Robert Hill wrote: > > In article <1997Aug4.firstname.lastname@example.org>, I wrote: > > > My program for a circle contained a stupid error. [...] > > Correcting the bug, I get 720578 obtuse out of a million, > > or 7200949 out of 10 million, reasonably close both to your figures > > and to the theoretical .7187 that has now been posted by Keith Ramsay. > > ... though still not as close as they should have been; but this may be > because the figure of .7187 itself contains a misprint of 8 for 9 > (since 9/8 - 4/pi^2 = 0.71971526543...). > > -- > Robert Hill > > University Computing Service, Leeds University, England > > "Though all my wares be trash, the heart is true." > - John Dowland, Fine Knacks for Ladies (1600)
And these compare favorably with the value 7196418 out of ten million that I posted earlier.
And I spent the entire weekend working on the exact value for a circle, expecting to finish up on Monday, when I saw the answer 9/8 - 4/pi^2 posted (and it is indeed the value which I subsequently found!).
But all that grundge and grind pales in comparision with the beautiful result of precisely 3/4 for normally distributed vertices. It will become one of my "hard" probablility problems the next time I teach post-calculus probability (most likely next summer).