If you cut a sheet of A4 paper in half you get two sheets of A5, which have half the area but maintain the same proportions of length to width.
Can we do the same in 3D? Yes we can!! Imagine a block with dimensions , and , with being the longest side.
If we "cut along the dotted line" and let be the longest side of the new blocks so formed, we need the proportions to remain the same,so we can write
or . Solving gives
and . For a proper "A" system we need A0 to have a volume of 1 m3, in the same way as an A0 sheet of paper has an area of 1 m2. So
m3 and making the dimensions of the A0 block 1260 mm x 1000 mm x 794 mm.
This extends naturally to higher dimensions, even though we can't physically construct the higher-dimensional blocks we can describe them mathematically. In four dimensions, the A0 hyperbox would have dimensions in the ratio and higher dimensions follow the same pattern.