## Monday, February 2, 2009

### Let's Get Started!

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (the course outline is below the slides); for parents to find out "How Was School Today;" to share your knowledge with other students. Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, contribute to the conversation and lets get down to some serious blogging!

Here are the slides from today (your homework is on slide 31 & 32). Answer your Riddle Me This? question right here in the comments to this post:

1. Hey It's Dion,
So for the riddle me this, I did some research and here is what I found. From what I can understand, it was derived from the Babylonians. For counting they used a base of 60 rather than 10. They had a ratio of a regular hexagon to a circumscribed circle. I believe this means a circle that is drawn inside of the hexagon? Anyways, the Babylonians knew that the perimeter of the hexagon to be exactly 6 times the radius of the circle. How they did I do not know. So they were able to divide said circle into 360 parts and were also able to create the value of Pi! Wow, thats amazing! I never knew that!!! Have fun everyone!!!! -Dion

2. There are 360 degrees in a circle because degrees are a simple and general unit used for measuring angles constituting a circle. In this case, a circle was divided into 360 equal angles forming 360 of the same units. Consequently, these units were named degrees by someone or some group of people. Ergo, one can infer that there are 360 degrees in a circle. Now of course, as Dion said, the ancient Babylonians based their number system on 60. 360 is a product of 60 and is considered to be a good number since it is divisible by a multitude of numbers. One can see that 360 is a lovely number, so that is one anecdote. Nevertheless, I can divide a circle into 444 equal angles and call the base unit trifours. However, who would want to work with that unit? It’s a hideous one and very offensive to the mind and eyes. All in all, there exists 360 degrees in a circle because history suggests it and circles can be divided into 360 equal angles.

3. It's as Dion and Sheldon Cooper said: the Babylonians loved the number 60 and they concluded that the circle has 360 degrees because of the hexagon and because of how easy it is to divide blah blah blah...

...but my question is WHY 60?

Me and my friend google decided to go find the answer xD

Apparently, a long time ago, the farmers of the world decided to count the days of the year so they can grow their crops at the right time so they could have a harvest. They counted 365 and since 360 is close to that number, it was most likely used to calculate things; like time, days, crop formations, and the like. So I guess these Babylonians were fascinated by this number and decided to use it in THEIR calculations. Or maybe they were the farmers? Who knows?

4. I believe that the babylonians decided that a circle would have 360 degrees. I found out that old astronomers who studied the stars noticed that they move 1 degree each day. So they decided to use 360 because it was close to the number of days in a year. It is also divisible by all the numbers from 1-10 except for 7.

5. Yeah, just like how everyone else stated that the idea of a 360 degree circle came from the Babylonians, who used a base of 60 instead of 10. They did not have decimal fractions and therefore found it difficult to deal with remainders when doing division. They agreed to divide the corner of an equilateral triangle into 60 degrees, because 60 could be divided by various numbers without remainder. If the angles at the corners of 6 equilateral triangles are placed together they form the angle formed by a complete circle. This is why there are 6 times 60 degrees of arc in a circle.

6. I looked up and found that "the Babylonians said that the perimeter of a hexagon is
exactly equal to six times the radius of the circumscribed circle,that was evidently the reason why they chose to divide the circle into 360 degrees."

7. So yea everyone has basically said this already. The reason that there are 360 degrees in a circle is because the Babylonians used a base 60 system instead of a base 10 system like we do today. They also associated the movement of the Earth with a circle. Since the calendars back then had only 360 days, they say that the stars moved 1 degree each night equalling 360 degrees. This is apparently also the reason that minutes have 60 seconds, hours have 60 minutes and hours and months get labelled from 1 to 12(according to David Mahoney). Another reason, which Laika has already stated, is that 60 and 360 are much more easily dividable than 10 and 100.

Sources:
http://www.smh.com.au/news/Big-Questions/Who-decided-that-a-circle-should-have-360-degrees-Why-not-400-or-320/2005/04/08/1112815713827.html

http://en.wikipedia.org/wiki/Degree_(angle)

8. i thought i would be the first one here, but i guess i was wrong...and everyone found the same answer as me already, so that's no fun...but yah, its just like they say: the Babylonians used 60 as a base number instead of 10 and something about a hexagon perimeter being 6 times the radius of the circumscribed cirle...that is the main reason why there are 360 degrees in a circle, 60 seconds in a minute, 60 minutes in an hour, etc.

9. As others have stated it was because of Babylonians. Babylonians used sexagesimal system, used base 60 instead of base 10. Babylonians knew that the perimeter of circle within a hexagon touching most points possible is six times the radius. An equilateral triangle, each angle is 60 degrees. Then six equilateral triangles (hexagon) is 360 dreggres?

10. This is Pacifico III by the way. I could safely assume that everybody has the answer to the question: "Why is a circle 360°?" And probably the first and second pages of Google.com is filled with these answers — but I guess I have to take a stab at the question either way. It's something about Babylonians using the number 60 as a base number, and the ratio of the perimeter of a hexagon and the circumference of the circle inside(circumscribed) said hexagon. And something about the perimeter of a regular hexagon is equals the radius of the circumscribed circle multiplied by six. And we get π out of those variables somehow. I'm making an assumption here that the six from what I said earlier and the number 60, makes 360. I'll stop there.

Sources: The first link that came up when I searched "circle, 360" in Google.com.

11. Oh darn, I should have done this earlier, I'm just going to sound redundant now! XD Oh well, here I go:
Well, just as everyone had already mentioned, according to scientific fact, "360 degrees" originated from the Babylonians whom used a sexagesimal system (where their base was 60, rather than 10, as aforementioned).
However figuring all of this out really depends on what kind of unit of measurement was used. The Babylonians pretty much invented a unit: the degrees. They inferred that in one degree there are 60 minutes and in 60 minutes there are 60 seconds (we now begin to see how magical the number 60 is)!
No one really knew exactly why this number seemed to be so appealing to them, but it is evident that it is an excellent factor for 360 and that 360 itself has many other factors that makes it easy to divide a circle into equal parts.
The British military on the other hand concluded that there are 400 gradients in a circle. Now, a gradient is smaller than a degree.
Mathematicians discovered the "radian" by taking a piece of string and wrapping it around a circle of about 1cm radius. They made marks 1cm apart on the string as it is wrapped around the circle and discovered that there were approximately 6 1cm markings!
All in all the units 360 degrees, 400 gradients, and 6 radians are all related, it just depends on the units of measurement used.
But I think it's safe to say that the reason why is that we all just like to work with easy numbers lol.

12. Haha uhmmm nothing new to add here... same general thing about Babylonians/Ancient Sumerians blah blah sexigesimal number system aka base 60 and the circumscribed circle in a hexagon (reminds me of cyclohexene or w.e that was in organic chem back in the day). Alternatively, we could choose the lazy way out and say "well thats just the way it is". But no...

Anyways to add a bit more degrees are only one way of measuring a circle, as are deegs (i think) which there are 100 of in a circle (base 10 for the win? O.o) and gradients as proposed by the British (of which i believe i read there were 400 of?) Anyways yeah thats my input for the day... Later! XD

13. oh yeah.. 6 radians too... k bye now

14. Everyone's pretty much giving the same answers, cause I guess they all did the same thing as me and googled it? Well, the answer I got was that the Babylonians used the Sexagesimal system, which means instead of counting by 10's, they counted by 60's.. It just made it easier for them . yeah, I guess all the information I have are repetition of what everyone else had said already. So that's all.

15. I think the circle has 360 degrees because the Babylonians said there were 12 months and 30 days in a month. It takes the sun about 360 days to complete a circuit(go around the world), thus they used 360 degrees to track the sun's movement.

16. From what I gather, the "the ancient Babylonians (not the Greeks), decided that a circle should contain 360 degrees". The reason they picked 360 is because they based their number system on 60. The reason they used 60 as their number base is because 60 and 360 have a lot of different factors. This makes it easy to divide the circles into different parts. So, the reason a circle has 360 degrees is because the ancient Babylonians used it as the unit of measurement and we kept it because it's easier and more convenient then using multiples of 10 in the case. (Information/quote found at/quoted from: http://mathforum.org/library/drmath/view/58395.html)