This one, I saw it a few time, so, probably you did also.
I am just curious to see what someone that know more than I do about math can tell me about this.
If I take a square box with thin wall and with the length of it side =1, The area of one side is 1 and the volume is 1
If on top of the box, I put another box with the length of its side = 1/sqrt(2) , the area of one side is 1/2 and its volume is 1/(2sqrt(2))
If on top of the box, I put another box with the length of its side = 1/sqrt(3) , the area of one side is 1/2 and its volume is 1/(3sqrt(3))
And if I keep doing this to the infinite.
the total area will be 1+1/2+1/3+1/4+1/5+ .....
Since this diverge, the total area will be infinite. To paint it, I will then need an infinite amount of paint
Its volume is 1+ 1/(2sqrt(2)) + 1/(3sqrt(3)) + 1/(4sqrt(4)) + 1/5sqrt(5)) + ....
Since this converge to around 2.6123, therefore I can fill all the boxes with 2.6123 m3 (or CF) of paint.
How is that possible, since the paint inside the boxes is obviously painting the walls