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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

944.0. "a way to get pi experimentally" by ULYSSE::ZITTA (ULYSSE in wonderland) Wed Oct 12 1988 10:40

    
    Let's imagine parallel lines on the ground .
    Now take a stick and let it fall on the floor .
    There are 2 possibilities :
    	-Either it will touch (cross) one of the lines
    	-Or it will fall between 2 lines without touching them.
    
    What is the probability for the stick to touch one of the lines
    ?
    
    Determine the length of the stick and the distance between the lines
    such that repeating this experiment a great number of times will
    give a method to determine the number pi experimentally .
    
    	gerard
T.RTitleUserPersonal
Name		DateLines
944.1The buffoon strikes!HIBOB::SIMMONSWed Oct 12 1988 10:521
    I say, don't you think any Buffon can solve this?
944.2is he needling us?LISP::DERAMODaniel V. {AITG,LISP,ZFC}:: D'EramoWed Oct 12 1988 11:133
     If you do, then try to Count how many.
     
     Dan
944.3Whatever CountsHIBOB::SIMMONSWed Oct 12 1988 12:071
    Was G. F. F. Buffon a Count?
944.4(��)ULYSSE::ZITTAULYSSE in wonderlandWed Oct 12 1988 12:4212
944.5oops!ULYSSE::ZITTAULYSSE in wonderlandWed Oct 12 1988 12:522
     
    Sorry I just saw note 499 !
944.6LISP::DERAMODaniel V. {AITG,LISP,ZFC}:: D'EramoWed Oct 12 1988 23:0214
     re .3
     
>>   Was G. F. F. Buffon a Count?
     
     I thought so.  But I checked in one of my books and it said:
     
          This remarkable problem stems from Georges Louis
          Leclerc, Comte de Buffon (1707-1788), who was the
          first man to clothe probability problems in
          geometric form.
     
     What's a _Comte_?  I always thought of him as Count Buffon.
     
     Dan
944.7comte = countPULSAR::WALLYWally Neilsen-SteinhardtThu Oct 13 1988 13:205
>     What's a _Comte_?  I always thought of him as Count Buffon.
    
    Just the French word for Count.  Calling him Count Buffon would
    probably offend his Gallic taste for precision, but it is close enough
    for us sloppy speakers of English.
944.8resultULYSSE::ZITTAULYSSE in wonderlandFri Oct 14 1988 11:4615
    
    When I posted this note I couldn't find its solution (don't laugh!).
    But now I can see different ways to solve it.
    
    Here is the result anyway :
    
    	Length of the needle = 2l
    	Distance between the equidistant parallel lines = 2a
    
    Probability that the needle touches a line = (2l/a*pi)
    
    So if you know l and a you can get pi.Or you can simplify by taking
    a needle of the same length than the distance .
    
    Good luck to those who want to check this week end!
944.9E(X)=p1*x1+p2*x2+p3*x3+...........ULYSSE::ZITTAULYSSE in wonderlandFri Oct 14 1988 11:538
    
    By the way,one solution involves an entity I don't know how to
    translate in English .
    In French it's called : Esperance mathematique
    		or          Valeur moyenne 
    Is simply "mean" the English mathematical term ?
              
    Thanks!
944.10LISP::DERAMODaniel V. {AITG,LISP,ZFC}:: D'EramoFri Oct 14 1988 12:468
     It looks like you are referring to the "expected value".
     "Mean" is often used instead, or "arithmetic mean" (as
     opposed to the geometric mean or harmonic mean).  "Average"
     or "average value" is another term, but might also be used
     for either of the other means, or for the median or mode of
     a distribution. 
     
     Dan