[Deejax]

Whoa, discovered a major flaw in my calculation. [img]graemlins/blush.gif[/img]
And when I tried to correct it my internet connection went down. [img]graemlins/madhell.gif[/img]

But here it is: The square isn’t square!
One side has length 2*radius = 2, but the other side is shorter. It is equal in length to the height of the triangle I described earlier.
Via pythagoras, the height of the triangle equals the square root (2²-1²) = sqrt(3) = approx 1.73.

Thus the surface of one rectangle (see, not square [img]smile.gif[/img] ) equals 3.46

This means that 91% of the layer is filled with coin. This results in a bottle filled with 1150 coins, weighing 4.72 kilo and costing 115 euro.


Ah, I see, you already discovered my mistake.

This calculation isn't just for square bottles. It calculates the average of the air in a layer. You use the fact that there is a repeating pattern. The fraction of air in one unit (one repetition, for example the rectangle) is the same as the fraction of air in the total (discounting what happens at the edges).
The major problem with this method is that you ingore any effects of the shape of the container. But it gives a good estimate if the size of the container is significantly larger then the size of the coins.