Thank you mark. These few little problems have generated more discussion
than I expected, and it's most enlightening to read them. Of course, your
contributions are always right on the money, even when some people don't
seem to 'get it'.
I'm still waiting for a useful response on the "Isn't that the limit?"
thread. That spherical triangle *doesn't* approach a plane triangle in the
limit as it becomes infinitessimally skinny. For example, the width of it
at half-height (at latitude 45 degrees) is *not* half the length of the
base. It is 0.707 times the length of the base, and that fact is
independent of how large the base, and persistes even as we go to the
limit. So the area is greater than (1/2)(base)(height) for any base
length, even down to the limit. This defies naive common sense, and is
another example of the hazards of common sense when applied to math or
physics. (Dare we mention this to students, however?)
I checked a number of calculus textbooks, and found they were not helpful
to students on this matter.
-- Donald
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Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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