# Heron formula for area of a triangle

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

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

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