An Angle Turns Through 1/360 of a Circle

Have you ever thought nigh how it’southward kind of weird that a circle has 360 degrees? At first idea, it seems like a rather random number to have called—why not 100, or 500, or 720 degrees? Was it really a random choice? Or was there actually some practiced reason that 360 was chosen to be the number of divisions in a circle?

Equally we’ll find out today, in that location was indeed a good reason. What was it? We’re not entirely sure. But we exercise have some pretty good ideas. And those ideas are exactly what we’re going to be talking nigh.

The When and Where of 360 Degrees

Every bit y’all probably know, these days nosotros humans like to carve up a circle up into 360 pie-shaped wedges. Each of these wedges contains an angle at its vertex, and we say that the size of this angle is one caste. As you besides probably know, degrees aren’t the only way we can measure angles. Angles are too measured in radians and sometimes (very rarely), they are fifty-fifty measured in obscure military units called gradians (which is why a lot of calculators accept “deg rad grad” buttons on them).

While nosotros don’t know exactly why the 360 degree convention was chosen (more on that in a minute), we do know approximately when and where it all started. At least we know that information technology came to exist a long, long time agone—equally in 4 or 5 one thousand years ago with the Babylonians, the Greeks, and perhaps other even more aboriginal groups.

Every bit to the question of
why
360 degrees was called, here’s what we think happened …

Reason #1: The Length of the Year

Fifty-fifty if y’all accept admittedly no idea right at this instant why there are 360 degrees in a circle, I bet that if you finish and retrieve for a few minutes you lot tin figure out one possibility. If after those few minutes you lot’re still not sure, call back about where else you’ve seen a number that’s close to 360 in your life. And if you’re even so stuck after that, think about the Lord’s day … the World … orbits … and calendars.

Got it?

You might conclude that the Sun moves about one/360 of the way along this circle every day.

The Earth takes i yr to orbit the Lord’s day. And a year is just a little more than 365 days. That means that the Earth rotates on its centrality a fiddling more than 365 times every yr. And it means that every solar day the Sunday appears to move about 1/365 of the way along a huge circle projected onto the sky that extends all the fashion around the Earth (called the ecliptic). If you lived a few millennia ago and didn’t have modernistic instruments to accurately tape the positions of objects in the heaven, yous might conclude that the Sun moves virtually one/360 of the way along this circumvolve every mean solar day, which is exactly what ancient astronomers did. And they then fabricated a leap and decided to split this circumvolve on the sky—and all circles—into 360 even parts so that the Dominicus would move through i part per day. Each of these parts was dubbed 1 caste, thus giving united states of america the idea that a circle contains 360 degrees.

Makes sense, right? And given that the aboriginal Babylonian and Western farsi calendars were both based upon 360-day years, information technology seems likely that this simple astronomical observation is the reason a circle contains 360 degrees.

Reason #2: Babylonians and Base-60 Numbers

Simply that’south not the end of the story. Because there are other reasonable ideas out there equally to the origin of the 360 degree convention. As we saw earlier, the Babylonians used a 360 day calendar. And, as information technology turns out, the Babylonians likewise used a base-60 number system (called the sexagesimal system). Simply as we use 10 dissimilar symbols to represent numbers in our base of operations 10 decimal organization, the aboriginal Babylonians used lx symbols to represent numbers.

Why does this affair? Well, 60 ten six = 360. This ways that 360 is a nice even multiple of the number base in the Babylonian system (which would have had the same aesthetic value to their brains that a nice even multiple of 10 has to ours). But there’s more to it than that. The Babylonians knew about equilateral triangles. And they knew that if yous bundled 6 of these equilateral triangles in a certain manner with the edge of i aligned on meridian of the edge of the side by side, the last one would end up coming together back up with the first. In other words, the total angle formed by 6 of these equilateral triangles would be the same as the angle effectually a circle. Given the Babylonian usage of 60 as their number base, they decided that each of the angles of an equilateral triangle would be 60 degrees. And thus, when you multiply these threescore degrees past the 6 equilateral triangles that combine to create a sort of circle, y’all go six ten sixty = 360 degrees. And thus, 360 degrees in a circle.

So, there’s that.

Reason #3: The Many Factors of 360

But that’south still non the cease of the story … because at that place’south some other reason to love the number 360. Namely, it’s evenly divisible past 2, 3, four, five, half-dozen, eight, 9, ten, 12, xv, 18, twenty, 24, 30, 36, twoscore, 45, 60, 72, 90, 120, and 180. That’s a lot of factors!

And that makes 360 a actually convenient number because it means we can carve up a circumvolve into 2, iii, 4, five, six, 8, ix, 10, 12, and so on even parts. It makes solving problems by mitt—which, mind you, was the only fashion to solve problems thousands of years ago—much easier.

While this alone doesn’t seem similar enough reason to have swayed people to define a circumvolve as having 360 degrees, information technology certainly wouldn’t have hurt. And it’s entirely possible that it was a combination of all three reasons (and mayhap others besides) that ultimately pb us to the definition of a degree that we still use today.

Wrap Upward

OK, that’southward all the ancient math we have time for today.

For more fun with math, please check out my book,
The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of keen math posted throughout the week. If you’re on Twitter, delight follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’south Quick and Muddied Tips to Make Math Easier. Cheers for reading, math fans!

Earth and Sun image from Shutterstock.