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That was quite convincing actually. I guess we all have this realization at some point in early math education. Why is it 360 degrees? Mainly because that's a

That was quite convincing actually. I guess we all have this realization at some point in early math education. Why is it 360 degrees? Mainly because that's a nicely divisible number, no other good reason. Sometimes you find a 400 degree system on calculators but it doesn't seem to be taught anywhere (is it a French thing?) Then at some point you get shown radians, which relates the arc length to the radius. That somehow seems natural, but it does mean there's going to be this constant lying around somewhere in your calculations. Parameterizing the angle as a proportion of how big it can be (number of full circles) seems pretty sensible. I mean if you can avoid the constant for at least some of your geometry, then why not?

krajzeg 4y ago
The 400 system is the grads or gradians, indeed originating from the French revolution. Nowadays I don't think they're used as the principal unit in any country. Wikipedia does mention it gets some use in specialized fields such as surveying, mining and geology.
- gfv 4y ago
  They are used indirectly through distance. At the time, the meter was defined as one ten millionth of the distance between the north pole and equator through the Paris meridian. That means that the meter corresponds to 1/100000 of a grad of latitude -- which is better read as "a kilometre is 1/100 of a grad". This is symmetrical to the nautical mile, which is one minute of arc.
severak_cz 4y ago
It's 360 degrees because of stars. One degree is how much stars move by one day.
- ncmncm 4y ago
  Or, as close as made no nevermind, oncet.
- vimsee 4y ago
  > One degree is how much stars move by one day. I was going to look that up to confirm it, but then I realized I could prove that statement true using some simple logic I already know. Earth does one cycle around the sun in 365 days. So at midnight looking straight up on a specific star (that is angled perpendicular of the rotating poles of earth) in the sky, the star you would have spotted on that day would appear slightly off the next day at midnight. It would only end up on the same spot on midnight after 365 days. So we are 5 days off, but I am going to believe it is true until someone is correcting me.
  - unclad5968 4y ago
    Wikipedia agrees with you, technically, except the theory specifically names the sun as the star used. However, the reference is a wolfram alpha article, which only references the book The Elements of Typographic Style. I've never read the book but using the sun position makes sense to me, so I will also choose to believe this until corrected.
fmajid 4y ago
360 comes from the Babylonians, who used base-60 for numbers much for the reasons you describe (and who gave us the 24-hour day, 60 minute hour and 60-minute second, not to mention the 7-day week). NATO forces have compasses labelled in mils or milliradians, which are not actually 1/1000 of a radian but as an approximation 1/6400 of a full turn. I still have my Silva military compass from 1989 graduated thus. https://en.wikipedia.org/wiki/Milliradian https://en.wikipedia.org/wiki/Milliradian
- quickthrower2 4y ago
  I heard that the reason is 1km away it makes a difference of 1m, so easy to figure out how far enemy troops are from each other.
  - jibe 4y ago
    It is even cooler than that. 1 milliradian is simply the distance (radius) divided by 1000, regardless of the unit of measure. So 1 km / 1000 = 1 m. At 100 m, 1 milliradian is 1 cm. At 1000 yards 1 milliradian is 1 yard. At 1 mile (5280 feet), 1 milliradian is 5.280 feet.
  - int_19h 4y ago
    More importantly, it can be used for ranging. The average human height is known, and (usually) so are the sizes of whatever vehicles the other side might be using. Thus, when observing things of known size through some optic with a reticle graduated in mils, you can easily determine the range to them. Which then gives you e.g. the amount of holdover necessary to hit the target with a gun (which can itself be expressed as number of mils on the reticle to aim above).
    - quickthrower2 4y ago
      Ah of course it is the other way around like you say. You know the size of things, you need to figure out the distance.
- ncmncm 4y ago
ComputerGuru 4y ago
Regarding the 400 "degree" system: they're called gradians and it's part of the centesimal system of angular measures according to Wikipedia. And your French guess was right, they have their origins in the French Revolution. More here: https://en.wikipedia.org/wiki/Gradian https://en.wikipedia.org/wiki/Gradian

krajzeg 4y ago

The 400 system is the grads or gradians, indeed originating from the French revolution. Nowadays I don't think they're used as the principal unit in any country. Wikipedia does mention it gets some use in specialized fields such as surveying, mining and geology.

gfv 4y ago
They are used indirectly through distance. At the time, the meter was defined as one ten millionth of the distance between the north pole and equator through the Paris meridian. That means that the meter corresponds to 1/100000 of a grad of latitude -- which is better read as "a kilometre is 1/100 of a grad". This is symmetrical to the nautical mile, which is one minute of arc.

severak_cz 4y ago

It's 360 degrees because of stars. One degree is how much stars move by one day.

ncmncm 4y ago
Or, as close as made no nevermind, oncet.
vimsee 4y ago
> One degree is how much stars move by one day. I was going to look that up to confirm it, but then I realized I could prove that statement true using some simple logic I already know. Earth does one cycle around the sun in 365 days. So at midnight looking straight up on a specific star (that is angled perpendicular of the rotating poles of earth) in the sky, the star you would have spotted on that day would appear slightly off the next day at midnight. It would only end up on the same spot on midnight after 365 days. So we are 5 days off, but I am going to believe it is true until someone is correcting me.
- unclad5968 4y ago
  Wikipedia agrees with you, technically, except the theory specifically names the sun as the star used. However, the reference is a wolfram alpha article, which only references the book The Elements of Typographic Style. I've never read the book but using the sun position makes sense to me, so I will also choose to believe this until corrected.

fmajid 4y ago

360 comes from the Babylonians, who used base-60 for numbers much for the reasons you describe (and who gave us the 24-hour day, 60 minute hour and 60-minute second, not to mention the 7-day week). NATO forces have compasses labelled in mils or milliradians, which are not actually 1/1000 of a radian but as an approximation 1/6400 of a full turn. I still have my Silva military compass from 1989 graduated thus. https://en.wikipedia.org/wiki/Milliradian https://en.wikipedia.org/wiki/Milliradian

quickthrower2 4y ago
I heard that the reason is 1km away it makes a difference of 1m, so easy to figure out how far enemy troops are from each other.
- jibe 4y ago
  It is even cooler than that. 1 milliradian is simply the distance (radius) divided by 1000, regardless of the unit of measure. So 1 km / 1000 = 1 m. At 100 m, 1 milliradian is 1 cm. At 1000 yards 1 milliradian is 1 yard. At 1 mile (5280 feet), 1 milliradian is 5.280 feet.
- int_19h 4y ago
  More importantly, it can be used for ranging. The average human height is known, and (usually) so are the sizes of whatever vehicles the other side might be using. Thus, when observing things of known size through some optic with a reticle graduated in mils, you can easily determine the range to them. Which then gives you e.g. the amount of holdover necessary to hit the target with a gun (which can itself be expressed as number of mils on the reticle to aim above).
  - quickthrower2 4y ago
    Ah of course it is the other way around like you say. You know the size of things, you need to figure out the distance.
ncmncm 4y ago

ComputerGuru 4y ago

Regarding the 400 "degree" system: they're called gradians and it's part of the centesimal system of angular measures according to Wikipedia. And your French guess was right, they have their origins in the French Revolution. More here: https://en.wikipedia.org/wiki/Gradian https://en.wikipedia.org/wiki/Gradian