Re: Guide to learn programming
I have taken programming of scientists as 1 of my subjects(im a science student). I have never learn programming before(we are using Python) and the lecturer only talked about the benefits and how elegant the Python is though our class has started for 3 weeks....
Here comes my first assignment, I just want to know what it wants me to do (i cant understand it...) Am i suppose to prove the formula in the first part or i can use the formula straight away? 2nd part i totally dont have idea...maybe just give up it...
The mathematical proposition
Consider a sequence formed by members of the geometrical progression with the base2, 2^n , n=0,1,2,....If to retain only 1st(left-most) digit in sequence member, we shall instead get the following:
It turns out that the distribution of digits(1,2,...0) in this sequence follows a certain law, which can be de-duced from a more general theorem proved in the beginning of the XXcentuary by the German mathematician HermannWeyl. One manifestation of this distribution law (quite evident already in the above sequence),that 1 occurs more often then anyother digit,and the overall frequency of 1s occurrence is about30%. The precise
formula for all the digits is known:
pi = lg(i1)lg(i), i=1..9(lg is the base 10logarithm)
Which means that p=lg20.301, while p1=lg90.046, ie, there are roughly 6 times more 1s than 9s. The very same formula for digit occurrences holds if to use any other number (except10 where p,q are mutually prime numbers) as the base for the geometrical progression, eg 3 ,5 and soon.
Can you prove this distribution property?Even if
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