Editing 2322: ISO Paper Size Golden Spiral
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| title = ISO Paper Size Golden Spiral | | title = ISO Paper Size Golden Spiral | ||
| image = iso_paper_size_golden_spiral.png | | image = iso_paper_size_golden_spiral.png | ||
− | | titletext = The ISO 216 standard ratio is cos(45°), but American letter paper is 8.5x11 because it uses radians, and 8.5 | + | | titletext = The ISO 216 standard ratio is cos(45°), but American letter paper is 8.5x11 because it uses radians, and 11/8.5 = pi/4. |
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==Explanation== | ==Explanation== | ||
− | + | {{incomplete|Created by a GRAPHICS DESIGNER. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}} | |
− | + | This comic strip is about how to annoy graphics designers and mathematicians, much like [[590: Papyrus]] and [[1015: Kerning]]. | |
− | + | An easy way to annoy many mathematicians is to make fanciful claims about the {{w|Golden Ratio}}. It's been claimed, with varying levels of credibility, to be detectable in many natural and humanmade situations, often with the dubious subjective claim that using the ratio in some particular way makes an image more "beautiful". The {{w|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. The result looks rather like Randall's drawing here. | |
− | + | 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 {{w|Paper_size#A_series|A Series}} of standard paper sizes. These papers aren't squares at all, but rectangles whose side lengths shrink by a factor of the square root of 2. 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 graphics designers and mathematicians. | |
− | + | ===Title text=== | |
− | The | + | The title text is a similarly themed joke, based partly on the fact that the US uses imperial units while much of the rest of the world uses SI units. The 11/8.5 ratio is the length/width ratio of {{w|Letter (paper size)|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 value of pi/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 width/length ratio of A Series paper ({{w|ISO 216}}) is exactly cos(45°), which is 1/sqrt(2). As for US Letter paper, 11/8.5 is not in fact close to pi/4, but it’s possible that Randall meant to write 8.5/11 instead of 11/8.5. To 4 decimal places, 8.5/11 = 0.7727 and pi/4 = 0.7854. |
− | + | In reality, the usage of radians vs. degrees is not a geographic or political decision, but generally is delineated by profession. Most engineering and science fields measure angles in degrees or fractions of degrees (arcseconds, or even milliarcseconds in fields like astronomy), while mathematicians and physicists generally use radians. Civil engineers may refer to the slope of a road by its {{w|Grade (slope)|grade}}, which is commonly expressed in terms of the tangent of the angle to the horizontal (either as a percentage or a ratio); for angles up to ~10 degrees, this is close to the value of the angle in radians. | |
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− | + | ==Supplementary maths== | |
+ | The difference between the "real" Golden Spiral squares and Randall's version is approximately either .2038 (for sqrt(2)-1.6180etc) or .08907 ((1/sqrt(2))-1.6180etc), depending on which way you're counting. Either way, the difference would be very noticeable.) | ||
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+ | The spiral shown is a logarithmic spiral with a growth factor of sqrt(2), and if the center of the spiral is at the origin, it may be graphed with r = C*2^(θ/π), for any positive constant C. | ||
==Transcript== | ==Transcript== | ||
+ | {{incomplete transcript|Do NOT delete this tag too soon.}} | ||
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:[Caption inside panel:] | :[Caption inside panel:] | ||
:The golden ratio is everywhere! | :The golden ratio is everywhere! | ||
:[Picture of the ISO standard paper sizes (i.e. A1, A2, etc.) placed so that they fit together perfectly, overlaid with a spiral resembling that of the golden ratio] | :[Picture of the ISO standard paper sizes (i.e. A1, A2, etc.) placed so that they fit together perfectly, overlaid with a spiral resembling that of the golden ratio] | ||
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− | :[Caption below panel:] | + | :[Caption below panel:]<br /> |
:How to annoy both graphic designers and mathematicians | :How to annoy both graphic designers and mathematicians | ||
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{{comic discussion}} | {{comic discussion}} | ||
− | + | [[Category:Math]] | |
[[Category:Comics with color]] | [[Category:Comics with color]] | ||
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