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Re: Straight Line





On Sat, 20 Sep 1997 PPARKER@TWSUVM.UC.TWSU.EDU wrote:

Date: Thu, 18 Sep 1997 22:36:22 -0600
From: Jim Green <JMGreen@sisna.com>


If a line is a curve, what is the difference between a non-straight line and
a curvy curve?

None; it's a historical usage now mostly seen in "line integral" or "line of
force" or "field line" to let "line" mean the same as "curve" or "path" or
"arc". Mathematicians generally treat "line" and "straight line" as
synonyms, making an exception for these historic remnants (which occur
mostly in applied areas).


Phil is correct. I'm surprised no one has cited a standard math dictionary
on this matter. I pulled Millington and Millington from my shelf, where I
find:

Line. Synonym of *straight line* in contrast to *curve*.

Curve. A one-dimensional configuration obeying some law. If the law is
expressed geometrically, it is a *locus*, or a set of points; if
algebraically, the *graph* of a function....

Straight line. The line, in *Euclidean geometry*, which passes through two
points in such a way that the length of the segment between the points is
a minimum.... In general the term *line* is synonymous with *straight
line*.

To get a second opinion, I looked at Douglas Downing's Dictionary of
Mathematics Terms:

Line. A line is a straight set of points that extends off to infinity in
two directions. The term "line" is one of the basic undefined terms in
Euclidean geometry, so it is not possible to give a rigorous definition of
line. You will have to use your intuition as to what it means for a line
to be straight. According to a postulate, any two distinct points
determine one and only one line. A line has infinite length, but zero
width and zero thicknes.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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