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Module by: Lawrence Baggett. E-mail the author

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Name: Integration Over Smooth Curves in the Plane C=2π r
ID: m36224
Language: English (en)
Summary: A brief introduction of the upcoming chapter by Lawrence Baggett. In this chapter we will define what we mean by a smooth curve in the plane and what is meant by its arc length. These definitions are a good bit more tricky than one might imagine. Indeed, it is the subtlety of the definition of arc length that prevented us from defining the trigonometric functions in terms of wrapping the real line around the circle, a definition frequently used in high school trigonometry courses. Having made a proper definition of arc length, we will then be able to establish the formula C=2πrC=2πr for the circumference of a circle of radius r.r.
Subject: Mathematics and Statistics
Keywords: integral, introduction, smooth curves
License: Creative Commons Attribution License CC-BY 3.0

Authors: Lawrence Baggett (lawrence.baggett@colorado.edu)
Copyright Holders: Lawrence Baggett (lawrence.baggett@colorado.edu)
Maintainers: Lawrence Baggett (lawrence.baggett@colorado.edu), Daniel Williamson (dcwill@cnx.org), Jared Adler (jca2@rice.edu)

Latest version: 1.2 (history)
First publication date: Oct 5, 2010 2:39 pm +0000
Last revision to module: Dec 9, 2010 4:50 pm +0000

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Version History

Version: 1.2 Dec 9, 2010 4:50 pm +0000 by Jared Adler
Changes:
links, summary added

Version: 1.1 Nov 25, 2010 8:40 am +0000 by Jared Adler
Changes:
initial publish

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American Chemical Society (ACS) Style Guide:

Baggett, L. Integration Over Smooth Curves in the Plane C=2π r, OpenStax_CNX Web site. http://cnx.org/content/m36224/1.2/, Dec 9, 2010.

American Medical Assocation (AMA) Manual of Style:

Baggett L. Integration Over Smooth Curves in the Plane C=2π r [OpenStax_CNX Web site]. December 9, 2010. Available at: http://cnx.org/content/m36224/1.2/.

American Psychological Assocation (APA) Publication Manual:

Baggett, L. (2010, December 9). Integration Over Smooth Curves in the Plane C=2π r. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m36224/1.2/

Chicago Manual of Style (Bibliography):

Baggett, Lawrence. "Integration Over Smooth Curves in the Plane C=2π r." OpenStax_CNX. December 9, 2010. http://cnx.org/content/m36224/1.2/.

Chicago Manual of Style (Note):

Lawrence Baggett, "Integration Over Smooth Curves in the Plane C=2π r," OpenStax_CNX, December 9, 2010, http://cnx.org/content/m36224/1.2/.

Chicago Manual of Style (Reference, in Author-Date style):

Baggett, L. 2010. Integration Over Smooth Curves in the Plane C=2π r. OpenStax_CNX, December 9, 2010. http://cnx.org/content/m36224/1.2/.

Modern Languages Association (MLA) Style Manual:

Baggett, Lawrence. Integration Over Smooth Curves in the Plane C=2π r. OpenStax_CNX. 9 Dec. 2010 <http://cnx.org/content/m36224/1.2/>.