Wednesday, January 25, 2006
Tuesday, January 24, 2006
Monday, January 23, 2006
Political Philosophy: The true nature of fascism
Not all those in Islam have an understanding like that found in this next link (in fact some even seem to consider Jews equal with Pagans in the need for eradication), but the article is interesting.
Sunday, January 22, 2006
Monday, January 16, 2006
Personal Update: Running ahead of my studies
Bernoulli numbers were defined by Jacob Bernoulli in connection with evaluating sums of the form ∑i^k.
The sequence B0, B1, B2, ... can be generated using the formula
x/(e^x - 1) =∑(Bn x^n)/n!
though various different notations are used for them.
The first few are: B0 = 1 , B1 = -1/2 , B2 = 1/6 , B4 = -1/30 , B6 = 1/42 , ...
They occur in many diverse areas of mathematics including the series expansions of tan(x), Fermat's Last theorem†, etc.
†Fermat's last theorem states that if n > 2 then the equation x^n + y^n = z^n has no positive integer solutions.
(Please note that in the second summation it is B sub-n times x^n, etc.)
It looks like I'll have to start a separate web page just to be able to publish mathematics symbols--this text editor for the blog is rather limited.
The sequence B0, B1, B2, ... can be generated using the formula
x/(e^x - 1) =∑(Bn x^n)/n!
though various different notations are used for them.
The first few are: B0 = 1 , B1 = -1/2 , B2 = 1/6 , B4 = -1/30 , B6 = 1/42 , ...
They occur in many diverse areas of mathematics including the series expansions of tan(x), Fermat's Last theorem†, etc.
†Fermat's last theorem states that if n > 2 then the equation x^n + y^n = z^n has no positive integer solutions.
(Please note that in the second summation it is B sub-n times x^n, etc.)
It looks like I'll have to start a separate web page just to be able to publish mathematics symbols--this text editor for the blog is rather limited.
Subscribe to:
Posts (Atom)