Convex bodies instead of needles in Buffon's experiment
(1997) In Geometriae Dedicata 67(3). p.301308 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 interline 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 interline 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1467203
 author
 Aleman, Alexandru ^{LU} ; Stoka, M. and Zamfirescu, Tudor
 publishing date
 1997
 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
 external identifiers

 scopus:0042233041
 ISSN
 00465755
 DOI
 10.1023/A:1004949008834
 language
 English
 LU publication?
 no
 id
 b68b14df4da5488e92da0bb12839991e (old id 1467203)
 date added to LUP
 20160401 12:12:06
 date last changed
 20220127 00:21:48
@article{b68b14df4da5488e92da0bb12839991e, 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 interline 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 = {{00465755}}, keywords = {{random convex sets  hitting probability  independent hitting events}}, language = {{eng}}, number = {{3}}, pages = {{301308}}, publisher = {{Springer}}, series = {{Geometriae Dedicata}}, title = {{Convex bodies instead of needles in Buffon's experiment}}, url = {{http://dx.doi.org/10.1023/A:1004949008834}}, doi = {{10.1023/A:1004949008834}}, volume = {{67}}, year = {{1997}}, }