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ON THE LONG RUN, EVERYTHING SETTLES DOWN

   

      If you toss a coin 5 times, 4 times you may get head and one time you may get tail.  Toss it 10 times, it may be head 7 times or 3 times tail.  Toss it 100 times. Roughly 50 times you will get head or tail.  If you do 10000 times, Most likely 5000 times we get head or tail.  A computer can easily simulate this process.  As the 'number' increases, we reach the fifty percent probability. 7/10 is not 50%  But 5007/10000 is.
     Let us roll the dice three times, it may be 2,4,6.  The average is 2+4+6/3 =4.  But, if we roll the dice many, many times and find the average, it will settle down exactly at 3.5.

  1,1,2,3,5,8,13....144,233....
     The above is the Fibonacci series, Adding the previous two numbers, you get the next number.  Now take successive numbers one by one and find their ratio.
    2/1 = 2
    3/2 = 1.5
    5/3 = 1.666
    8/5=1.6
  13/8 = 1.625
 21/13 = 1.615...
 233/144 = 1.6180
 377/233 = 1.6180...
  On the long run, the ratio settles down at 1.6180....It is called golden ratio.  It appears everywhere in nature.

     Let us take one simple formula
   e= 1*(1+1/n)ˆ1*n
put n=1
 e= 1*(1+1/1)ˆ1*1 =2
Put n=3
e= 1*(1+1/3)ˆ1*3 = 2.37
As the n increases, what happens?
      n                                 e
      1                                 2
      2                                 2.25
      3                                 2.37
      5                                  2.488
      10                                 2.5937
      100                              2.7048
      1000                            2.7169
      10000                         2.71814
      100000                       2.718268
      1000000                     2.7182804
    'e' settles down at 2.718... It is an very important mathematical and physical constant.

      Triangle has three sides.  Pentagon has 5 sides.  Polygon has many sides.
If number of sides in a polygon is go on increases, it will approach a circle.
     Normal body temperature, BP. pulse rate, sugar level is determined by taking average in a large sample of population.  As the size of the sample increases, the the value approaches accurate level.

FOOT NOTE:   Fluid situations, dynamic changes, diseases, chaotic traffic, flood, economic crisis, all stabilizes at some point.  One has to treat the problem and wait patiently.   
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