#CircleDegrees #Geometry #Mathematics #360Degrees #CircleMeasurement
If you’ve ever wondered why circles are specifically divided into 360 degrees and not 100, then you’re not alone. The concept of circle measurement and the degree system may seem arbitrary at first, but there are actually some interesting historical and mathematical reasons behind it.
In this article, we’ll dive into the fascinating world of geometry and explain why 360 degrees is the standard measurement for circles. So, buckle up and prepare to expand your mathematical horizons! 🌐
###The History of 360 Degrees
The origin of 360 as the standard measurement of a circle can be traced back to ancient civilizations, particularly the Babylonians and the Sumerians. These ancient cultures were pioneers in the field of mathematics and astronomy, and they played a crucial role in shaping our understanding of geometry.
1. Babylonian Number System:
The Babylonians had a base-60 number system, which is believed to have influenced the division of the circle into 360 degrees. This system’s divisibility by many different numbers made it convenient for practical and mathematical purposes.
2. Astronomical Significance:
The Sumerians were also deeply interested in astronomy, and they observed that the sun appears to move across the sky in a full circle over the course of a year. They divided this circular path into 360 equal parts, which corresponded to the 360 days in their calendar.
###Mathematical Reasons for 360 Degrees
While the historical origins offer some insights into the 360-degree measurement, there are also mathematical reasons why this number is particularly practical for circular calculations.
1. Divisibility:
The number 360 has many divisors, such as 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. This makes it easier to work with fractions and angles in calculations, providing a level of versatility that other numbers, such as 100, lack.
2. Trigonometric Functions:
The use of 360 degrees aligns neatly with trigonometric functions such as sine and cosine, as well as the unit circle. These functions have periodic behavior that is coherent when based on 360 degrees.
3. Historical Continuity:
Over time, the 360-degree system has become deeply ingrained in mathematical and scientific conventions. It would require significant effort to shift to a new measurement system, and the benefits may not outweigh the costs of such a transition.
###Alternative Measurement Systems
While 360 degrees is the standard for measuring circles, there are alternative systems that have been proposed or used in specific contexts.
1. Grad:
Some engineering and scientific disciplines use a unit of measurement called a grad, also known as a gon or grade, which divides a circle into 400 units. The grad offers easier calculations and is used in fields such as land surveying and military applications.
2. Radian:
In advanced mathematical and scientific contexts, radians are often used for measuring angles. One radian is equal to the angle subtended by an arc of a circle that has the same length as the radius. Radians are particularly useful in calculus and trigonometry due to their close relationship with circular functions.
###In Conclusion
While the choice of 360 degrees as the standard measurement for circles may seem arbitrary at first glance, it has strong historical and mathematical foundations. The historical influence of ancient civilizations, the practicality of divisibility, and the alignment with trigonometric functions all contribute to the enduring dominance of the 360-degree system.
So, the next time you encounter a circle in your mathematical or scientific pursuits, you can appreciate the rich history and mathematical logic behind the 360 degrees that define it. After all, circles are anything but straightforward when you start digging into the details! 📐
Having 100 degrees doesn’t make things any easier, really. We mostly talk about angles in triangles, or other acute angle situations, so then you’d mostly have numbers like 25, which still aren’t round and which are harder to subdivide into the angles we normally consider significant like halves and thirds of a right angle.
The only subdivision of a circle that naturally falls out of circle math is radians, where one radian is the angle whose arc length is equal to the radius, and a full circle is 2π. But that’s a pain in casual conversation or for specifying any angle that isn’t a simple fraction of π, so we might as well go with whatever we’re used to using, which happens to be 360 degrees.
They could be. You could make up your own unit for 100th of a circle. And call it a Centagree.
We use a unit that is a 360th of a circle, because it’s more convenient. There are more numbers that can easily be broken out without using decimals.
The Babylonians made it up. They thought it was cool that there are so many ways to divide it up. It’s also why we have 60 minutes in an hour, 60 seconds in a minute. There are also 60 arcminutes in a degree and 60 arcseconds in an arcminute. It’s factors of 60 all the way down.
The ancient Babylonian calendar said that there are 12 months of 30 days, and thus 360 days in a year (which got periodically adjusted by big-ass leap years to make up for the 5.25 missing days). This was based on their understanding of astronomy and charted by the movement of constellations.
in ~200 BC the Greek astronomer Hipparchos of Rhodes was studying ancient Babylonian astronomy and needed to do some angular calculations, as astronomers very often do. Since the Babylonian constellations where assumed to move through 360 days, Hipparchos divided a circle into 360 parts, and the concept of the 360-degree circle was born.
We kept this system because it’s actually pretty good, since 360 can be evenly divided very many ways, though these days radians are in more common use because they’re even better.
But it all comes from ancient Greeks studying a fucked-up calendar that was considered ancient by the ancient Greeks.
360 is just what we wanted to use. These are called “degrees”.
100 can be (and sometimes IS) used. These are called “gradians”.
There is a very deep mathematical reason why we **really** should be using “2 times Pi” as the value of a full rotation. These are called “radians”.
– The simple reason is “do a quarter rotation” is “normal”. And “do a 90 degree rotation” is bonkers if you think about it. Perhaps “do a half-Pi rotation” is also bonkers … but at least it’s natural mathematically.
– the deep math reasons are because of calculus and complex numbers. inverse tangent of 1 is exactly equal to a quarter rotation. And you can calculate it like this:
arctan(x) = x – (x^3 / 2) + (x^5 / 5) – (x^7 / 7) + …
arctan(1) = 1 – (1 / 2) + (1 / 5) – (1 / 7) + … = pi/4
The value that pops out of that is Pi/4. So really radians is the natural way.
Plus 1 rotation of a circle of radius `1` is 2 * pi * 1 = 2*Pi
360 actually comes from the number of days in a year. When early civilizations tried to measure a year they often came up with numbers a little over 360. Thinking the world was made by gods and made sense they decided 360 made sense.
As in a year the stars circle the earth if looked at at the same time, the idea of a year and a circle were very tightly related to each other.
So every degree represents a day.
To add to the other responses, when the French were developing their “metric” system following the French Revolution, they did come up with [a 10-based system for angles](https://en.wikipedia.org/wiki/Gradian).
Rather than splitting a circle into 100, they split a right-angle into 100. One gradian, or gon, if 1/400 of a full turn (or 9/10ths of a standard degree). While it didn’t take off as much as other decimal measurements, it is still used – particularly in some areas of surveying and mining, especially by the French. Many scientific calculators will have an option to give angles in gradians (along with degrees and the mathematically-more-satisfying radians).
They also developed a decimal system for time; from 1794 to 1800 the French Republican calendar divided the day into 10 hours, with each hour having 100 minutes, and each minute having 100 seconds (giving a slightly shorter second, one decimal second lasting only 0.86 conventional seconds).
The ancient people who first figured out a lot of circle math did not use a base-10 number system like ours. They used a base-12 number system and counted the knuckles on their not-thumb fingers. 12 is a pretty nice number like 10. It divides evenly by 2 and 3. It was convenient for their math so that’s what they picked. (You can make a lot of arguments it’s more convenient than base-10, but base-10 is still pretty good and we’re real used to it.)
So they divided a circle into 360 degrees. They divided each degree into 60 “minutes”. They divided each “minute” into 60 “seconds”. They picked these numbers because 5 * 12 felt convenient to them I guess. Now you also sort of see how we ended up with our time-telling system: they divided that circle into 12 then reckoned why not keep the minutes/seconds divisions since it was convenient to have more divisions at smaller scales.
I think this was the Babylonians, I’m not sure. Either way, whichever people did it were the biggest empire at the time so they got to teach everybody how to do things. Eventually they fell, but people were used to using these systems and didn’t feel like changing them. How’d people end up with base-10 for other things? The *next* empire showed up with base-10, but didn’t have all of the geometry and other math the Babylonians did, so they just lifted it and kept it as-is because it’s stupid to rewrite an entire branch of math just to change the base, it’s smarter to just keep building on what’s there.
Because we made it up. Back when they were figuring out geometry, they divided circles into 360 because it can be broken down evenly into a lot of different numbers.
360 is a multiple of, and can evenly be divided into: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360 pieces.
100 only has 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Being able to break it down in more ways without dealing with fractions or decimals turned out to be useful.
In addition to what other people are saying, during the creation of the metric system, there was an attempt to create a base ten version of angle. The Gradian.
There are 100 Gradians in a right angle. This sounds nice and reasonable, until you realize what angles come up the most often in practical situations. 30, 45, 60 and 90
45 degrees turns into 50 grad, and 90 degree turn into 100 grad. Those ones work perfectly fine.
However, 30 and 60 degrees turn into 33.33 and 66.66 grad. If you are changing into a base ten decimal system, have two of the most common values be repeating decimals is awkward and unwieldly. While scientists were perfectly happy to switch to to kilograms and meters, nobody wanted to switch to Gradians.
Some people split it up into 400 (“gradians”), some people split it up into 2*pi (“radians”). 2pi is the nicest for calculus, if it’s just for geometry then it doesn’t matter at all.
Early astronomers realized the earth moved approximately 1/360th each day.
When we got more accurate we realized that 365.2425 is closer to the actual total number of days and we adjusted.
But a lot of early mathematicians ascribed significance to 360 because of this observation.