Nick: 
Dad, we always measured angles in degrees.
I wonder, how do people on other planets measure
angles? 
Michelle: 
What
a question, Nick! Think about it, who could
know? 
Dad: 
Actually,
I really like this question. You know, guys,
such questions may seem “dumb”
at first, but sometimes they lead to very
important discoveries. In fact, Nick’s
question is reduced to this: “is there
a somewhat natural measure of angles?”
Certainly so far nobody knows how the aliens
measure angles, but I’m 99.9% sure that
it’s not in degrees. 
Michelle: 
Why not? 
Dad: 
Because
a degree is an artificial measure that arose
historically and is not based on the laws
of nature. What is one degree? 
Michelle: 
It’s
1/360 part of a circle. 
Dad: 
But where
did the number 360 come from? 
Michelle: 
I don’t
know. 
Dad: 
This
number was introduced by astronomers in ancient
Babylon (at least 3000 B.C.). No one knows
for sure why they settled for this number.
At those times, it was already known that
the yearly cycle consists of 365 and 1/4 days,
even though astronomers didn’t know
yet that the earth revolves around the sun. 
Michelle: 
Maybe
they just rounded 365 and 1/4 to 360 and decided
to use one “day” sizing 1/360
part as a unit measure for angles? 
Dad: 
Maybe. 
Nick: 
But why
didn’t they take 365? How is it worse? 
Dad: 
Perhaps
they chose 360 because it has more divisors.
In other words, the number 360 splits into
whole parts much better than 365. You can
verify it yourselves. In any case, it’s
clear that angle measure based on the number
360 is artificial. The same thing, by the
way, applies to the decimal number system.
It was formed only because we have 10 fingers
on our hands. In math, and especially in computers,
it is often more convenient to use other number
systems such as binary or octal, in which
the bases are powers of two. 
N: 
So, is
there a “natural” measure of angles? 
D:

Yes, there
is. And that measure is called a radian.
I think aliens might use it since like us
they study the same nature. 
M: 
Is radian
measure difficult to define? 
D: 
No, pretty
simple. … 


