Why is a Circle 360 Degrees, Why Not a Simpler Number, like 100?

Fun fact: Babylonians had sixty fingers.

Remember a maths lesson aged 11 where we were asked, why 360°. I offered that it was highly factorisable, and the teacher was, like, meh. The answer she was looking for was that 360 was close to the number of days in a year. Pleased to be vindicated some 46 years later!

Thank you for explaining this. I lived for 3 decades and not even once heard anyone say why 360 is better than any other number, not even in school. I was always met with: "Well, it just is, live with it." I finally have understanding behind why that number is good for circles.

This makes a lot of sense. But why are the Americans using it then?

I'm so used to the decimal way, I totally hadn't realized there is another way to count with your fingers without just lifting each individual finger. That was unexpectedly eye-opening.

I remember being quite flustered when I first learnt about radians. I thought it was incredibly stupid because I KNEW there were 360 degrees in a circle. Just wish the teacher had introduced the subject of radians by pointing out that the 360, and thus the size of a degree, is completely arbitrary.

This comment will get 360 likes PS:52 likes are huge thank you all PS:HOLY 136 LIKED PS: THANK Ohmygoddddddd wow but more than 360?

I struggled with math in school, but I actually guessed that was going to be the reasoning because I could see that so many numbers went into 360 evenly. 👍🏻

There was an article in the “Journal of Irreproducible Results” between 1980-1985 that had a fabulous, detailed article about how we should switch to ten-based time. It was a very well thought out and explained article, suggesting 100 seconds in a minute, 100 minutes in an hour, etc. They even figured out how to deal with 10 days per week, 10 days per month, everything would be so easy! Every couple of years I search for that magazine and article, with no luck. I would feel deeply indebted if somebody had a copy, or was able to find it!

It also has to do with calendars, time, astronomy, and living on a spherical planet. Before we used the 365 day calendar there were 360 day calendars. The 30 day months tracked the lunar cycle. 360 days/ 30 degrees to a zodiac sign equals 12 months as well. Observing the sky for navigation and charting the seasons gave us the numbers to work with. 360/15 degrees equals 24 hours in a day and the further divisions of minutes and seconds lend to our coordinate for GPS as well.

Never asked this question myself. But now that you have mentioned it, thanks!

A good and informative video. I especially liked the point about highly composite numbers. A reminder too that the old British or 'Imperial' measurements of inches and feet, ounces and pounds and stones, pints and gallons are more easily divisible into halves, quarters, eighths etc - as in dry measures of wheat and liquid measures of beer etc.

6 circles of the same size also fit perfectly around a circle. If you use a compass you can further divide from the centers of those and make a protractor.

I always thought 360 got the nod not only because it was so highly composite (I guessed that part correctly), but also because it happens to be very close to the number of days in a year, so that we have 1 second or arc being 1/60th of a minute, 1 minute of arc being 1/60th of a degree, 1 degree of arc being 1/360th of an Earth revolution (i.e., a day) and 1 Earth revolution being (roughly) 1/360th of a Solar orbit (i.e., a year). I'm sure that would have been a useful metric for early navigators to predict star positions and plot vectors therefrom.

The decimal system which has become the universally adopted system for doing maths was developed in India.

That the task of dividing up the circle in equal parts is so common in têchnology is probably the reason the unit for angle has resisted decimalisation. In most other measuring tasks, dividing in equal parts is not quite so common. (Adherers to systems of units based on a monarchs body parts notwithstanding) Not surprisingly, the field where the 100° to the right angle unit 'gradian' could establis itself, surveying, does not often have to divide the circle, but measures relative angles between points on the earth.

as a surveyor I'm used to grads. A full circle has 400g , each grad has 100cents and each cent has 100ccs (cents of cents)

When I was in high school, I spent about a month trying to really train myself to learn the Base 12 multiplication table. One subtle advantage of Base 10 is that it takes care of the number 5, which is actually quite "unintuitive" in division. So while 12 has more factors, 10 has the advantage of "consuming" a weird number and making it easy to divide or multiply by 5. In base 12, you face similar problems with 5 as you do with 7 in base 10 (and retain the same difficulties of 7), for only the advantage of making multiples of 3 easier to count out (which they are already quite simple in base 10).

I feel a little more educated now. Thank you!

So if we take a number like 2520 which is divisible by all number from 1 to 10 then will it be better than 360, right?