Hmmm. Maybe math is done more rigorously and less intuitively these days. When I was in high school, Buffon was done in three simple steps.
Change the length of needle and change the problem from probability of line-crossing to expected count of line-crossings.
What happens to the expected count if the needle is bent?
What happens if you bend a needle of length pi into a circle and drop it on a ruled sheet with spacing of 1 unit?
Yes, this is the beautiful conceptual solution to the problem, but it’s not universally known. I saw it in these two places:
http://blog.sigfpe.com/2009/10/buffons-needle-easy-way.html
http://golem.ph.utexas.edu/category/2010/03/a_perspective_on_higher_catego.html
Yes, that seems quite nice. I had not seen that approach before (or if I have have no recall of it).
Hmmm. Maybe math is done more rigorously and less intuitively these days. When I was in high school, Buffon was done in three simple steps.
Change the length of needle and change the problem from probability of line-crossing to expected count of line-crossings.
What happens to the expected count if the needle is bent?
What happens if you bend a needle of length pi into a circle and drop it on a ruled sheet with spacing of 1 unit?
Yes, this is the beautiful conceptual solution to the problem, but it’s not universally known. I saw it in these two places:
http://blog.sigfpe.com/2009/10/buffons-needle-easy-way.html
http://golem.ph.utexas.edu/category/2010/03/a_perspective_on_higher_catego.html
Yes, that seems quite nice. I had not seen that approach before (or if I have have no recall of it).