mathematical principal

Mathematical Principal

A crucial factor in the development of the DIN A format was the application of the metric system to the entire surface of the paper. From the basic size with a surface of 1 square metre, measuring 841×1189 mm and with a relationship of 1:√2 (1:1,41) between the sides, a format series was created which can be divided along the centre infinitely and still retain exactly the same proportions as the original. All A formats except the largest are generated through successively halving the format one size up (parallel with the short sides) in a series from A0 down to A7. Decimated millimetres are rounded off. Each paper size is named according to the series to which it belongs, and according to how many times the paper has been divided in order to make that size. In other words, an A4 sheet is part of the A series and has been created by dividing the original size A0 four times.

The relationship between the sides in the A format makes it easy to reduce and enlarge images. An A3 becomes an A4 when reduced by 71%, and an A4 becomes an A3 if enlarged by 141% in the photocopier. An A3 enlarged by 200% becomes an A1.

The link to real life contributed to the success of the DIN 476 format. The fact that the starting point is an A0 that is folded or cut to create the other sizes in the series relates to how we actually deal with paper in practice. Since the format retains its proportions when folded, only a small assortment of envelopes, stationary, binders and archive boxes is needed.

Porstmann’s idea was that the uniformity of the paper format would benefit the public thanks to cheaper and more efficient paper storage, handling and reproduction. Less waste also meant timber could be saved, an issue that Porstmann was committed to.