Editing 2748: Radians Are Cursed
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A correct version of the second fact would be that a radian has the same value (1) as the radius of the unit circle. | A correct version of the second fact would be that a radian has the same value (1) as the radius of the unit circle. | ||
− | The third fact states that one radian is equal to 57. | + | The third fact states that one radian is equal to 57.3 degrees. This is indeed true (albeit rounded). The circumference of a circle is 2pi radius-lengths, so the angle of a complete circle is both 2pi radians and 360 degrees. Thus 1 radian equals 180/pi degrees. This fact is again labeled "normal." |
− | The fourth and final fact states that because it was determined in earlier facts that a radian is equal to the radius of the unit circle as well as 57. | + | The fourth and final fact states that because it was determined in earlier facts that a radian is equal to the radius of the unit circle as well as 57.3 degrees, then the radius of the unit circle must be equal to 57.3 degrees. This is usually not how degrees are supposed to work, because they are a measure of angle, not length. Hence, this fact is labeled "cursed" by Randall, leading to the comic's title. (However, since the radian is also an angular measure, the second fact could be viewed as equally cursed.) |
The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog: http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument. | The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog: http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument. |