# Talk:2322: ISO Paper Size Golden Spiral

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It annoys me that the hover text says 11/8.5 = pi/4, when 8.5/11≈0.77272727272 and pi/4≈0.78539816339. Claiming 8.5/11 equals pi/4 would be a much more beleiveable lie. 162.158.79.37 15:29, 19 June 2020 (UTC)

The title text has since corrected this error!108.162.219.170 07:14, 25 June 2020 (UTC)

The explanation says that the A series "side lengths shrink by a factor of the square root of two" but that's not true. The width of A(n+1) is half the length of A(n) as depicted. The sqrt(2) ratio referenced is between the length and width of any one piece of paper.172.69.62.124 15:35, 19 June 2020 (UTC)

The side lengths do shrink by a factor of sqrt(2): the width of A(n) is sqrt(2) times the width of A(n+1), the length of A(n) is sqrt(2) times the length of A(n+1). Your statement that "the width of A(n+1) is half the length of A(n)" is also true, but it does not contradict that each step in the A-series shrinks the sides by a factor of sqrt(2). Zmatt (talk) 16:09, 19 June 2020 (UTC)

Fixed it 162.158.74.61 15:43, 19 June 2020 (UTC)

Hi ! How come 11/8.5 = Pi/4 ? First one is more thant 1, second one is less than one... Although Pi/4 and 8.5/11 (or the reverse) are pretty similar, as usual in "let's annoy mathematicians" Randall's style...

I think y’all just got nerd sniped by Randall’s title text.

https://xkcd.com/spiral/ --188.114.103.233 17:22, 19 June 2020 (UTC)

I understand why it annoys mathematicians (it's not the golden ratio), but why does it annoy graphics designers? Please add explanation!

I suspect that what would annoy many (if not most) graphic designers (especially Americans) is the claim that the ISO standard for paper sizes (which is very rarely used in the US) is inherently and objectively beautiful, along with the implication that everyone should switch to using the international standard.
The usual graphic for this is vertical and has the paper sizes getting smaller going towards the top left corner, not positioned in a spiral.
More scientifically-minded designers would be just as annoyed as (most) mathematicians are by the persistent myth that there is something inherently beautiful about the "golden ratio" in the first place, but unfortunately they are probably not in the majority.172.69.50.76 17:50, 21 June 2020 (UTC)
I'm a graphic designer, and this doesn't annoy me. Perhaps because I'm not particularly fond of the golden ratio. I can only speak for myself. BleepBox (talk) 15:32, 30 June 2020 (UTC)

It should be noted that the logarithmic spiral this comic implies it is would actually go outside the bounds of the paper. The leftmost point of the spiral would be about 6.4mm to the left of the left edge of the A1 sheet. Zmatt (talk) 18:39, 19 June 2020 (UTC)

This drawing (as opposed to the singular mathematical formula behind the idealised spiral for the partitioning used) basically takes a simple quarter-oval across each distinct sheet size (with, as essentially mentioned elsewhere, the root(2) ratio between sides) alternating x/y and y/x as major and minor axes respectively. Even if it is not obviously discontinuous (x and y inflection transitions occur subtly) any derivative of the curve (as polar, say) would show jumps in gradient at each stage - probably an inclined-stepped/saw-toothy pattern whereas the true logarithmic line would demonstrate itself as a continuous function at any such level of derivation. The true spiral line followed from origin outwards would almost (not quite, because of the polar gradient) hit the 'outer edge' first in line with the ultimately recursive centre-point then withdraw again to hit the next transition slightly 'inward' of the next level out. The Golden Spiral approximation uses squares for each quarter, which therefore does not switch major and minor axes, but still changes the curve and thus has the same not-quite-Golden nature. Although it's hard to describe, as you can see from my poor attempt that's probably inadvertently fallen foul of more specialised Pure Mathematics terminology due to the Pedant's Curse... ;) 162.158.155.240 22:23, 19 June 2020 (UTC)

Mathematicians get annoyed by the claim that the golden ratio is everywhere. I love Disney's "Donald in Mathmagic Land" but they make some outrageous claims about the golden ratio's place in art and architecture. BTW, the ISO system of paper sizes is awesome! You can photocopy two A4 pages side-by-side, reduced to fit exactly on a single A4 page.

Also they get pi wrong. --162.158.79.209 22:18, 20 June 2020 (UTC)
I think you mean that half of A4 is A3 ;o) 108.162.249.248 05:02, 24 June 2020 (UTC)

Isn't grade closer to degrees than to radians? Djbrasier (talk) 15:03, 20 June 2020 (UTC)

It's two different things. The "grade" of a slope is just the rise divided by the run, commonly expressed as a precentage. It is not an angle measure but the tangent of an angle measure. It is commonly used in North America for surveying and engineering purposes. "Gradian" is a badly named angle measurement that, worse, is often referred to informally as "grade" from "centigrade".It is an angle measure, though a useless one: ten-ninths of the measure in degrees. The gradian is commonly used for surveying and engineering in some parts of Europe. The text in the current explanation confuses them, which is common due to the bad naming of the second measure. 162.158.187.197 16:45, 20 June 2020 (UTC)

A friend of mine, attempting to do graphic design, once created an approximate golden spiral using the boxes diagram with quarter circles. He then laboriously produced a logo by making copies of the spiral and using pieces of it for each curve. I then informed him that all the curves in his image were just circular segments. 172.69.69.44 16:36, 20 June 2020 (UTC)

108.162.216.216 15:21, 23 June 2020 (UTC)

The reason ISO paper sizes use an aspect ratio equal to the square root of two is that makes enlarging or reducing in copiers work better. With the US sizes, when you enlarge or reduce to the next standard size up or down, you have to choose between cutting off part of your original or leaving some blank space, because US standard paper sizes aren't the same shape.

It was done before photocopiers could do reduction or enlarging as cutting in half always produces the same shape of page.

108.162.216.216 15:21, 23 June 2020 (UTC)

I never knew this, but it is no surprise. :P 108.162.249.248 05:03, 24 June 2020 (UTC)