Hey JO, You all know the binomic formulas I guess. Let's look at the first: [itex](a+b)^2=a^2+2ab+b^2[/itex] Now this can be interpretet as the area of a square with the sides [itex](a+b)[/itex]. And that means the area of the square is decomposed into the components [itex]a^2[/itex],[itex]2ab[/itex] and [itex]b^2[/itex]. And this can also be done for a cube in three dimensions with [itex](a+b)^3[/itex] and so on. My question is now if there is a similar formula for the area of a circle? Or in higher dimensions for a sphere or torus ?