Editing 2322: ISO Paper Size Golden Spiral
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==Explanation== | ==Explanation== | ||
| − | This is | + | This comic strip is about how to annoy graphic 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 human-made 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 | + | 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 human-made 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, but in landscape instead of portrait (this diagram is commonly drawn in portrait). These papers aren't squares at all, but rectangles whose side lengths shrink by a factor of the square root of 2. Additionally, the paper sizes shrink by a factor of one half, so the area is filled in a geometric series. This is sometimes called a ''silver'' rectangle, although the {{w|Silver ratio}} is actually 1+√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 graphic designers and mathematicians. | 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, but in landscape instead of portrait (this diagram is commonly drawn in portrait). These papers aren't squares at all, but rectangles whose side lengths shrink by a factor of the square root of 2. Additionally, the paper sizes shrink by a factor of one half, so the area is filled in a geometric series. This is sometimes called a ''silver'' rectangle, although the {{w|Silver ratio}} is actually 1+√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 graphic designers and mathematicians. | ||
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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°, this is close to the value of the angle in radians. | 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°, this is close to the value of the angle in radians. | ||
| − | The difference between the "real" Golden Spiral squares and Randall's version is approximately either .2038 (for √2-1.6180…) or .08907 ((1/√2)-1.6180…), depending on which way you're counting. Either way, the difference would be very noticeable. | + | The difference between the "real" Golden Spiral squares and Randall's version is approximately either .2038 (for √2-1.6180…) or .08907 ((1/√2)-1.6180…), depending on which way you're counting. Either way, the difference would be very noticeable.) |
The spiral shown is approximately a logarithmic spiral with a growth factor of √2, although it has been edited slightly to make it fit neatly inside the rectangles. | The spiral shown is approximately a logarithmic spiral with a growth factor of √2, although it has been edited slightly to make it fit neatly inside the rectangles. | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
[[Category:Math]] | [[Category:Math]] | ||
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