One of the most interesting equations, and one of the most famous ones too, I believe, is this:
a^n + b^n = c^n, where a,b,c is an integer >0 and n is an integer >2.
Fermat got interested in it, and myriads of mathematicians thereafter.
One of the matematicians working with this equation is Sophie Germain (1776 - 1831) who has one of the most interesting life stories. She was a lady matematician in the area no women worked before. There is even a set of integers that is named after her.
The problem is now solved: There are no a,b,c, and n that can solve the equation. This is not interesting. What's interesting IMHO is that a seemingly simple equation is so difficult to deal with. Not many mathematicians can understand the proof. But in its simpler form it is understandable for amateur mathematicians. Like the case n=4 and some more.
Simon Sing brought the attention to this equation in his book "Femat's Last Theroem".
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Originally posted by talvtalA mathematical identity is one that remains constant regardless of the values of the variables in it.
An identity of what?
ex.
(sin(A))^2 + (cos(A))^2 = 1
no matter what value you substitue for "A" the equation is true.
although now I'm slightly confused because there are no variables in e^(pi*i) = -1
?
Edit: ok actually its just a special case (x=pi) of
e^(ix) = cos(x) + i*sin(x)
- Joined
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Originally posted by joe shmoAnd while im at it
A mathematical identity is one that remains constant regardless of the values of the variables in it.
ex.
(sin(A))^2 + (cos(A))^2 = 1
no matter what value you substitue for "A" the equation is true.
although now I'm slightly confused because there are no variables in e^(pi*i) = -1
?
Edit: ok actually its just a special case (x=pi) of
e^(ix) = cos(x) + i*sin(x)
I don't have a favorite yet, but one i'm currently looking at
y" + (k^2)y = 0
its soluion relates to Eulers identity.