Re: Area of Sphere - History

In article <foc4av$41d$1@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Dave Seaman <dseaman@xxxxxxxxxxxx> wrote:
On Tue, 5 Feb 2008 21:16:41 -0800, Marty Luka wrote:

"Dave Seaman" <dseaman@xxxxxxxxxxxx> wrote in message
news:foajvs$81o$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Tue, 5 Feb 2008 12:57:21 -0800 (PST), mynameisrabbit@xxxxxxxxxxx wrote:
On 5 Feb., 20:46, "[Mr.] Lynn Kurtz" <ku...@xxxxxxxxxxxxxxx> wrote:

..................

Obviously, every perpendicular intersects the sphere's center.

It's perpendicular to the polar axis. The interesection
point is not at the center unless the starting point is on the equator.

The ratio of the projection on the cylinder to the ratio of the
area on the sphere can be made greater than any arbitrary
number by taking a point close enough to the sphere's
north pole.

The areas are equal. The proof is by integration.

This is possible, using calculus. As Archimedes did not
have calculus, he had to use the idea of limit, and it is
not difficult to show it that way.
--
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
.

Relevant Pages

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