Re: A tough question about elementary mathematics

In article <4gr3uuF1orr1aU1@xxxxxxxxxxxxxx>,
Robert J. Kolker <nowhere@xxxxxxxxxxx> wrote:
Gerry Myerson wrote:


Is it true that natural logs & radians predate calculus?

Napier re-invented logarithms in the 1500s..

If you take into account the fact that Archimedes invented integral
calculus in the 3rd century b.c.e. the answer to your question is no.

Did Archimedes invent integral calculus? I am inclined
to question this; the oldest use of integration (with
some measure) of which I am aware is about 5000 years
old, and the idea of integrating with respect to length
measure was present in 16th century Euclidean geometry.

Fermat integrated x^(p/q) without using any of the ideas
of differential calculus; the Greeks had the "definition"
of the Riemann integral, but could not put it into words.

Also, I do not know of logarithms before Napier. One can
show quite easily that the derivative of a^x with respect
to x is a^x * log_e(a), e something to be determined.
And if angles are measured in some units, the derivative
of sin(x) = Q*cos(x). This can be done using tri-operational
algebra, even without showing limits exist, and works if they
do exist.




--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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