on 4/25/2002 3:11 PM, Ma Be at [EMAIL PROTECTED] wrote: (regarding A4 vs. other paper sizes) > what's important... area > or the dimensions of the paper > or something else?
The answer is "something else". That something is the SHAPE of the paper, or more specifically, the aspect ratio (ratio of its length to its width). Of course we would expect the general shape of a rectangle to be best, but should it be long and skinny, or short and fat, or squarish? The answer is "the length should be equal to the width multiplied by the square root of two". Why? Because that makes it possible to make smaller sizes with the exact same shape (rectangle with the same aspect ratio). Thus, a series of paper sizes can be generated starting with some arbitrary size that has the length equal to the square root of two times the width and then, by cutting it in half parallel to the short side, and repeating this as many times as necessary. The advantage here is not how long or wide it is (whether measured in cm or in.) nor what it's area is (in square anythings), but merely that they are all the same shape. The great advantage of this is two fold: (1) all paper sizes (in one series) can be produced by starting with some arbitray starting size and the right shape, and then successively cutting in half to produce all the remaining sizes in the series WITHOUT ANY WASTED PAPER; (2) printed matter on any one size paper in a given series can be reduced or enlarged to fit the next size in the series and it WILL FIT EXACTLY on the page because each size has the same ratio of length to width. These advantages are great and so, I favor the A series of papers (of which A4 is the most convenient for letter writing) or any of the other series designed to accomplish this. IT MAKES NO DIFFERENCE WHETHER THE STARTING POINT IS METRIC OR NON-METRIC. Because the constraints of geometry force us to have sizes that are NOT simple whole numbers (due to the square root of two), almost none of the sizes is going to have sides measured in simple whole numbers, whether measured in centimetres or inches. It is BECAUSE ITS SHAPE IS IMPORTANT that the A series is better than the old US standard sizes, NOT BECAUSE IT IS "METRIC". I favor the A series and specifically A4 for letter size because of its advantageous shape; regardless of whether it has simple numbers for its length and width in ANY set of units. I also favor adoption of the metric system in the USA, but not because A4 paper is one sixteenth* of a square metre in area. I favor both metric and A4 paper but the two issues are unrelated. Regards, Bill Hooper physics professor (retired), Florida, USA *P.S. Some recent messages on this subject have referred to A4 paper as being one eight of a square metre in size. I think that is incorrect; it is one sixteenth. the A series stats with A0 being one full square metre in area. A1 is half of A0; A2 is one half of A1 or 1/4 of A0, A3 is half of A2 or 1/8 of A0, and A4 is one half of A3 or 1/16 of A0. I just checked this by measuring a sheet of A4 paper and found its area to be 0.0620 m^2. Considering the accuracy of my measurements, this is certainly close enough to exatly 1/16, which is 0.0625 ======================== Keep It Simple - Make It Metric! ========================
