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You are not logged in. #1 20051026 02:37:28
SteradianWhat is the angle in the center of a sphere making 1.000 steradians? igloo myrtilles fourmis #2 20051026 03:27:05
Re: SteradianWow. Tough question. I can't think of how to go about solving that, but if anyone else wants to have a go, I've got a nugget of knowledge that might help. Why did the vector cross the road? It wanted to be normal. #3 20051026 07:21:07
Re: SteradianWould the cone angle be 1 radian (180/pi degrees) ? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #4 20051028 04:39:57
Re: SteradianI'm working on an approach to this problem by first working out the area of a sphere by using slices of cones. If I get that to work out to 4 pi r² for the surface area of a sphere, then I'll use the same procedure to go just part of the way forming the steradian. Wish me luck. I'll let you know how it goes. So far, I intend on doing a computer approximation since I am not good at Calculus, and would need help even getting the calculus equation. igloo myrtilles fourmis #5 20051028 13:54:04
Re: SteradianA unit of measure equal to the solid angle subtended at the center of a sphere by an area on the surface of the sphere that is equal to the radius squared: The total solid angle of a sphere is 4π (4 pi)steradians. Character is who you are when no one is looking. #6 20051210 07:33:24
Re: SteradianIrspow, could I learn your surface of rotation stuff for this steradian calculation?? igloo myrtilles fourmis #7 20051210 09:26:39
Re: SteradianI don't know if a surface of revolution will help in this problem as it calculates a volume. Anyway it works like this. Last edited by irspow (20051210 09:33:26) #8 20051210 11:01:29
Re: SteradianNow I have never heard of these steradians before, but after a little research it appears that: #9 20051210 15:12:20
Re: Steradian(Put a ":" in front of "pi" and you get π, see http://www.mathsisfun.com/forum/viewtop … 623#p17623) "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #11 20051211 12:19:00
Re: SteradianJohn, I was trying to verify my suggestion that the interior angle was indeed correct at 90/π²°. This was because if you multiply this by 360° you will get the amount of square degrees in a steradian. #12 20051212 10:19:08
Re: Steradian
Tell me if this is the same thing? This is way over my head unless I learn a lot. which by the way was created with [ m a t h ] \int 2\pi f(y) \sqrt{1 + (dx/dy)^2} dy [/ m a t h ]
I finally figured out that you are making a series of hollow pipes that get Last edited by John E. Franklin (20051212 11:07:42) igloo myrtilles fourmis #13 20051212 11:24:42
Re: SteradianYes John, that is precisely what I was trying to write. As far as my efforts to figure this thing out this is what I have come up with. Last edited by irspow (20051212 11:25:29) #14 20051212 14:39:38
Re: SteradianI can't believe the progress you made!!!!!! Note that I am missing the 2 for 2. This is because I used the formula for the surface area of a cone and you divide by two. Cone Area Piece=dSlant 1/2 2 π y (I'm rotating around the xaxis, so y is R base of cone) y' is y prime or derivative in above; I'm very sloppy still; I need reform. Where and , which I got from a table, and then I gave up and read your post. I must have made a mistake on the 2, but I thought I'd let you know just in case. I tried figuring out the rotation myself and must have failed by a factor of two somehow. ... I just examined what I did, and it turns out I was lucky to get as close as I did because I should have used slices of cones, not the whole cone. And slices of the cones would involve something I can't figure out yet. It would be a slice of a cone at the base, incrementally thin. Somehow the 1/2 goes away, don't ask me how. But the surface area of a cone can be shown "unfolded" as a bunch of triangles, and the area of a triangle has the 1/2 in it, that's a simple explanation I saw a few weeks ago. ... But you are way ahead of me. How come your formula didn't get really messy with the derivative of the circle?? Your substition? I'll have to try to learn all this when I can. Bye. Last edited by John E. Franklin (20051212 14:59:21) igloo myrtilles fourmis #15 20051212 15:18:30
Re: SteradianI saw that you posted in another thread about the arc length integral, very good. (useful too) Try to remember that one it comes in handy ofter. I actually solved the integral that I was having so much trouble with. Last edited by irspow (20051212 15:21:05) 