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Lichtenberg Ratio

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Lichtenberg Ratio

Postby hcbowman » Thu Jul 28, 2005 9:01 am

Having wrongly supposed that the standard dimensions for sheets of paper (US Letter, A4, etc) would approximate the golden ratio, I recently lost a bet while learning the definition of the Lichtenberg Ratio:

The ratio of the square root of two to one.

This ratio is the basis for the standard ISO paper sizes (A4, B5, etc). It has the advantage that when a sheet with dimensions of this ratio is appropriately cut into halves, the resulting two sheets also have the same ratio (an A3 sheet cut in half yields two A4 sheets, etc.).

A consistent height-to-width ratio among page sizes has an immediate benefit for scaled photocopies. For example, the proportion of text to margins is preserved when copying a B5 page from a book to A4 paper. This is not true for US sizes, such as from US letter to US legal.

Thanks to KatyBr, whose new sig quotes Prof. Lichtenberg.

--Cliff
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Postby Garzo » Thu Jul 28, 2005 3:17 pm

I'm not sure how one would drop Lichtenberg ratio into conversation. However, saying that, I'm not sure how I'd drop many of these silly words into conversations.

I really don't like it when someone sends me an e-mail attachment in MSWord (where's my bug spray?!), set up for US letter size paper with one-inch margins. I really wonder how the US economy can survive on such funny things. Saying that, the British Empire beat up people with naught more than sticks for years and got away with foolscap.

However, the Lichtenberg ration is one of those really good ideas that no one even notices now. I wonder how people in the US can resize things on a photocopier without an
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A4->A5
button. Just to make things interesting, I noticed that Nihon uses a different shape for the B series: nice!

-- Garzo.
"Poetry is that which gets lost in translation" — Robert Frost
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Postby Flaminius » Fri Jul 29, 2005 3:11 am

So, foolscap is not common in Imperium Britannicum any more?

Garzo wrote:Just to make things interesting, I noticed that Nihon uses a different shape for the B series: nice!

-- Garzo.


Curious. I use only A series paper these days and never thought of comparing our B and EU B. How can they (or we, in case we are the minority) call two different things by the same name?

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Postby Garzo » Fri Jul 29, 2005 12:27 pm

For some reason my document folders are foolscap, but that's because they fit my filing cabinet very nicely. All the documents are in metrical paper formats, mostly A4 and A5.

The B-series is the geometric mean between subsequent sheets in the A-series (i.e. the magnification factor between A4 and B4 is the same as that between B4 and A3). However, the Japanese standard (which does seem to be the minority, sorry) defines the B-series as the arithmetic mean of areas of subsequent A-series sheets (i.e. the mean area of an A4 and A3 sheet is that of a B4 sheet). The international B4 size is 250 x 353 mm, whereas the Japanese B4 is 257 x 364 mm: a noticeable difference.

-- Garzo.
"Poetry is that which gets lost in translation" — Robert Frost
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Postby M. Henri Day » Fri Sep 16, 2005 3:28 pm

It is a bit surprising in this so-called era of globalisation, that we can't agree on standards of mass, length, area, etc (remember Mars Climate Orbiter ?), much less paper sizes, or - my favourite bugbear, seeing that they differ completely between Norway and Sweden - for ring binders....

Henri
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