# Heron formula for area of a triangle

Submitted by Structure on Sun, 07/11/2010 - 07:32.Let ABC be a triangle, and a=length(BC), b=length(CA) and c=length(AB).Let

Then area S of the triangle is

We know that

so

Similar

so we have

and

# Inverse of Fourier transform

Submitted by Structure on Sat, 05/15/2010 - 06:57.Let be the Fourier transform of a function f in . We shall prove that

Let g be another function in . We have

From this relation for

# Second order partial differential of implicite function

Submitted by Structure on Thu, 12/03/2009 - 18:03.Let an equation defined by a function

Suppose we can apply the implicit function theorem in a neighborhood of a given point (a,b,c).

So we suppose

and

Then there is a function z=f(x,y) with f(a,b)=c; G(x,y,f(x,y))=0 or

We have