
Full Circle: The complicated history of why there are 360 degrees in a circle - Hooke
https://www.historytoday.com/history-matters/full-circle
======
kens
One circle unit that strikes me as strange is the "mils" used for military
targeting: there are 6400 mils in a circle. The benefit of this is that 1
meter wide at a distance of 1 kilometer corresponds to 1 mil. So if your tank
misses the target by 5 meters and the target is 1 km away, you adjust the
angle by 5 mils, nice and easy to compute.

A bit of math shows that this unit is a milliradian (since sin 1/1000 ≈
1/1000). The strange part is that there should be 6283.18... mils in a circle
but that's too inconvenient, so they round it to 6400. In other words, they
are using milliradians with the value of 3.2 for π.

~~~
dresstotheleft
And that is just the NATO convention. There are several others in use across
the globe -
[https://en.wikipedia.org/wiki/Milliradian#Definitions_for_ma...](https://en.wikipedia.org/wiki/Milliradian#Definitions_for_maps_and_artillery)

------
blauditore
I always thought this was somehow motivated by great divisibility, since prime
factors of 360 are 2, 2, 2, 3, 3, 5. This means you can work with integers
most of the time when dividing a circle, since all but four numbers in 1-15
are divisors.

~~~
roelschroeven
That large number of divisors was the reason for the Babylonians to use
base-60, I've always been thaught. I always assumed the the 360 degree circle
was a consequence of that, but this article contradicts that.

Actually I don't think the article does a great job proving its thesis ("In
school we learn there are 360 degrees in a circle, but where did the 360 come
from? When it is pointed out that the Babylonians counted to base-60, rather
than base-10 as we do, people often ask if there is a connection. The short
answer is no.").

The article's conclusion is "So, although angles come from the Greeks, the 360
degrees comes from Babylonian astronomy". And it explains, more-or-less, how
the Babylonians came to use 360 degrees for astronomy: because they had a
habit of dividing things into 12 part, subdivided in 30. But that doesn't
preclude they choose 12 and 30 (instead of, say, 13 and 28) because both are
divisors of their base number 60.

Wikipedia points in that direction (but admits no-one really knows):

"Some ancient calendars, such as the Persian calendar, used 360 days for a
year.[citation needed] The use of a calendar with 360 days may be related to
the use of sexagesimal numbers."

"Another theory is that the Babylonians subdivided the circle using the angle
of an equilateral triangle as the basic unit and further subdivided the latter
into 60 parts following their sexagesimal numeric system.[7][8] 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."

Another Wikipedia-quote agrees with your point of view:

"Another motivation for choosing the number 360 may have been that it is
readily divisible: 360 has 24 divisors,[note 1] making it one of only 7
numbers such that no number less than twice as much has more divisors" "

~~~
im3w1l
An arc-minute is a 60th of a degree. And an arc-second is a 60th of an arc-
minute. This strongly points to a base-60 origin imo.

~~~
gumby
The minute ("small part") and second ("even smaller part") come from the era
of clockmaking as they were pointless when your timekeeping resolution was
crude.* We are quite lucky that hours and then minutes were divided into 60
sections rather than 10, 12, or 100. This may have come from the system you
describe (arc minutes, seconds, thirds, etc) which is much older.

* or not just crude but completely different; e.g. Babylonian and Roman hours varied in length each day as the time from sunrise to sunset was divided into twelve equal sections and sunset to sunrise implicitly the same. IIRC the constant-duration hour goes back only to marine navigation a few hundred years ago

~~~
Wowfunhappy
> We are quite lucky that hours and then minutes were divided into 60 sections
> rather than 10, 12, or 100.

So let's say there's 20 hours a day, since presumably we'd still want to have
two daily clock rotations. Those hours could then be divided into 100
"minutes" with 100 "seconds" each.

If I'm doing my math right, this would mean:

• 1 alternate-universe hour = 1.2 current-universe hours

• 1 alternate-universe minute = 0.72 current-universe minutes

• 1 alternate-universe second = 0.432 current-universe seconds

I could very much deal with this. Current-universe seconds are a bit too long
for the level of precision I want with that unit, and I don't think the < 30%
change in the length of a minute or hour would matter much once I adapted.
And, as a consequence, unit conversions would become so much easier!

I don't think we're lucky at all. :(

~~~
gumby
Going to base 10 is a step _backwards_ because 10 has so few factors. The
meter would have been massively easier to use had it been base 12 or 60.

Perhaps you can get the Mars colonists to adopt a different system. The
martian day is _just_ close enough to the terrestrial day to make adapting the
terrestrial system for it quite annoying.

~~~
roelschroeven
> Going to base 10 is a step backwards because 10 has so few factors. The
> meter would have been massively easier to use had it been base 12 or 60.

Only when you also use that same base for everything else too. The decimal
system works so well because it uses the same base as the number system we use
(almost) everywhere.

And actually I don't really think the lack of divisors is really a problem in
base 10. It may be different if you're used to imperial units, but when using
the decimal system you don't think in fractions all that much. You either use
more places after the decimal point, or move to a smaller unit.

~~~
gumby
Well at the time the meter was designed, base 12 was quite common for money
and measurement.

I have lived in an Imperial system country, the modified version used in the
USA, and multiple metric countries as well as using a mixture of cgs (SI) and
mks depending on what work or study I was doing and still, for customary
activity, find a dozen the most convenient. When doing science it doesn’t
matter.

------
Koshkin
Theories abound:

 _Babylonian math has roots in the numeric system started by the Sumerians, a
culture that began about 4000 BCE in Mesopotamia, or southern Iraq, according
to USA Today.

“The most commonly accepted theory holds that two earlier peoples merged and
formed the Sumerians,” USA Today reported. “Supposedly, one group based their
number system on 5 and the other on 12. When the two groups traded together,
they evolved a system based on 60 so both could understand it.”_

[https://www.thoughtco.com/why-we-still-use-babylonian-
mathem...](https://www.thoughtco.com/why-we-still-use-babylonian-
mathematics-116679)

------
donquichotte
Ah, measures of angle. One of my favourite is the Warsaw Pact Millirad, of
which there are 6000 in a full circle, a full 6.25% less than the 6400 NATO
mils.

------
everyone
I'm confused by their description of the ecliptic..

" For them, Venus was a single object and they observed its changing position,
along with the other planets and the moon. These positions all lie on the same
great circle, called the ecliptic, defined by the apparent motion of the sun
as seen from the earth during the course of a year. "

Isnt the ecliptic basically a line (or very very skinny ellipse) from Earths
perspective as we are on that great disc ourselves?

Also "For them, Venus was a single object" so for us its not??

~~~
T-hawk
Venus: some ancient cultures recognized its "evening star" and "morning star"
appearances as the same object; some thought they were two different
phenomena.

The ecliptic, physically, is the plane of Earth's orbit around the Sun. It is
so named because that is where eclipses happen, when the Moon crosses that
plane. (Or other planets; we call that event a transit, but that's the same as
a very annular eclipse.)

The projection of that plane as viewed on the sky from Earth is a great circle
(or slightly offset, because the observer is on Earth's surface not at its
center.) If the Earth were transparent, you could see the entire circle. In
reality, you see a segment of it from horizon to horizon, as a line.

All the planets and the moon seem to stay near the ecliptic in the sky,
because their orbits are within a few degrees of coplanar with Earth's.

~~~
everyone
I'm realising I look at this differently to the article writer + u. I would
say, the ecliptic is a great disc. But when your _on_ a disc, from _your_
perspective that disc looks like a straight line, not a circle...

------
adelHBN
It's amazing that Babylonians did this without any modern equipments. Recently
I learned that 2500 years ago Persians (the Persian New Year was last week)
predicted the Spring Equinox with a certainty of 5 minutes. This is crazy.
Very impressive. Sad how the Middle East lost its technological and scientific
edge over the centuries.

------
playworker
My Dad was once gifted a Silva compass which he gave to me to take on a Boy
Scout expedition, everyone was baffled by the fact it had 400 "degrees" marked
on it.

Maybe we need to go metric with our circles too:
[https://en.wikipedia.org/wiki/Gradian](https://en.wikipedia.org/wiki/Gradian)

~~~
sllabres
Surveyors seems to use Gradian/gon often.

There is still another circle measurement, the mil which is 6400 for one turn.
But I just learned by reading the wikipedia page, that there is not only the
6400 NATO mils I knew, but also 6000 Warsaw Pact mils or 6300 Swedish "streck"

~~~
BurningFrog
Swedish "streck" = (short) line.

------
amelius
But why are there 2*pi radians in a circle, instead of defining it as pi?

EDIT: I meant redefining pi instead of the radian.

~~~
Ono-Sendai
You mean pi should have been defined as the ratio of the circumference of a
circle to the radius, instead of to the diameter? Probably, yeah :)

Better yet, I think the unit of angle we should use is the 'full rotation'
('rot'?)

So instead of 360 degrees, or 2pi radians, we say 1 rot.

The many factors of 2pi in common equations imply we got this wrong.

~~~
amelius
I like this idea of "rot" more than "tau", except "rot" is already a stand-in
for "∇⨯" in mathematics.

~~~
Ono-Sendai
Maybe calling it a 'turn' instead.

~~~
SamBam
That has been a proposal, and is part of the nice aspects of using τ instead
of π.

> The second reason is that τ corresponds to one turn of a circle, and you may
> have noticed that “τ” and “turn” both start with a “t” sound.

[https://tauday.com/tau-manifesto#sec-one_turn](https://tauday.com/tau-
manifesto#sec-one_turn)

------
adelHBN
This was awesome. Thanks for sharing it. Amazing how much has come from the
Fertile Crescent.

------
LarryDarrell
So time is a flat circle then?

~~~
greggyb
More of a Jeremy Bearimy sort of shape.

------
rendall
I also note that History Today, as an English company, is no longer GDPR
compliant. "Take this tracking or get out. Honey badger don't care"

