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I would disagree with "steradian."  I think an earlier writer put it
well - for parts of a circle we distinguish between an arc (a portion of
a circle), the angle subtended by the arc, and the length of the arc
(angle times radius).   Steradian is the equivalent of the angle, not
the arc...

In fact, http://www.physlink.com/Education/AskExperts/ae174.cfm uses the
analogy directly:  "Steradians are a measure of the angular 'area'
subtended by a two dimensional surface about the origin in three
dimensional space, just as a radian is a measure of the angle subtended
by a one dimensional line about the origin in two dimensional (plane)
space. Steradians are equivalently referred to as 'square radians.'"

Earlier today Herbert Prinz pointed out that in German there's a
distinction between the solid angle and the section of the sphere
subtended by it; the latter is called a "Kugelkappe" which translates
literally as "sphere/ball cap"

Lu Abel

Robert Eno wrote:
> Thanks to all for a most informative discussion.
>
> Just to let you know, I contacted a mathematician at the University of
> Waterloo Department of Pure Mathematics to pose this question. He didn't
> even bat an eye at the idea of some crackpot from the netherworld asking
> for
> obscure information. Unfortunately, he did not have an answer but he
> promised to run it by his colleagues and get back to me. I in turn, will
> report back to the list if I get an answer other than the ones provided. He
> did, however, suggest that "steradian" may be an appropriate description.
>
> Robert
>
>
> ----- Original Message -----
> From: "Alexandre E Eremenko" 
> To: 
> Sent: Thursday, March 30, 2006 4:08 PM
> Subject: Re: Mathematics Question
>
>
>> Dear Robert,
>>
>> It is possible that I misunderstood your question.
>> It was not clear whether you asked about "arc" or
>> about "arc measure".
>>
>> For a mathematician, an arc is a geometric object, a set,
>> something you can see. "Arc measure" is just a number.
>>
>> It is like a difference between the lot of land on which your
>> house stands and the number which is how many acres are
>> in this lot of land. Or the difference between you, yourself,
>> and your height:-)
>>
>> The set itself (=the geometric object, the piece of the sphere)
>> in 3 dimensions is called variously a "cap" a "cup" or "sperical disc".
>> Its SIZE is measured in square radians and called the "solid angle"
>> as many list members pointed out.
>>
>> Thunk of the sentence "this cap has the solid ange of 0.0003 square
>> radians"
>> as an analog of the sentence "this lot has the area of 1.25 acres".
>>
>>
>> Alex.
>>
>>> On Wed, 29 Mar 2006, Robert Eno wrote:
>>>
>>> > A math question for list:
>>> >
>>> > Given that a segment of a circle
>>> > is called an "arc", can anyone
>>> > tell me what its two-dimensional
>>> > equivalent on a sphere is called?
>>> >
>>> > Robert
>>> >
>>>
>>>
>
>

   

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