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#1 Re: Guestbook » Don't Post here! » 2008-04-10 06:53:39
Some people I know like numbers very much...
Ramanujan was lying on his deathbed in Chennai, India when his english chum G.H.Hardy took a plane from Cambridge to visit him in India. Well you see , he came to see him for the last time and complained to his indian friend:-
Hardy:- the taxi cab i took has the most un-interesting number..
Ramanujan:- which number?
Hardy:- 1729.
Ramanujan:- Hey there wait!!!! 1729... is NOT un interesting!
Hardy:- ...!
Ramanujan smiled weakly and said:-
- You see : 1729 is the smallest number which can be written as
1729 = 10^3 + 9^3
and
1729 = 12^3 + 1^3
that is, 1729 is the smallest number which can be broken down into two cubes in 2 different ways...
and the next such number is a very very large one in fact...
(internet source- life of Srinivasa Ramanujan)
#2 Re: Help Me ! » Math Lines and Vectors help Q3 » 2008-04-10 06:33:29
question 2 is a favorite problem in high school vectors. i hope my small answer would be enough 
Qu:
what is the vector equation of a Plane ( containing points P, say) which is parallel to xy plane and passes through point A (4,1,3) ??
well
(1) as the plane is parallel to the xy plane, then... it is perpendicular to the z axis!!!
so, the normal vector is the k vector.
normal vector n = c k,
where c is a number and k is the vector along the z axis.
(2) if the plane passes through point A(4,1,3) then from anywhere in the plane, take a point P. We can contruct a vector lying on the plane itself
AP = OP - OA
which is at right angles to the normal vector of the plane.
(3) as vectors n and AP are at right angles to each other, their dot product is zero.
So, n. AP = 0
the vector equation is:
k. ( r - OA) = 0
#3 Re: Help Me ! » What is that ringed or double ringed integral? » 2008-04-10 06:09:02
Hi there!! I just wanted to write something not too foolish I hope..
A complex function is a function of complex number(s)
It can be assimple as f(z) = z^2 which is the square of the complex number z
A contour integral is obtained when you integrate f(z) w.r.t z
from one point on the complex plane ( the Argand diagram) to another point.
Usually when the path you follow starts from a point P & makes you travel along a path that brings u back again to the same point, this is probably the reason we use the french word Contour ( round about) integral... . {end of little comment.}
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