I only have one question: When they first
measured the earth around its biggest
circumference, why did they not do it in such a
way to make the nautical mile a bit different
that it would fit into at least the fifty rather
than the 60. 50 is at least half of the hundred
and easier to handle.
I think you're right on target. Degrees date from
early measuring the earth, when they facilitated
calculating.
60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 30
50 is divisible by 2, 5, 10, 25
It's been a long time since I took geometry, but
I think I can draw degrees with a compass and straight edge.
including drawing 72°, but it's not easy.
<http://en.wikipedia.org/wiki/Degree_(angle)>
History
A circle with an equilateral Chord (geometry)
(red). One sixtieth of this arc is a degree. Six
such chords complete the circle
The selection of 360 as the number of degrees
(i.e., smallest practical sub-arcs) in a circle
was probably based on the fact that 360 is
approximately the number of days in a year. Its
use is often said to originate from the methods
of the ancient Babylonians.[2] Ancient
astronomers noticed that the stars in the sky,
which circle the celestial pole every day, seem
to advance in that circle by approximately
one-360th of a circle, i.e., one degree, each
day. (Ancient calendars, such as the Persian
Calendar, used 360 days for a year.) Its
application to measuring angles in geometry can
possibly be traced to Thales who popularized
geometry among the Greeks and lived in Anatolia
(modern western Turkey) among people who had
dealings with Egypt and Babylon.
The earliest trigonometry, used by the
Babylonian astronomers and their Greek
successors, was based on chords of a circle. A
chord of length equal to the radius made a
natural base quantity. One sixtieth of this,
using their standard sexagesimal divisions, was
a degree; while six such chords completed the
full circle.
Another motivation for choosing the number 360
is that it is readily divisible: 360 has 24
divisors (including 1 and 360), including every
number from 1 to 10 except 7. For the number of
degrees in a circle to be divisible by every
number from 1 to 10, there would need to be 2520
degrees in a circle, which is a much less
convenient number.
Divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10,
12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90,
120, 180, and 360.
[edit]
India
The division of the circle into 360 parts also
occurred in ancient India, as evidenced in the
Rig Veda:
Twelve spokes, one wheel, navels three.
Who can comprehend this?
On it are placed together
three hundred and sixty like pegs.
They shake not in the least.
(Dirghatama, Rig Veda 1.164.48)
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