Now this, Nelsn, takes contemplation! At least you supplied me with
the Rig Veda here. We are getting to the point where math and
philosophy and theology converge.
Are you aware of that? The gods put the puzzles out and man tries to
get a grasp on it all. He did not do too badly, athough the Tower of
Babel is very much evident. We all talk in different tongues to manage
the mystery of creation and humanity.
Marta
On Jan 4, 2009, at 18:17 pm, Nelsn Helm wrote:
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 onchords 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)
_______________________________________________
The next Louisville Computer Society meeting will
be January 27 at MacAuthority, 128 Breckinridge Lane.
Posting address: MacGroup@erdos.math.louisville.edu
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_______________________________________________
The next Louisville Computer Society meeting will
be January 27 at MacAuthority, 128 Breckinridge Lane.
Posting address: MacGroup@erdos.math.louisville.edu
Information: http://www.math.louisville.edu/mailman/listinfo/macgroup
