Re: Does the Calculus rest on Euclid?

Lee Rudolph wrote:
"Nathan" <ntspam2@xxxxxxxxxxxx> writes:

Yes, the equation s = r * theta is nowadays used to define the
measure of an angle.

And as I said, that's deplorable (because it rests on--even if it
is not "derived from"--the notion of arc length, which is far subtler
than that of area, from which it could equally well be derived; note
that HvA himself seems to find arc length trickier than area, and
who can blame him?).

I don't get it. How is arc length "far subtler" than area?
It seems to me that they have very much the same sorts of
difficulties.

On a basic level, in terms of intuition and motivation, I find arc
length simpler. Everybody understands measuring how far you
walk along a certain path.

For beginning calculus students, area is obviously simpler,
since the integrals are easier :-)

If you actually try for rigorous definitions in terms of limits,
I think these two concepts are equally complex.

.

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