Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

12
Geometric Curve-Drawing Devices as an Alternative Approach to Analytic Geometry: An Analysis of the Methods, Voice, and Epistemology of a High-School Senior

David Dennis

University of Texas-El Paso

Jere Confrey

Cornell University

When the concept of analytic geometry evolved in the mathematics of 17th-century Europe, the meaning of the term was quite different from our modern notion. The main conceptual difference was that curves were thought of as having a primary existence apart from any analysis of their numeric or algebraic properties. Equations did not create curves; curves gave rise to equations. When Descartes published his Geometry in 1638 (trans. 1952), he derived for the first time the algebraic equations of many curves, but never once did he create a curve by plotting points from an equation. Geometrical methods for drawing each curve were always given first, and then, by analyzing the geometrical actions involved in a physical curve-drawing apparatus, he would arrive at an equation that related pairs of coordinates ( Dennis, 1995; Dennis & Confrey, 1995). Descartes used equations to create a taxonomy of curves ( Lenoir, 1979). This tradition of seeing curves as the result of geometrical actions continued in the work of Roberval, Pascal, Newton, and Leibniz. As analytic geometry evolved toward calculus, a mathematics developed that involved going back and forth between curves and equations. Operating

-297-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited page

Bookmark this page
Designing Learning Environments for Developing Understanding of Geometry and Space
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen
/ 506

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.