Re:Hillwalkers should love the Comte de Buffon (2020)
by murbard2 on Monday July 26, 2021 @10:23AM
(#27959696)
This is missing an interesting argument regarding "Buffon's noodle".
A straight needle crosses a gridline with probability (4 / pi) (l / t) where l is its length.
Surprisingly, a flexible noodle of length l also crosses an expected (4 / pi) (l / t) gridlines. To see why consider that the noodle can be approximated by a set of N straight segments of length (l / N). While the events of different segments crossing a gridline are correlated, the expected number of crossing for each segment is (4 / pi) (l / (N t)) and since, expectation is linear, the expect number of crossings for the noodle is still (4 / pi) (l / t).
A straight needle crosses a gridline with probability (4 / pi) (l / t) where l is its length.
Surprisingly, a flexible noodle of length l also crosses an expected (4 / pi) (l / t) gridlines. To see why consider that the noodle can be approximated by a set of N straight segments of length (l / N). While the events of different segments crossing a gridline are correlated, the expected number of crossing for each segment is (4 / pi) (l / (N t)) and since, expectation is linear, the expect number of crossings for the noodle is still (4 / pi) (l / t).