Theory NO.0: Pappus Theorem


Today I wanted to add some sophisticated theorem about which we dont learn at school.

This theorem says that if you have a 2D figure with well known gravity centre you can easly calculate any 3D figure volume that comes from rotating the 2d figure. It goes like this:

Volume=the distance that the gravity centre moved x area of 2D figure

It could be also used in inverse, to calc the gravity centre. For ex. suppose that we have to calc the gravity centre of a half-circle. Lets rotate it 360 degress around the straight edge in ghost motion… Oh we get a sphere and the volume of sphere is well known! So we get 4/3 \pi r^3=2 \pi k \times \pi r^2 /2 \rightarrow k =  4 r /(3\pi)


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