On Sun, 2009-11-22 at 23:33 -0800, Dale Tronrud wrote: > I could be describing my angle as > 1.5 radians, 1.5 degrees, or 1.5 cycles (or 1.5 of the mysterious > "grad" on my calculator).
I thought that use of degrees is based on dividing a circle into 360 parts - roughly one per day (then in geography they somehow divide a degree "day" into 60 minutes - not 24 hours, go figure). Such agreement, while workable, leads to some ugly results (just like geocentric system is actually workable but cumbersome). For instance, if angles are measured in degrees and x<<1 sin x ~ pi * x / 180 Not a big deal, really, but this is one reason to use radians instead, since then you get sin x ~ x On the other hand, Christoffa Corombo would add 12 minutes to Santa Maria's longitude when traveling 12 extra nautical miles westward on his voyage to what he thought was India. I wonder how enraged he would be should mathematician appear on the deck and start arguing that he should add 0.00349 radians instead. There are many other examples of such agreements. For instance, the singular choice of axes permutation in P21212 is to make sure that two-fold is along c. We could agree instead to always have a>b>c - it's workable, but we would have to keep two more space groups around (hope I didn't make too many factual mistakes here). I witnessed once a physics professor having a psychotic break when someone mentioned SI units during discussion of Maxwell's equations. Well, electrical engineer will probably try to electrocute you if forced to measure current in franklins per second (i.e. statamperes) because a theoretician wants to get rid of Coulomb's force constant. PS. By the way, did you notice that pi^2 ~ g ? I remember reading long time ago that this is due to the early choice of the meter length as that of a pendulum with two seconds period of motion. Talk about anthropic principle... --
