Which Mesopotamian culture devided circles into 360 degrees?
It seems to be a pretty handy number for navigation since it can be divded evenly so many ways. But is it better than a decimal system for dividing circles? That is, would a circle with 100 degrees be more logical and easier to work with in the long run? Was such a system ever proposed?
I don’t know who was the first to do so. Certainly the Babylonians did.
As for where it comes from – surely it is not coincidental that the year has 365 1/4 days (plus change). I could easily see rounding down to 360 for the sake of simplicity (plus all that easy divisibility). And especially if a lot of your math already revolved around calendars to begin with.
Before the invention of the Hindu-Arabic way of writing numbers, I can’t think of any advantage to making the number of “degrees” something like 100. Even since then but before modern digital calculators, decimal notation hasn’t necessarily been easiest to calculate with.
A grad is an alternative to the degree, in which there are 100 grads in a right angle, and 400 in a circle. Every scientific calculator I’ve ever used has a “grad mode,” but I’ve never seen grads used in any real-world context.
In all likelihood, the origin of having 360 degrees in a circle is probably astronomical. That is, there are roughly 360 days in a year.
I don’t know off-hand of any system that uses 100 degrees in a circle, but gradians are close. There are 400 gradians in a circle. The gradian was originally intended to be a “metric” unit of angles, as I understand it.
How useful or logical a unit is depends entirely on what you’re doing with it. Degrees are pretty darn useful for most practical “laymen’s” geometry like building structures. For most mathematical purposes, on the other hand, the radian is a much more convenient unit. I don’t really see a niche where a 100-degree circle would be more convenient, because as you pointed out, 360 degrees are divisible by a proportionally large number of divisors. The gradian never gained much momentum, and this is probably why. It was less useful for the types of applications where people typically used degrees, while being no more convenient for those applications where radians are typically used.
I would suspect that somebody just counted how many finger-widths it took to go around the horizon. The 365 days thing might be a neat coincidence. I have never bought into the idea that in those olden days there were only 360 days in a year. Those guys could count.
Assuming they used the finger-widths method you propose, they’d 1) have to have very accurate finger sizes, and 2) have to hope that they were on totally level ground (for miles around) in order to make the horizon anything more than “useless” as a frame of reference.
Without modern equipment, “360ish” is about as close as any ancient astronomer could hope to get.
They could, but there are records of 360 years (often with a 5 day inter-year period to make up the difference). It’s too close, in my mind, to be a coincidence.
In at least some ancient calendars, there were 360 “official” days of the year, punctuated by five days every year that “didn’t exist”, at least, not on the calendar. Since those five days “didn’t exist”, of course one couldn’t do any work on them, so it was just a big five-day-long celebration.
So yes, they knew how to count, but they also knew how to recognize a good excuse for a party.
And if you were going to use finger-widths as the basis for your unit system, wouldn’t it have been more natural to use the thumb than the pinky finger? I can hold out my thumb for comparison a lot more easily than I can my pinky.
This question transcends circles and is related to, the metric vs imperial debate.
The answer is: It depends if you’re doing engineering or natural measurement. For raw measurement, decimals are easiest. For engineering, the divisibility comes in very handy. This is why contractors will stick to their 12 inches to a foot, 16 fraction to an inch, thankyouverymuch.
P.S. the 60-minutes-to-an-hour thing is very much related. And blast the crazy French for trying to change it.
On the other hand, when I worked with a civil engineer, all our prints, tapes, and measuring wheels were measured in decimals of a foot. For one thing, it meant that we could simply drop all the stationing measurements into a calculator and go from the largest to the smallest measure without any conversions, at all.
That’s what I do when we’re out looking at the sky and I want to tell somebody else how far to look from some recognizable star. Unfortunately you’ll only count around 180 thumb-widths since they’re more like 2 degrees.
And the objection about a featureless horizon is a good one, Really Not All That Bright, so I find it easy to imagine that a team of “surveyor types” might get out on some flat spot and proceed to move sticks around a circle, counting as they went, until they were back at the beginning. I mean, something as important as how many degrees in a circle shouldn’t be left to one guy, his finger, and some tally device. It would be a government project.
Or sometimes their calendars were lunar, and an annual year of 12 lunar months came up even shorter, about 354 days/year. It was fairly common for intercalary days to synchronize the seasons to be inserted as needed by decree. The Romans did this before the Julian calendar was instituted. One reason that Julius Caesar wished to reform the calendar was that the college of pontiffs charged with determining the intercalary days was manipulating the calendar for political gain, extending terms of office for favored officials, delaying elections by legislative bodies, and so on.
Whereas good ol’ July Caesar and his protege Caesar August wouldn’t have dreamed of manipulating the calendar for political gain. No, perish the thought!