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Dan in Philly
science forum beginner

Joined: 14 Jun 2005
Posts: 5

Posted: Fri Jul 21, 2006 2:25 am    Post subject: Newton discoveing calculus

I've heard many times that Isaac Newton discovered the calculus (or Leibniz,
whomever). Does that mean nobody had done any sort of "let N go to infinity"
prior to him?

exercise: we took a circle, divided it into N slices, and calculated the
ares of the sum of the rectangles. Then we let N go to infinity, and
obtained pi R squared. Had nobody done that prior to Newton/Leibniz?

Dan in Philly
Gene Ward Smith
science forum Guru

Joined: 08 Jul 2005
Posts: 409

Posted: Fri Jul 21, 2006 2:32 am    Post subject: Re: Newton discoveing calculus

Dan in Philly wrote:
 Quote: I've heard many times that Isaac Newton discovered the calculus (or Leibniz, whomever). Does that mean nobody had done any sort of "let N go to infinity" prior to him?

No. Some features of calculus go back to Archimedes. Much of it was
first discovered in southern India during the Europeam middle ages. At
the same time that Newton and Leibniz, et al, were working, some
similar ideas were being worked on in China and Japan.

 Quote: I ask because, in advanced algebra in high school, our teacher had us do an exercise: we took a circle, divided it into N slices, and calculated the ares of the sum of the rectangles. Then we let N go to infinity, and obtained pi R squared. Had nobody done that prior to Newton/Leibniz?

Something like that is how Archimedes showed that the area of a
parabola is 2/3 the base times the height. Archimedes also proved pi is
between 3 10/71 and 3 1/7 by dividing a circle into slices.
fishfry
science forum Guru Wannabe

Joined: 29 Apr 2005
Posts: 299

Posted: Fri Jul 21, 2006 4:49 am    Post subject: Re: Newton discoveing calculus

"Dan in Philly" <djr8@aol.com> wrote:

 Quote: I've heard many times that Isaac Newton discovered the calculus (or Leibniz, whomever). Does that mean nobody had done any sort of "let N go to infinity" prior to him? I ask because, in advanced algebra in high school, our teacher had us do an exercise: we took a circle, divided it into N slices, and calculated the ares of the sum of the rectangles. Then we let N go to infinity, and obtained pi R squared. Had nobody done that prior to Newton/Leibniz?

Newton turned vague ideas of limits into a systematic method for solving
a wide class of problems. That's why he gets the credit.

In terms of history, the ancient Greek Eudoxus is credited with the
"method of exhaustion," which is the forerunner of integration.

And the first proof of what's now called the Fundamental Theorem of

But Barrow doesn't get the credit because he didn't follow through to
turn his insights into a systematic subject. Instead, Barrow gave his
Lucasian Chair over to Newton, and retired to the study of Divinity.

Such is history.
dmmcmah@gmail.com
science forum beginner

Joined: 10 Apr 2006
Posts: 7

Posted: Fri Jul 21, 2006 5:24 am    Post subject: Re: Newton discoveing calculus

fishfry wrote:

 Quote: But Barrow doesn't get the credit because he didn't follow through to turn his insights into a systematic subject. Instead, Barrow gave his Lucasian Chair over to Newton, and retired to the study of Divinity. Such is history.

According to the Wikipedia article on the Fundamental Theorem of
Calculus Barrow had the central idea that led to the fundamental
theorem of calculus but did not prove it. The Wikipedia article claims
a Scottish mathematician named James Gregory proved the fundamental
theorem of calculus.

http://en.wikipedia.org/wiki/James_Gregory_%28astronomer_and_mathematician%29

Barrow gave up his chair to Newton because he recognized Newton's
genius. Newton also applied calculus to solve physics problems, which
is why he invented calculus in the first place-to explain forces and
gravitation.

David McMahon
Author of Calculus In Focus
http://www.quantumphysicshelp.com/calculus.htm

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