Humblest apologies to all supporters of British weights and measures for daring to mention A4 paper on a recent posting. I think I was told to refer to foolscap in future (if prosecuted, in my defence I shall adduce as evidence that BWMA's in-house magazine 'The Yardstick' is printed in A4 size).

Correct me if I'm wrong, but I think:

FOOLSCAP is 18 3/4" x 14", while

FOOLSCAP FOLIO is 13" x 8"

and I think most people take 'Foolscap' these days to mean the smaller 13" x 8" size. I'll refer to that as 'Foolscap' below.

A4 is stated to be 297mm x 210mm, or roughly 8 1/4" x 11 3/4".

It is of interest to see the ratio of the length of the short side to the long side in each case:

FOOLSCAP (FOLIO): 1 : 1.625

A4: 1 : 1.414


GOLDEN RULE

The Foolscap size (13" x 8") is very close to what is called the 'Golden Rule' - what is said to be the ideal shape for an oblong, which is:

1 : 1.6180339 (corect to 7 decimal places).

A4 size is thus a long way off from it.

Look at most pictures (landscape or portrait), look at the Greek Parthenon, or Georgian windows, and that ratio of around 1 : 1.6 comes up time and again.

The ratio 1 : 1.6180339 derives from the so-called Fibonacci series, er, after mathematician Fibonacci.

This works by adding the last two numbers together to make the next one, thus:

1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
etc.

Keep dividing each new figure by the last one. e.g. 13 by 8 (foolscap), or 1597 by 987, and you get closer and closer to the 'Golden Rule' or 'Golden Mean' number of 1.6180339.

This pattern of growth can be seen throughout nature, two common examples being the arrangement of the diamond shaped blades on a pine cone, or the arrangement of sunflower seeds as they grow on the head of a sunflower.

The number itself has some strange properties.

Add 1 to 1.6180339 and you get 2.6180339.

The square root of 2.6180339 is 1.6180339.

Divide 1 by 1.6180339 and you get:

0.6180339.

I guess the moral of this tale is that Fibonacci would probably prefer to write his love letters on Foolscap, even if the A4 size had been available to him.

Tony Bennett

I think the idea with metric paper sizes is that the ration is 1:sqrt(2) so that cutting the paper in half leaves you with two halves that have the same aspect ratio of the original sheet.

All metric paper sizes have that aspect ratio. Of course, this presumes that one aspect ratio is suitable for all purposes, which isn't likely.

In imperial units, a sheet of paper measuring 8½" by 12" would be sufficently close to this ratio; this is only one inch longer than the standard 8½" by 11" used here in the US.

If you really wanted to come close to the golden mean, how about 10½" by 17"?

Better yet, 8½" by 13¾" gives you an aspect ratio of 1:1.6181818...

This size paper could be easily made by trimming ¼" off of US "Legal" standard 8½" by 14" .

Tony, that was me that mentioned your use of A4 recently. Also,I thank you very much for this thread as I was about to look up the whole golden section thing on the net (having forgotten what I knew about it). And yes, I myself refer to the smaller foolscap as foolscap (without the folio).

>All metric paper sizes have that aspect ratio. Of
>course, this presumes that one aspect ratio is
>suitable for all purposes, which isn't likely.

Oh, "imperial" sheets have variable aspect ratios, so you can stretch and squeeze them ? Wow, I have to get one of those...

Ralf

Actually the definition of the golden ratio is that of a rectangle where the ratio of the length of the shorter side to the longer is the same as that of the longer side to their sum.

Can't remember just now the numerical formula but I seem to recall sqrt(5) comes into it. It can be worked out algebraically though.

A lot of different paper sizes with different aspect ratios are used in industry, not merely the golden ratio or root2 ones. Check the various aspect ratios of books and newspapers, for instance. The standard paperback is very close to golden ratio though.

The golden ratio is 0.5(1 + sqrt(5)):1 = 1.61803398875:1 expressed as the ratio of the longer side to the shorter side.

Or 0.5(sqrt(5) - 1):1 = 0.61803398875:1 expressed as the ratio of the shorter side to the longer.

Pip, that appears as gibberish before mine eyes...

pip is absolutely right of course, that the ratio of the shorter side to the longer side in the 'Golden Ratio' must be exactly the same as the ratio of the longer side to the sum of the two sides.

Thus:

Short side to long side:

1 : 1.6180339

Long side to the sum of the two sides:

1.6180339 : 1.6180339 + 1 (i.e. 2.6180339)

which works out as exactly (give or take the eighth decimal place onwards) as:

1: 1.6180339

which happens also to be the 'Fibonacci Ratio'


Tony Bennett

Frederick II of Sicily was a cool guy at whose court the sonnet form was invented and writing poems in vernacular Italian began and works of Greek science were translated for the first time in over a thousand years.

He himself studied birds and wrote a treatise on the falcon.

One time Frederick decided to have a tournament at his court, but instead of a contest of mounted knights it would be a battle of mathematicians.

He had a Master John of Palermo compile some ingenious problems and the mathematicians (of whom Fibonnaci of Pisa was one) competed in separate chambers to see who could solve them first. It is recorded that Fibonacci trounced the other mathematicians.

One of Fibonacci's books (I've handled a 19th C Latin
edition) was dedicated to Frederick II.

I suppose A4 isn't really metric, as the size isn't metric. Also, as I think Vivian Linacre has pointed out, it is divided in 2, 4, + multiplied by these too, (i.e 1/2, 1/4, etc.).

That said, however, it is good to use other sizes too, based on our own weights + measures. I, personally, use 10" x 8", A4, and Foolscap (the 13"x8" variety).

Good 10"x8" paper is available from a place in Lyme Regis that also does "T4", "T2", etc. sizes based on sub-divisions of the square yard. Apparrently this buisiness hass been going ages + uses "tree-free" hemp paper.

Foolscap, of course, is available from various small printing shops, and from B.W.M.A..

The basis of the A-series is A0 = 1 sq.m, which is metric enough. But thereafter it's binary, not decimal: A1 = 1/2 sq.m, A2 = 1/4 sq.m, A3 = 1/8 sq.m, A4 = 1/16 sq.m, etc..

Seriously, I think with that "I don't like the 'A' paper series because an A0 sheet is exactly 1 m^2" discussion you're scraping the bottom of the barrel.

Ralf

<<
I suppose A4 isn't really metric, as the size isn't metric. Also, as I think Vivian Linacre has pointed out, it is divided in 2, 4, + multiplied by these too, (i.e 1/2, 1/4, etc.).
>>

A4 is derived form metric measure.

1 sheet of A0 has an area of 1 m^2
2 sheets of A1 have an area of 1 m^2
4 sheets of A2 have an area of 1 m^2
8 sheets of A3 have an area of 1 m^2
16 sheets of A4 have an area of 1 m^2.

Since the ratio of length to breadth of A0, A1, A2, A43, A4 etc is always the same, it is a simple mathematical exercise to prove that this ratio is 1:sqrt(2). The rest follows.

One of the advantages of the "A" serises of paper is that if one wishes to photo-reduce two sheets of A4 onto a single sheet, this can be done quite easily. If one attempts this with foolscap, quarto, letter, legal aper, there will be an annoying strip on the edge of the reduced copy.

I was thinking about the so called 'golden section' and the first thing I thought was "hang about! If you have a rectangle one mile in length and one kilometre in width, you have the golden section!". It actually works out to be just under 1: 1.61

Even though this is one of the rare occasion of metric *up*sizing, I would prefer the ream to be, once again, of 480 sheets and not this 500 nonsense.

Bryan Parry wrote: "Even though this is one of the rare occasion of metric *up*sizing, I would prefer the ream to be, once again, of 480 sheets and not this 500 nonsense."

You're never satisfied, are you ?

Marcus Kuhn of Cambridge University ha published an extremly informative article on the Internet about A4 paper (http://www.cl.cam.ac.uk/~mgk25/iso-paper.html). Althought this paper is pro-A4, it is well-balanced in the way in which it advises US readers on the existance of A4 paper.

It is noteworthy that Kuhn does not mention foolscap paper at all - as far as he is concerend foolscap ceased to be useful in 1959 when the UK switched over to using metric paper.

Kuhn's article also touches on items such as the standard sizes and tolerances for punched holes (holes 6mm in diameter and 80mm apart set 20 mm from the edge of that pages) and alos on the way in which the weight of paper is specified. Typically metric paper is specified as 80gsm (grams per square metre). Since it is easy to show that 16 sheets of A4 paper have an area of one square meter, (the dimensions of A4 are designed that way), it follows that 1 sheet of A4 80 gsm paper weighs 5gm (useful for calculating postage rates without a letter scale).

I would strongly recommend that anybody who is interested in paper standards read Kuhn's article.

Britain did NOT "switch over to metric paper" in 1959. Not even if you pretend that A4 is a metric size (A0 is, the rest are binary not decimal submultiples and thus not actually metric). Through to at least the end of the seventies typing paper was usually foolscap and essentially all photocopying machines were (they used a cadmium sulphide process and smelled funny). Cambridge University Physics department and Marconi Space and Defence used such machines with foolscap coated paper till the mid-eighties at least.

^ I still see foolscap about, although not often. And A4 is often shown as "A4/8½x11.75" (How do you write 'three over four' using alt codes?)

Conrad, there are often patterns and numbers in our system of measures, that are repeated. The underlying (semi/pseudo, pehaps) logic, however, and the meaning of these measures is obscured by metrication of our units of measure. This comes in many forms- decimalisation, the "metric pound" and so on- none are acceptable. Upon having our sizes metricated, people will scofff at us and point their fingers as if we were some circus freak. "*Guffaw* look at that stooooopid system! Man, is it retarded. It's illogical! Look! LOOK! So many feet by so many feet is the standard carpet size, but that is almost so many by so many metres in size. Why not change it.... blah.... [nods towards a recent post by someone else]". In short (and in coherence, as it were), it really bugs me (as it does Paul), how the metrication of life in this country is used as a tool to beat Imperial over the head.

13x8"= 1:1.625
6½x4"= 1:1.625
9¾x6"= 1:1.625

I really like this.

Alt 0188 = ¼
Alt 0189 = ½
Alt 0190 = ¾

Check the character map (try Start/Programs/Accessories/Character Map/Times New Roman). It's the easiest way.

Thanks Paul, but through trial and error I found it in anyway.

So you did. I should have noticed.

My company year ends on 31-July-2002. At the year end I open a new set of files for the new year and box the files from the previous year but one (ie I am now boxing files for the year 2000/2001).

I keep my correspondence in buff folders. I foolishly bought some "cheap" buff folders for the year 2000/2001 and have now realised that they are foolscap folders. The document boxes that I have are designed for A4 paper. All my correspondence is on A4 paper. The result is that I have to cut each of my folders so that they fit into the my document boxes.

Since A4 paper has been the standard in the UK for two decades or more, I feel that Foolscap and Quarto paper should have a warning label on them "Warning - this stationery in not A4 stationery". This will remove the time-wasting exercise of having to trim what is now non-standard stationery to fit standard stationery containers.

I expect everyone knew this and I didn't, but I'm told that in Vivian Linacre's book on Customary Weights and Measures, he explains how the name 'foolscap' came to be given to 13" x 8" paper - by Oliver Cromwell. Having executed the King, whose head was imprinted on all foolscap paper in the realm, Cromwell was apparently asked: "Whose head goes on the paper now?". He is alleged to have replied: "Put any fool's cap on it".

Sorry if I've got the story slightly wrong

Tony Bennett