The history of the 360 degree circle is ancient and in places
apocryphal. Supposedly it came from the Mesopotamians and perhaps
eventually it was introduced in Europe by the Arabs. One of the
Mesopotamian peoples, the Sumarians, divided the year into 12 months of
30 days each, that is, 360 days. The relationship between the circle and
the length of the year was the celestial sphere; the Mesopotamians were
good astronomers and they estimated that the star field seemed to
advance 1/360 of a circle each day. The numbers 6, 12, and 60 were
considered to have special powers. The Greeks reinforced the uniqueness
of 60 degrees when they noted that the radius of a circle was the same
length of a chord, six of which would fit across the circumference of a
circle. See
http://www.wonderquest.com/circle.htm
http://en.wikipedia.org/wiki/Degree_(angle)
Early off-coast navigation in Europe was at least in part inherited from
the Arabic peoples, who used celestial navigation on the Sahara as well
as in the Mediterranean. For example, they determined latitude by
Polaris using a kamal, which evolved into the quarterstaff of Europe.
That eventually led to the backstaff and then the octant and sextant. It
was a natural step to apply vertical angles to the horizontal and thus
to divide azimuth into degrees, though this competed with the system of
points (1/32 of a circle). Modern mariners still use both degrees and
points. A well-trained lookout can estimate an angle distended between
the bow (or stern) and a sighted object to the nearest point, but
careful navigation requires finer resolution for steering.
Until the invention of mechanical clocks and the rise of celestial
navigation in Europe, the hour was generally the "finest" unit of time.
Celestial navigation demanded finer time measurements and this led to
the rise of the minute and, later, the second. This demand for finer
units of time by people who navigated in degrees made the division of
the hour into 60 minutes of 60 seconds each a natural step. We ended up
with an hour of 3600 seconds (60 times 60) because an hour of 360
seconds (60 times 6) would not have divided it finely enough.
Jim
Pierre Abbat wrote:
On Tuesday 24 March 2009 02:24:53 Pat Naughtin wrote:
You may recall that I have worried about this issue in the past. It
appals me that the SI does not have a unit for angles that can be
conveniently used for designing and constructing buildings. There are
probably more angle measures done on the building sites of the world
than anywhere else in our societies. All that carpenters and plumbers
have — by default — is the old Babylonian degrees, minutes, and
seconds as radians have almost always been useless to them. My
recommendation some years ago was that the CIPM and the CGPM should
recognise that the initial unit of the metric system was the quadrant,
that this unit name could be reduced to the unit name quad, and that
and builders, sailors, and all of us could measure all of our angles
in quads (symbol q) and milliquads (symbol mq).
The problem with quads or gons is that 60 degrees, a common angle with the
useful property that its cosine is 0.5, is an infinitely long decimal number
of them. 45°, which is 50 gons, is commonly used for bay windows, but if two
wings of a building are oblique to each other, the angle is sometimes 45° and
sometimes 60°. There's no reason I can see for dividing the degree in 60,
except tradition, and dividing it decimally would make arithmetic easier, but
for dividing the quadrant by a multiple of 3, there is a reason.
Pierre
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(C) 931.212.0267
(H) 931.657.3107
(F) 931.657.3108
