Re: Numbers

["Daryl L. Taylor" <Daryl@DARYLSCIENCE.COM>]

Ah, but as his own writings show, he did, indeed, use the method of
exhaustion to calculate the area of a circle. He stopped his calculations of
a 'unit' circle, d=1, with a 96-sided polygon both inscribed (lower limit)
and circumscribed (upper limit). He was actually calculating the area of
that circle. It just happens to be PI. If this isn't the method of
exhaustion, I don't know what is. (Unless it's teaching my 9th period
class...)

He then used the same methods for volumes. I just can't see this as saying
it's calculus. It's one of the foundations of it, but...

Daryl L. Taylor, Fizzix Guy
PAEMST '96
Internet Educator of the Year '03
Williamstown HS & Engineering Academy, Rowan University NJ
www.DarylScience.com <http://www.DarylScience.com>
609.330.9571

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-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@lists.nau.edu]On Behalf
Of John Cockman
Sent: Tuesday, November 04, 2003 11:49 AM
To: PHYS-L@lists.nau.edu
Subject: Re: Numbers


By calculus, I mean his method of using the sum of an infinite number of
objects to calculate a volume, not the method of exhaustion used to
calculate pi.

John

----- Original Message -----
From: "Daryl L. Taylor" <Daryl@DARYLSCIENCE.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, November 04, 2003 10:51 AM
Subject: Re: Numbers


> I have to argue a little with John's statement below... Archimedes didn't
> use Calculus. With all due respect to John and PBS... He used a
calculation
> method called "Method of Exhaustion" common to the 'ancient' Greeks. I
point
> you to a simple explanation at
> http://www.ima.umn.edu/~arnold/graphics.html.
> Even Reviel Netz's Nov 01 2002 Science mag article does not imply that
> Archimedes 'used' calculus. The truly astonishing thing is that Archimedes
> knew of and attempted to use the concept of infinity. Conventional wisdom
> states the Greeks shunned infinity and never dealt with it. Apparently
> Eureka-Man did.
>
> However, to take the leap to the statement that "Archimedes used Calculus"
> is akin to saying that Newton used Quantum Mechanics. Each, Archimedes and
> Newton, used methods, created conclusions, and laid important foundations
> that were needed for future developments, yes. However, as Newton was fond
> of saying, "...it is because I have stood on the shoulders of giants." (Or
> was that David?...)
>
> Daryl L. Taylor, Fizzix Guy
> PAEMST '96
> Internet Educator of the Year '03
> Williamstown HS & Engineering Academy, Rowan University NJ
> www.DarylScience.com <http://www.DarylScience.com>
> 609.330.9571
>
> This email prepared and transmitted using 100% recycled electrons!