Why 360?

[ChrisP]

Why are there 360 degrees in a circle, asked No2 child. Answered the question with the age old answer to questions to which you don't know the answer to ie send them to bed with no tea.
SWIMBO spotted the gap in the knowledge department and imediatly started the wifely duty of "taking the P**s". I know all the bits about the relationship between the minutes of arc and nauticle miles etc. but why 360 degrees?

Answers would be apreciated as No2 has been in her bedroom for 3 weeks now and is getting bored. It has however done wonders for her diet.

ChrisP;o)

 

[byron]

Jeeze! Chris! I thought that when they changed from 240 pennies to the £ to 100 they also changed from 360' in a circle to 100' If they haven't this explains a lot, no wonder I keep ending up in Bolougne when aiming for Calais ;-)

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[Guest]

Dont knock it!! Think yourself lucky you dont have to use the engineering units of "radians" - each radian is equivalent to 57.28 degrees!!!

360 is easy to divide up into bits.

PZ

 

[Guest]

It was an approximation to the number of days in a year. The position of the stars or some such moves by one degree per night, to the accuracy available at the time, or so I remember reading...

 

[KevB]

Who\'s been asking Jeeves? <NM>

*

 

[byron]

In everyone's experience it is usual to measure angles in degrees. We learn early in childhood that there are 360 degrees in a circle, that there are 90 degrees in a right angle, and that the angle of an equilateral triangle contains 60 degrees. On the other hand, to scientists, engineers, and mathematicians it is usual to measure angles in radians.
The size of a radian is determined by the requirement that there are 2 radians in a circle. Thus 2 radians equals 360 degrees. This means that 1 radian = 180/ degrees, and 1 degree = /180 radians.

The reason for this is that so many formulas become much easier to write and to understand when radians are used to measure angles. A very good example is provided by the formula for the length of a circular arc. If A and B are two points on a circle of radius R and center C, then the length of the arc of the circle connecting them is given by


d(A,B) = R a,
where R is the radius of the sphere, and a is the angle ACB measured in radians. If we measure the angle in degrees, then the formula is


d(A,B) = R a/180,
These formulas can be checked by noticing that the arc length is proportional to the angle, and then checking the formula for the full circle, i.e., when a = 2 radians (or 360 degrees).

I wrote all the above Yeh! Right! Well! I might under duress admit there's a possibility I copied and pasted it.


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[ParaHandy]

In the beginning..........

There were the ancient Babylonians who could only count in 6s eg there number base was 6 and 360 is a number easily divisible by 2, 3, 4, 5, 6 etc so it stuck.

Much later a load of greek bods were sitting in a circle and worked out that the circumference of a circle was a function of the radius. In fact there are 2pi radii and they said that the circumference subtended by one radius is a radian. Sadly, the world's flat as everybody knows so they got beheaded, raped and pillaged by the Romans.

 

[salamicollie]

Indeed why - orienteerers and the miliatry use Mils (6400 in a circle) which is ~10m at 1000m though orienteering compasses only marked for hundreds of mils

The logic in this is it easier to follow a 5 deg course (just like the typical small boat compass) and its a lot easier correct gunfire which is done in units of 50 or 100m add/drop and left/right if you can directly relate angle to distance without getting the trig tables out

 

[boatone]

Beheaded, raped and pillaged

One trusts not in that order................

TonyR
boatone@boatsontheweb.com
www.boatsonthethames.co.uk

 

[ChrisP]

Think I'll send myself to bed without any tea.

 

[adarcy]

Re: ? No Way Byron

Dear Byron

<<The size of a radian is determined by the requirement that there are 2 radians in a circle>>

Please do tell where you copied and pasted your info from, so I can put it in my blacklist.
I am afraid that is duff info. A radian is not 180 degrees, ParaHandy is correct, it is the angle subtended on the arc of a circle by the length of the radius. According to the person who wrote the "your" stuff, the circumference of a circle equals twice the radius - err what happened to a diameter and pi ?

Sorry for the nitpick

Anthony

 

[Robin2]

Re: ? No Way Byron

Here Here (or is it Hear Hear???)

There are PI radians in 180 degrees - I was obviously dozing when I read Byron's contribution yesterday.

Whatever that big white dog is up to must have confused him!

 

[byron]

Re: ? No Way Byron

Hey! what do I know anyway, I can't even spell the word maffematicks. I copied it in good faith from where I do not know now.

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