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Q: Sum of the angles of a tetrahedron in steradians - for pafalafa ( No Answer,   10 Comments )
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 Subject: Sum of the angles of a tetrahedron in steradians - for pafalafa Category: Science > Math Asked by: jeffsmith-ga List Price: \$10.00 Posted: 12 Aug 2005 07:14 PDT Expires: 16 Aug 2005 08:40 PDT Question ID: 554911
 ```What is the value, in steradians, of the sum of the solid internal angles of a random tetrahedron (as an analodue to the sum of the internal angles of a random triangle being 2*pi radians)? Or is that sum not constant? I'm pricing this at just 10 dollars but I will give a handsome tip if you provide quite a good reply. Maybe you might be interested in the question yourself. js``` Clarification of Question by jeffsmith-ga on 12 Aug 2005 07:18 PDT `Sorry, the sum of angles of a triangle is pi radians (180 degrees). Oops!` Request for Question Clarification by pafalafa-ga on 12 Aug 2005 16:34 PDT ```Whew, Jeff. It's been quite a number of years since my last attempt at any solid geometry. And I've never been all that handy with steradians! That said, it seems to me a tetrahedron is simply four triangles, so that the sum of their angles would 4 times the sum of a single triangle, or 4*pi radians. That should hold for all tetrahedrons, regular or not. Am I missing something? Mathtalk-ga, where are you? Any comments would be appreciated. pafalafa-ga``` Request for Question Clarification by pafalafa-ga on 12 Aug 2005 17:16 PDT ```Ooops, just noticed the comments below, which apparently reflect quite a bit more sophisitcated understanding of things than my own. Hope you have all the information you need at this point. Cheers, paf``` Clarification of Question by jeffsmith-ga on 12 Aug 2005 17:55 PDT ```Never mind, pafalafa. You showed your ability by providing this incredible answer to my previous question. And I suppose I owe you 10 extra dollars for that, too, as pinkfreud had the kindness to answer what seemed to be an offhand question about Hans Eysenck and received the gratuity of 50 dollars for both his replies. This might have been unfair to you, given the different qualities of your respective replies to the wildcard characters question. js```
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 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: racecar-ga on 12 Aug 2005 13:18 PDT
 ```http://answers.google.com/answers/threadview?id=160247 12*arccos(1/3)```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: racecar-ga on 12 Aug 2005 13:23 PDT
 ```That is for a regular tetrahedron. The sum is different for different tetrahedrons. You can see this by taking the limit of a very flat tetrahedron. One vertex approaches a solid angle of 2pi, the other 3 approach zero, so the sum of the solid angles tends toward 2pi, which is different from the value for a regular tetrahedron.```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: jeffsmith-ga on 12 Aug 2005 14:39 PDT
 ```Thank you for answering. This pretty much covers it. I guess it is worth something, too, so expect a 2 dollar question from me. js```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: pinkfreud-ga on 12 Aug 2005 14:44 PDT
 ```Jeff, Racecar isn't a Google Answers Researcher, so his assistance isn't compensable. Looks as if you've gotten a nice freebie from one of the site's most helpful users! ~Pink```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: jeffsmith-ga on 12 Aug 2005 16:32 PDT
 ```Sorry about racecar. Having trouble with my eyesight lately. And I thought I would age gracefully!```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: racecar-ga on 15 Aug 2005 00:23 PDT
 ```Hi jeffsmith-ga, Glad my comment was helpful. As you can see, I was interested in the same question a while back.```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: jeffsmith-ga on 15 Aug 2005 08:12 PDT
 ```Hi racecar. I take this question, when posed, to be one of the true marks of an inquiring mind (especially if the questioner has not studied Mathematics). Sorry again for mixing you up with a Google researcher. js (Dimitri B.)```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: jeffsmith-ga on 16 Aug 2005 07:01 PDT
 ```Since pafalafa has apparently disdained to give just any sort of answer to this question and collect 10 dollars, I will presently cancel this question. js (Dimitri B.)```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: pafalafa-ga on 16 Aug 2005 07:09 PDT
 ```Hi Jeff (or is it Dimitri?). First off, I never properly thanked you for steering this question to my attention. So....Thanks! I hope you don't feel I'm ignoring you. But I certainly don't feel I can post an answer to a question that...well...I haven't answered (and don't really feel competent to answer). So, I've just left the question here, content that you seem to have gotten the answer you need from the comments section. Hope to see you again one of these days. paf```
 Subject: Re: Sum of the angles of a tetrahedron in steradians - for pafalafa From: jeffsmith-ga on 16 Aug 2005 08:40 PDT
 ```Ok, paf, I suppose that's clear enough. Thank YOU for taking the time to post yet another comment. I will now retire the question. D.B.```