![]() ![]() The width and length of A Series paper ( ISO 216) is always given in whole millimeters, and the width/length ratio is very close to cos(45°) (which is 1/√2=0.707…) As for US Letter paper: to 4 decimal places, 8.5/11 = 0.7727 and π/4 = 0.7854. The value of π/4 radians is indeed equal to 45 degrees, although Randall takes the cosine in one case and uses the raw angle in the other case in order to get a close coincidence of values. The 11/8.5 ratio is the length/width ratio of US Letter paper, which is 11 inches by 8.5 inches (another common size in the United States is US Legal, which is 14" by 8.5"). The title text is a similarly themed joke, based partly on the fact that the US uses customary units while the vast majority of the rest of the world uses SI units. By mistaking the A Series for something connected with the Golden Ratio, and perpetuating the tradition of making dubious claims about the Golden Ratio, Randall has successfully annoyed both graphic designers and mathematicians. This is sometimes called a silver rectangle, although the Silver ratio is actually 1+√2. ![]() Additionally, the paper sizes shrink by a factor of one half, so the area is filled in a geometric series. These papers aren't squares at all, but rectangles whose side lengths shrink by a factor of the square root of 2. However, Randall hasn't used the Golden Ratio at all he's just drawn a spiral ( not the Golden Spiral) through a common diagram showing the A Series of standard paper sizes, but in landscape instead of portrait (this diagram is commonly drawn in portrait). The result looks rather like Randall's drawing here. The Golden Spiral is a spiral whose growth factor is this ratio a common (though slightly geometrically inaccurate) way to illustrate the spiral is to draw curves through a set of squares whose side lengths shrink according to the Golden Ratio. It's been claimed, with varying levels of credibility, to be detectable in many natural and human-made situations, often with the dubious subjective claim that using the ratio in some particular way makes an image more "beautiful". This type of annoyance seems much like that displayed in 590: Papyrus and 1015: Kerning.Īn easy way to annoy many mathematicians is to make fanciful claims about the Golden Ratio. This is another comic on How to annoy people, here both graphic designers and mathematicians. (In fact, the ratio is a number that begins 1.32472… and carries on forever).Title text: The ISO 216 standard ratio is cos(45°), but American letter paper is 8.5x11 because it uses radians, and 8.5/11 = pi/4. It turned out that the ratio 1.325, which gives you the rectangle that creates the Harriss spiral has been written about – it is known as the “ plastic number” – but Harriss could find no previous drawings of the spiral. His first concern was that maybe someone else had had, in fact, drawn the spiral “One thing about mathematical discoveries and mathematical art is that even if the process is completely new there is no guarantee that someone else has not already explored it.” “It’s more difficult to make something mathematically satisfying that people haven’t seen before.” “It’s not hard to make something that no one has seen before,” he said. But he was particularly delighted because he arrived at the spiral using a very simple mathematical process. Harriss was overjoyed when he first saw the spiral because it was aesthetically appealing – one of his primary aims was to draw branching spirals like you might find in Islamic art or the work of Gustav Klimt. ![]()
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