Why 360-degrees?

[Qfwfq]

Why not, say, 400-degrees to describe circumference of the circle?

As you please.

 

I know the military often divide the circumference into 4000 parts, for reckoning bearings on topographic maps.

[Damo2600]

I wasn't disagreeing with you Robust.

 

If you read my post again you will see. If a circle were 400 degrees then:

 

radius/radian would not give a 1 degree arc of a circle would it.

 

It would still give a degree based on a 360 degree circle.

 

Sorry if I didn't make that clear enough.

Damien

[Damo2600]

Qfwfq,

 

The question is why do they value the degrees of a circle to be 360. That's a valid point. The military may not but why do mathematicians usually use 360 degrees?

You didn't address the question.

 

Damien

[wrong]

Qfwfq,

 

The question is why do they value the degrees of a circle to be 360. That's a valid point. The military may not but why do mathematicians usually use 360 degrees?

You didn't address the question.

 

Damien

 

 

I was under the impression that it was really convenience,yes a loose association with a year but also 360 is divisible by 1,2,3,4,6,8,9,10 12,15,18 & 20

[C1ay]

Qfwfq,

 

The question is why do they value the degrees of a circle to be 360. That's a valid point. The military may not but why do mathematicians usually use 360 degrees?

You didn't address the question.

 

Damien

Robust did when he posted that it dated back to the Babylonians. You have to remember, it was an era that used sundials for timekeeping.

[Qfwfq]

You didn't address the question.

I did!!! Indeed I did!

 

First thing I said was: "As you please" :Alien:

[Qfwfq]

You have to remember, it was an era that used sundials for timekeeping.

What's that got to do with Australian igloos?

 

Unless you meant that 360 is a very practical number. I agree, it sure is! It's almost as practical as a sundial. Not a bad invention that, takes quite a bit of craftsmanship too. Tradition has it they usually have some motto on them, as well as a lot of artwork mixed in with the graphics for reading the time. One fine example, not far from the town I live in, has the motto: sine sole sileo

[C1ay]

What's that got to do with Australian igloos?

 

Unless you meant that 360 is a very practical number. I agree, it sure is!

 

I did. For the era the circle was easy to divide into 360 parts, the same with the year. I seem to recall that the Babylonians used base 60 for their math as well. I suspect this had a lot to do with them using 360 divisions instead of 400. What do you think?

[wrong]

I did. For the era the circle was easy to divide into 360 parts, the same with the year. I seem to recall that the Babylonians used base 60 for their math as well. I suspect this had a lot to do with them using 360 divisions instead of 400. What do you think?

 

 

Your correct C1ay the Babylonians and Mesopotamians both used base 60 they also ascribed a mystical relevance of the fact that a the sides of a hexagon are equal to the radius of the circumscribed circle. In base 60 , 60x6 makes sense.

As a side issue I'm only a newbie at this forum but I'm enjoying the reading

[Qfwfq]

I suspect this had a lot to do with them using 360 divisions instead of 400. What do you think?

Obviously. They were well aware of the virtues of 60, plenty more factors than 10 = 2 * 5.

 

They must have religiously thought the real year had exactly 360 days, with those extra 5 & 1/4 days being some satanic influence or something.

[Damo2600]

Hi Qwfwq,

 

You are excused then. LOL.

 

Damien

[Turtle]

___It is not clear to me that Babylonians used a base 60 system; isn't it just a system based on 60? The difference being that for Base 60 you need 59 different characters & a zero, & a columnar arrangement based on powers of 60 & I don't recall ever seeing such notation in math history.

[C1ay]

___It is not clear to me that Babylonians used a base 60 system; isn't it just a system based on 60? The difference being that for Base 60 you need 59 different characters & a zero, & a columnar arrangement based on powers of 60 & I don't recall ever seeing such notation in math history.

Look here - http://www.google.com/search?q=sexagesimal

[Turtle]

___In reading some of those references, I offer this one in support of my statement it is not Base sixty but a system based on 60:

http://it.stlawu.edu/%7Edmelvill/mesomath/sumerian.html

 

From this article: The sexagesimal place-value system greatly facilitated calculations, but, of course, at the end of the day, the final answer had to be translated back into the underlying metrological system of units. So a problem would be stated in proper units and the solution would be given in proper units, but the intermediate calculations were carried out in the new sexagesimal place value system.

:Alien:

[C1ay]

___In reading some of those references, I offer this one in support of my statement it is not Base sixty but a system based on 60:

http://it.stlawu.edu/%7Edmelvill/mesomath/sumerian.html

 

From this article: The sexagesimal place-value system greatly facilitated calculations, but, of course, at the end of the day, the final answer had to be translated back into the underlying metrological system of units. So a problem would be stated in proper units and the solution would be given in proper units, but the intermediate calculations were carried out in the new sexagesimal place value system.

:Alien:

I didn't mean that they used base 60 exclusively, just that it was one of the systems they used.

[Turtle]

___Acknowledged C1ay. I still have a nit pick with what they used being called Base 60. One of the articles from your link made the point that the Babylonian system needed a context to begin, that is if there was no value for a 'place' in a number the 'place' was left out. That is equivalent to us just writing a 1 for 100 & expecting you to know what is meant.

___It is a matter of semantics I admit, but I still contend theirs was a system based on 60, not a base 60 system.

[C1ay]

___Acknowledged C1ay. I still have a nit pick with what they used being called Base 60. One of the articles from your link made the point that the Babylonian system needed a context to begin, that is if there was no value for a 'place' in a number the 'place' was left out. That is equivalent to us just writing a 1 for 100 & expecting you to know what is meant.

___It is a matter of semantics I admit, but I still contend theirs was a system based on 60, not a base 60 system.

That's really a different issue. Nobody had a zero in their number system until

around 2000 - 1800 BCE. The Babylonians didn't have a symbol for zero until somewhere around 300 - 200 BCE. They are credited by the math community as having developed the base 60 numbering system though..

 

On the subject of zero, there is a good book out there entitled "Zero: The Biography of a Dangerous Idea" that's got about 250 pages on the history of zero. I found it quite interesting.