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Writing and Reading as Technology (14): Magical Paper Sizes; or, The Golden Non-Ratio

We often have convenience now because someone did the maths before.

Ben Sparks

With apologies to subscribers who received this out of order due to my enthusiasm for the subject matter…

“Seriously? 297mm? Why not 300mm?”.

I know this is a genuine question because the words still echo in my memory from my school design classroom where one of my fellow students railed at the perversity of the world in that exact manner. My memory does not supply any detail about whether he received an answer, but I fear he was left to wallow alone in his own misery. Let us consider the rest of this piece as a response to this poor boy’s unresolved anguish.

It is true though – anyone who has ever wanted to mark half way across the long side of their paper has experienced the vague resentment that occurs when you realise you now need to measure 148.5mm and your ruler does not even have half millimetre divisions.

I invite you to take a rectangular piece of paper that is not A4 shaped. You can always just tear a bit off your A4 paper and then neaten it up to a rectangle. With your non-A4 rectangle, try folding it in half along the shortest line of symmetry. You will observe, in a spectacular anticlimax, that you now have a piece of paper half the size, and a different shape. Possibly, you started with a ‘squarey’ rectangle and now you have a ‘long-thin-rectangle’, or vice versa.

Now do it with an A4 sheet. You probably already know what happens. You get an A5 piece of paper. It is half the size (of course it is, you just folded in half). What’s more, it is the same shape. Technically a similar shape, of course, but the sides are in the same ratio. This is something of a shock, if you ponder it, because rectangles do not normally behave like this.

This is not an accident. It is possibly one of the greatest innovations of the 18th century. To take just one modern example: teachers have been using it to literally halve their photocopying budget for years. You want two copies on one page? Great – they fit exactly! Any other paper shape (say, ‘letter size’, or 8.5 by 11 inches, for all you North Americans out there) is sadly wasteful in comparison because your two half size copies leave an awkward gap on the original page.

Ben Sparks – Why A4? – The Mathematical Beauty of Paper Size

See also:

Writing and Reading as Technology (1): Transforming Fire; Slow Burn
Writing and Reading as Technology (2): Half-baked Beginnings
Writing and Reading as Technology (3): Marginal Revolutions
Writing and Reading as Technology (4): Innovation at Play; or, A Loaded Pun
Writing and Reading as Technology (5): Literacy as Infrastructure for Thought
Writing and Reading as Technology (6): Stop Press. Who invented moveable type?
Writing and Reading as Technology (7): History’s First Mass Literacy Campaign?
Writing and Reading as Technology (8): Augmenting Reality
Writing and Reading (and visual art) as Technology (9): Virtual Realities
Writing and Reading as Technology (10): Elizabeth Eisenstein on the Printing Press and the End of the Information Famine
Writing and Reading as Technology (11): Writing Rules
Writing and Reading as Technology (12): Elizabeth Eisenstein on How the Printing Press Changed Books

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