Why 360 degrees

[The man formerly known as]

Does anyone know the reason a full circle has 360 degrees and not 400 or 100 or any other rounder number.

What was the reason for choosing 360?

[wobblyprop]

In 1936, a tablet was excavated some 200 miles from Babylon. The mentioned tablet, whose translation
was partially published only in 1950, is devoted to various geometrical
figures, and states that the ratio of the perimeter of a regular hexagon
to the circumference of the circumscribed circle equals a number which in
modern notation is given by 57/60 + 36/(60^2) (the Babylonians used the
sexagesimal system, i.e., their base was 60 rather than 10).

The Babylonians knew, of course, that the perimeter of a hexagon is
exactly equal to six times the radius of the circumscribed circle, in fact
that was evidently the reason why they chose to divide the circle into 360
degrees (and we are still burdened with that figure to this day). The
tablet, therefore, gives ... Pi = 25/8 = 3.125.



Hope that helps

[FlapsOne]

wobblyprop

You really must get out a bit more!!!!!!!

[wobblyprop]

hey, google is a wonderful thing :D

[Captain Stable]

360 is divisible by 2,3,4,5,6,8,9,10,12,18,20.... etc.

100, 400, etc. are not.

[MightyGem]

Hmmm...there was me thinking that pi was 22/7.

[Flash2001]

The fact that our French cousins defined the metre originally as being 1/40,000,000 of the circumference of the earth, on the meridian through Paris of course, suggests that there was a plot afoot to use gradians (Grads) as the standard unit of angular measure. I don't know who uses grads these days but it's an option on most good calculators.

[Captain Stable]

MG, a better approximation for pi is 355/113.

Alternatively, you could use 3.14159265358979323846264338327950288419716.... ;)

[ETOPS]

And don't forget that 1 minute of latitude is a nauticle mile.......

[knobbygb]

Captain Stable hits the nail on the head. You really must learn to think of numbers in terms of ALL their many factors, not just the factor of 10. The more prime factors the better.

In 'real' maths Radians are used. These make life much easier as they are directly related to the ratio pi (one radian =360/2*pi, approx 57 degrees). This tends to make many of those nasty fractions disappear up their own a**e.

If only we navigated to radians. I might be able to steer a bit more accuratley if the units were that big (only seven unique directions instead of 360), although I wouldn't actaully be able to arrive anywhere particularly accuratley.;)

[Cyclic Hotline]

I was taught in elementary nautical navigation that all basic measurement of time is based upon astronomical observation.

This resulted in the year (a convenient circle) being based upon the closest round number, ie: 360 days.

I also recall being told that the British military operated a 400 degree system, but do not know anything about the theory behind it.

This theory is supported by this story from the net;
360 degrees. (http://www.usatoday.com/news/healthscience/science/wonderquest/2002-06-21-circle.htm)


The 360-degree circle is 4400 years old

Q: Why does a circle have 360 degrees, why not 100 degrees? Also why is a degree 60 minutes and a minute 60 seconds.

A: We delve back to arrive at a probable answer. A line of ancient peoples (Sumerians, Akkadians, and Babylonians) who lived in Mesopotamia (now southern Iraq) invented writing, observed the skies, and invented a 360-degree circle to describe their findings. About 3000 BC, the Sumerians invented writing. They also had a calendar, dating from 2400 BC, that divided the year into 12 months of 30 days each, that is, 360 days.

The Sumerians watched the Sun, Moon, and the five visible planets (Mercury, Venus, Mars, Jupiter, and Saturn), primarily for omens. They did not try to understand the motions physically. They did, however, notice the circular track of the Sun's annual path across the sky and knew that it took about 360 days to complete one year's circuit. Consequently, they divided the circular path into 360 degrees to track each day's passage of the Sun's whole journey. This probably happened about 2400 BC.

That's how we got a 360-degree circle. Around 1500 BC, Egyptians divided the day into 24 hours, though the hours varied with the seasons originally. Greek astronomers made the hours equal. About 300 to 100 BC, the Babylonians subdivided the hour into base-60 fractions: 60 minutes in an hour and 60 seconds in a minute. The base 60 of their number system lives on in our time and angle divisions.

A 100-degree circle makes sense for base 10 people like us. But the base-60 Babylonians came up with 360 degrees and we cling to their ways – 4,400 years later.

(Answered June 21, 2002)

[Pax Vobiscum]

Flash2001 asked who uses grads?

In the UK the road signs indicating a hill (remember, we don't have mountains here :D ) ahead have numbers like 10%, 14% which is the slope in grads (probably an ISO standard?). Oldies like me can divide the number into 100 to get the equivalent in old money (1 in 7, 1 in 10, etc.)

PV

[oxford blue]

I would take issue with Flash 2001. The yard is a damn fine unit. It is a measurement on a human scale. It was based on a human dimension (the length from Henry VIII's fingertips to the centre of his chest with his arms outstretched. He must have been a big chap!)

It is a useful measurement because it's about the right size. You can measure a field in yards but you can also measure a suit in it.

The French also had their pre-metric units. These were just as homely and folksy as the British. There was a French yard, a French pound, a French league, etc.

When the Revolution came, there was a mood of throwing away all the old illogical things. There had to be a new unit of length, to go with the new calendar (which didn't last) and the new political order (which didn't last). But the measurements have lasted.

This was because they chose something about the right size.
They knew that it had to be about a yard long, otherwise it wouldn't work as an everyday unit.

I don't think it had anything to do with grads. If it had been based on pure logic, surely they would have had 10,000 kilometers to the circumference of the Earth, not 40,000. No, I'm sure that they knew the answer they were looking for before they asked a minion to sort out the details (which is how most management works!)

[Flash2001]

Gentlemen

I don't know much about the British Isles only having spent a few months there but:

In the civilized world a slope expressed in % is given as the tangent of the angle expressed as a percentage, that is to say 100*rise/run. It has nothing to do with grads.

I rather agree about the yard though, the only difficulty is that of exhuming Henry XIII every time an instrument needs to be referred to the national standard. Same problem with King John and the foot. You could dig up just about any renaissance adult to get the inch (Length between the thumb knuckles) and save wear and tear on used royalty.

As the foot is now defined in terms of the yard and the yard in terms of the metre, it must be hard on the pride of various kings when they look down (Or up) and find themselves defined by the speed of light, which now defines the metre.

[Cornish Jack]

This MAY be an urban myth........:D
A Royal Air Force Regiment instructor was giving a lesson on fields of fire. To illustrate the subject (this was in 'chalk and talk' days) he drew a chalk circle which extended to the edges of the blackboard.
"You will all recognise this as a circle. An arc is part of a circle. As you all know, there are three hundred and eighty degrees in a circle."
At this point there was a slightly embarrassed hiatus until one brave young recruit piped up...
"Excuse me corporal, but there are only three hundred and sixty degrees in a circle."
A further pregnant pause while said corporal glared at the unfortunate young man. "What this airman hasn't noticed but the rest of you obviously have, is that what I have drawn here is a B****Y BIG circle".
For those who haven't had the pleasure of service in Her Britannic Majesty's Air Force, the RAF Regiment were not noted for the extent of their education.

[Crusty Ol Cap'n]

Guys, Read "The Riddle of the Compass" by Amir Aczel. Interesting book and gives a couple of possible answers to the question of why we use 360 degrees for a circle.:cool: :p :confused: