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# Are there 360 degrees in a circle?

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BoggyB
 Voting Style: Open Point System: Select Winner Started: 4/7/2015 Category: Education Updated: 3 years ago Status: Post Voting Period Viewed: 1,036 times Debate No: 73040
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7 comments have been posted on this debate. Showing 1 through 7 records.
Posted by mostlogical 3 years ago
I hope you agree with me here, if someone decided a long time ago the sun was 100 miles away for whatever reason despite being able to measure things in miles on Earth, and everyone accepted this as fact, but many generations later someone accurately approximated the distance of the sun, people should accept that whoever said the sun was 100 miles away was wrong.

True, someone created the concept of degrees just like with any measurement, and used the number of degrees in a line (not a circle) to measure the angles inside polygons. When someone says a circle has 360 degrees they are also saying that a square has the same number of degrees, and it has twice the number of degrees as a triangle etc. Basically they are thinking 'it is not possible to know, so let's give it a value' just like with the example I have shown above about the sun.

You say that a curved line can't be given an angle, yet a circumference of a circle can be measured exactly despite that line being curved, of course no-one can write it down exactly because it would go on forever but that's why we use approximations for Pi such as 22/7. With angles, you can get better approximations; I've shown the method to do that - by putting a polygon inside a circle with more and more sides. A straight line has one side, and a curved line (or circle) has one side too, which is why the number of degrees in a circle are almost identical to those in a triangle, not a square.

I'm sure there are formulas which can show how much a line "appears" to have curved, but this is not the same thing as finding the number of degrees inside a shape.
Posted by BoggyB 3 years ago
I argue that a circle should be accepted for having 360 degrees because it was created. Someone created the concept of "degrees." It wasn't discovered like you seem to think. If I took a right angle and divided that angle into 9 parts, and called each part a "chunk," I would've created a new measurement. There would be 4 x 9 "chunks" in a circle=36. Some decided a circle should be divided into 360 different parts, and each part would be called a "degree."

I finally understand what you are trying to convey with your argument. Unfortunately it is incorrect. Since the first 15cm line is straight, we can say it is 180 degrees. The second line can't be attributed an angle because it is a curved line. Angles can only be measured between two straight lines connected at a vertex. A curved line has a different formula for determining its curve than a straight line. if we took both your 15cm lines and connected them at a vertex, we wouldn't be able attribute an angle in degrees to that angle, because both of the lines need to be straight. Likewise, the curved line can't be given a degree like you say, because for it be curved, means the level of degree wouldn't be constant like you claim. It was a good attempt at trying to think outside the box, but it defies the laws of math and isn't true.
Posted by mostlogical 3 years ago
You argue a circle should be accepted as having 360 degrees because someone decided, but if a long time ago someone decided an octagon should have 400 degrees rather than 1080 because it seemed special in some way, would that mean an octagon has 400 degrees? Or an anomaly?

If you imagine a straight 15cm line beside another line 15 cm long that's curved but which appears straight, and use your protractor you will find the second line has slightly less than 180 degrees. If that second line was extended to a metre so you can see it's curvature, the angle of that line has not changed, it has remained exactly the same. I've just calculated that angle and demonstrated how the angle can't become a whole number i.e. 180. When the ends of the line come close to meeting it still has slightly less than 180 degrees, and when they meet it will not change this fact.
Posted by BoggyB 3 years ago
In reality, a polygon with infinite sides might look like a circle with our eyes, but we aren't talking about a situation like that. We were debating a mathematical principle, which is a circle. I'm arithmetic, a circle has ONE, CURVED side. Notice "one," and "curved." A polygon, must have at least THREE sides that are all STRAIGHT. No matter how close to a circle a polygon might be, it isn't, because it is made up of multiple STRAGHT sides, while a circle is one CURVED side. There is nothing else to say. Your logic has been mixed up, and is leaning towards rejection and denial of mathematical facts, rather than intuitive thinking.
Posted by mostlogical 3 years ago
I have read your arguments, and I've explained that there is no difference between a circle and a polygon with infinite sides, so they can be treated in the same way. If they were different then the rationality and value of Pi would be unknown.
Posted by BoggyB 3 years ago
The reason your logic doesn't work is because a circle isn't a polygon. Did you even read my debate? I stated it numerous times throughout. Go back and see all the times I explained it and the sources which also show it is not a polygon. A circle isn't infinite sides it is one side, a curved line. A polygon has at least three sides (a circle has one) and all sides of a polygon are straight (a circle has one curved line). A circle is not a polygon, thus your method doesn't work.
Posted by mostlogical 3 years ago
My logic is based on a triangle having 180 degrees, this means one corner of a square will have 90 degrees i.e. twice as less. If you imagine the lines from a square extending to give you this shape # you can see a line has 180 degrees like a triangle because 90 + 90 = 180. Changing the number of degrees in a triangle does not change the fact a triangle has the same number of degrees as a line.

You can apply this logic to calculate the angles for any sided polygon (they can all be divided into triangles) including one with infinite sides i.e. a circle, and you will find a circle does not have the same number of degrees as a square.
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