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...
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