the event of intersecting some line in one of the two families of parallel lines is independent of the event of intersecting some line in the other family. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
random convex sets - hitting probability - independent hitting events
in
Geometriae Dedicata
volume
67
issue
3
pages
301 - 308
publisher
Springer
ISSN
0046-5755
DOI
10.1023/A:1004949008834
language
English
LU publication?
no
id
b68b14df-4da5-488e-92da-0bb12839991e (old id 1467203)
date added to LUP
2009-09-16 13:00:40
date last changed
2016-06-29 09:03:49
@article{b68b14df-4da5-488e-92da-0bb12839991e,
  abstract     = {An arbitrary fixed convex set in ${\bf R}^2$ is considered as are two families of equally spaced parallel lines making angle $\alpha$ with each other. It is assumed that the inter-line distance in each family of parallel lines is greater than the maximum width of the convex set. A congruent copy of the convex set is placed randomly (centroid uniform in one particular parallelogram cell and orientation uniform on $[0,2\pi))$. A simple formula for the probability that the randomly placed set intersects at least one of the lines is obtained. A consequence of the formula is that there exists at least one angle $\alpha$ (depending on the convex set) such that the event of intersecting some line in one of the two families of parallel lines is independent of the event of intersecting some line in the other family.},
  author       = {Aleman, Alexandru and Stoka, M. and Zamfirescu, Tudor},
  issn         = {0046-5755},
  keyword      = {random convex sets - hitting probability - independent hitting events},
  language     = {eng},
  number       = {3},
  pages        = {301--308},
  publisher    = {Springer},
  series       = {Geometriae Dedicata},
  title        = {Convex bodies instead of needles in Buffon's experiment},
  url          = {http://dx.doi.org/10.1023/A:1004949008834},
  volume       = {67},
  year         = {1997},
}