Richard Suchenwirth 2002-12-29 - *Letter* and *Legal* paper formats are popular in the US and other places. In Europe and elsewhere, the most widely used paper format is called *A4*. To find out how big a paper format is, one can measure an instance with a ruler, or look up appropriate documentation. The *A* formats (DKF - I believe these are defined in a DIN document somewhere...) can also be deduced from the following axioms:

- A0 has an area of one square meter
- A(n) has half the area of A(n-1)
- The ratio between the longer and the shorter side of an A format is constant

How much this ratio is, can easily be computed if we consider that A(n) is produced from A(n-1) by halving it parallel to the shorter side, so

2a : b = b : a, 2 a2 = b2, b=sqrt(2) a, hence b : a = sqrt(2) : 1

So here is my Tcl implementation, which returns a list of height and width in centimeters (10000 cm2 = 1 m2) with two fractional digits, which delivers a sufficient precision of 1/10 mm:

proc paperA n { set w [expr {sqrt(10000/(pow(2,$n) * sqrt(2)))}] set h [expr {$w * sqrt(2)}] format "%.2f %.2f" $h $w } % paperA 4 29.73 21.02

Detailed info on the format A, which is from ISO 216, can be found here [L1 ]. Michael Schlenker