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| Robert Eno wrote:
|
| > Just to make sure I got this right, please have a look at the diagram
| > on the
| > following website:
| >
| > http://whatis.techtarget.com/definition/0,,sid9_gci528813,00.html
| >
| > Is the lens-shaped figure in red called a steradian or does this term
| > refer
| > only to the cone shaped figure in the centre of the sphere?  I am looking
| > for the name of the red lined shape.

and Herbert Prinz answered
 It appears that I misunderstood your question. You said "arc" and I
| thought "angle". What you really wanted was the name for the curved
| surface of a spherical cap (i.e. the surface without the flat bottom),
| right? I am not sure whether there is a name for that, at least I am not
| aware of  any.

============================

I think Herbert has just coined the appropriate term that refers to an area across the surface of a
sphere, equivalent to an arc along the periphery of a circle, when he called it a "spherical cap".
"Cap" is a word that describes precisely what Robert Eno requires; and indeed I have seen it so used
in technical articles (can't recall where). It should be adopted. It has a rather different meaning
to "solid angle", in that solid angle refers to what is subtended at the centre of the sphere by
such a cap at its surface. Just as with a circle, in which an arc, on the periphery, has a different
meaning to an angle subtended at the centre, though one refers to the other, and they are measured
in the same units.

Going back to solid angle, a physicist would normally measure it in "steradians". There are 4.pi
steradians in a sphere, just as there are 2.pi radians in a circle. So the whole sky occupies about
12.5 steradians to an observer floating in space, and about half that to someone at sea. Solid angle
can also be measured in square degrees; more properly degrees-squared, a patch in the sky that
subtends 1 degree by 1 degree, or a corresponding area if it doesn't have a square shape. The Sun,
and the Moon, each occupies about 0.2 degrees-squared.

There are other expressions for solid-angle in folk-speech. For describing the smallness of a solid
angle, recall the familiar cliche of an ominous cloud which starts off "no bigger than a man's
hand". That's quite a good unit of solid angle, in that it refers to an well-known area (that of the
human hand) at a defined distance (the length of the human arm).

Another expression, for expressing the largeness of a solid angle, often referring to a growing area
of blue sky, appears in the cliche "big enough to patch a Dutchman's trousers". Not quite such a
good unit, as it's unclear just how far away said Dutchman should be beheld from. Nevertheless, the
"Dutchman's trouser" might make a picturesque, and large, unit of solid angle. Apologies to all
Dutchmen, of course.

George.

==================

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

   

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