Lets start a thread for all the math knick-knacks you learnt to do physics. I'll start. Reading the Feynman Lectures, For finding the centre of mass. Using the pappus theorem when a 2D object is rotated about a plane that is perpendicular to the ones it exists in i.e. mutually perpendicular to the planes an object exists in, and it is rotated in this plane, the distance travelled by the centre of mass times the area of the 2D object is the volume of the 3D object generated by rotation. For example, taking a semicircle of radius r, let the COM be a distance X from the flat side of the semicircle. When you rotate about the flat side, distance travelled by COM = 2 x pi x X Area of semicircle = pi x r^2 x 1/2 Area of 3D object generated = 4/3 x pi x r^3 When you equate, you get X = 4r/3pi I thought this was fantastic!!