How many degrees in a sphere?

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Balkash
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How many degrees in a sphere?

Postby Balkash » Sat May 31, 2008 9:06 pm UTC

I know there are 360 degrees in a circle. How many are in a sphere? And can you explain it please. Everyone I asked has said 360 degrees in a sphere, but it just doesn't make sense to me. A circle is 2D, a sphere is 3D. Adding that third dimension makes me think it would have more degrees because there is more to it. Help

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jmorgan3
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Re: How many degrees in a sphere?

Postby jmorgan3 » Sat May 31, 2008 9:11 pm UTC

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Balkash
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Re: How many degrees in a sphere?

Postby Balkash » Sat May 31, 2008 9:27 pm UTC

Assume the constant is 1. To obtain the solid angle in steradians, multiply the fractional area by 4*pi. If I want the whole sphere, the fractional area would be 1? So 4*pi = 12.56637 steradians. So there are 4*pi steradians in a sphere, like there are 360 degrees in a circle?

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Cosmologicon
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Re: How many degrees in a sphere?

Postby Cosmologicon » Sat May 31, 2008 9:31 pm UTC

Yep, 4pi steradians, and 129,600/pi = 41,252.961... square degrees.

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Re: How many degrees in a sphere?

Postby Balkash » Sat May 31, 2008 9:36 pm UTC

Thank you and thank math. Things make sense again.

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the tree
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Re: How many degrees in a sphere?

Postby the tree » Sun Jun 01, 2008 11:28 am UTC

Bear in mind that 360 degrees in a circle is a very arbitrary labelling. 2Pi radians in a circle is slightly less arbitrary and tends to get used more often as you continue learning maths.

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Cosmologicon
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Re: How many degrees in a sphere?

Postby Cosmologicon » Sun Jun 01, 2008 9:19 pm UTC

True, but I can tell you that square degrees get used a heck of a lot more than steradians in astronomy when referring to a field of view, although the latter do come up every now and again (eg. the Pan-STARRs 3pi steradian survey). I don't know who all uses solid angles very often, but I'm sure astronomers must account for a huge fraction thereof.

kevbrown
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Re: How many degrees in a sphere?

Postby kevbrown » Thu Jun 05, 2008 2:53 am UTC

I can't wait for CNN's Anderson Cooper AC41,252.961
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Fat Kat
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Re: How many degrees in a sphere?

Postby Fat Kat » Thu Jun 05, 2008 11:38 am UTC

Cosmologicon wrote:True, but I can tell you that square degrees get used a heck of a lot more than steradians in astronomy when referring to a field of view, although the latter do come up every now and again (eg. the Pan-STARRs 3pi steradian survey). I don't know who all uses solid angles very often, but I'm sure astronomers must account for a huge fraction thereof.


Lighting designers - the luminous intensity of a light source is measured in lumens (light output) per steradian.
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Re: How many degrees in a sphere?

Postby cheo » Sat Feb 17, 2018 2:44 pm UTC

360 degrees x 4 x 1/2 Radian = Surface Area of Sphere 41,252 degrees square

41,252 divided by 4 = Area of a Circle in degrees square 10,313.24031

41,252 multipied by 1/3 Radian = Volume of a Sphere in Cubic Degrees 787,873.524

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cyanyoshi
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Re: How many degrees in a sphere?

Postby cyanyoshi » Sat Feb 17, 2018 7:37 pm UTC

cheo wrote:360 degrees x 4 x 1/2 Radian = Surface Area of Sphere 41,252 degrees square

41,252 divided by 4 = Area of a Circle in degrees square 10,313.24031

41,252 multipied by 1/3 Radian = Volume of a Sphere in Cubic Degrees 787,873.524


Area typically has dimensions of length squared, and volume is length cubed. Since angles are effectively dimensionless, I'm confused what you are actually calculating here.

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Sizik
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Re: How many degrees in a sphere?

Postby Sizik » Sat Feb 17, 2018 11:12 pm UTC

cyanyoshi wrote:
cheo wrote:360 degrees x 4 x 1/2 Radian = Surface Area of Sphere 41,252 degrees square

41,252 divided by 4 = Area of a Circle in degrees square 10,313.24031

41,252 multipied by 1/3 Radian = Volume of a Sphere in Cubic Degrees 787,873.524


Area typically has dimensions of length squared, and volume is length cubed. Since angles are effectively dimensionless, I'm confused what you are actually calculating here.


A radian is 360/(2pi) = 57.3 degrees, so on a sphere who's radius is 57.3 units long (thus the circumference of a great circle is 360 units), the area of the sphere is 4*pi*r2 = 41,253 units2.
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Eebster the Great
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Re: How many degrees in a sphere?

Postby Eebster the Great » Mon Feb 19, 2018 12:27 am UTC

This is definitely the first time I've seen someone try to use degrees cubed. Is there a name for the natural unit of hypersolid angle, where there are like 4π2 of them in a 3-sphere or whatever?


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