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Topic: "dilation" misused in geometry texts?
Replies: 2   Last Post: Jan 19, 2007 7:18 PM

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 Annie Fetter Posts: 2,090 Registered: 12/3/04
"dilation" misused in geometry texts?
Posted: Jan 19, 2007 4:26 PM

I received the following email from a former colleague, Judy Brown. I sent her an answer, but mentioned that it would be interesting to ask y'all what your opinion is. She said, "Post away, and let me know what happens." So here 'tis:

Hi Annie

I have a geometry question for you concerning the term Dilation. I know that you can always believe everything you read on the web but the following definition is on the mathwords website [http://www.mathwords.com/d/dilation.htm ]. All the other sources I've checked are either very vague or explicitly state that a dilation can expand or shrink. This definition actually indicates that most textbooks are incorrect. I'd appreciate your opinion.

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Dilation
A <http://www.mathwords.com/t/transformations.htm>transformation in which a <http://www.mathwords.com/g/geometric_figure.htm> figure grows larger. Dilations may be with respect to a point
(<http://www.mathwords.com/d/dilation_geometric_figure.htm>dilation
of a geometric figure) or with respect to the
<http://www.mathwords.com/a/axes.htm> axis of a
<http://www.mathwords.com/g/graph_of_an_equation_or_inequality.htm>graph
(<http://www.mathwords.com/d/dilation_graph.htm> dilation of a graph).

Note: Some high school textbooks erroneously use the word dilation to refer to all transformations in which the figure changes size, whether the figure becomes larger or smaller. Unfortunately the English language has no word that refers collectively to both stretching and shrinking.
Pronunciation: Dilation (die-LAY-shun) has only three syllables, not four.

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Thanks
Judy

Date Subject Author
1/19/07 Annie Fetter
1/19/07 Walter Whiteley
1/19/07 talmanl@mscd.edu