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Topic: Is y = mx + b linear?
Replies: 9   Last Post: May 15, 2000 10:42 PM

 Messages: [ Previous | Next ]
 Robert Hill Posts: 529 Registered: 12/8/04
Re: Is y = mx + b linear?
Posted: May 15, 2000 1:23 PM

In article <8fo83o\$mfm@mcmail.cis.McMaster.CA>,
kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) writes:

> [...]

> :>> Is y(x) = mx + b a linear function?
>
> [...]
>
> Habits are hard to break: some people are so much in a hurry (or so they
> think) that they tend to abbreviate, often to the detriment of clarity.
>
> The function that transforms x into m*x+b is called a "linear polynomial
> function", to place it in the sequence "constant, linear, quadratic,
> cubic, ...". It is a burden of tradition we have to live with, even if it
> clashes with more recent conventions. Now some drop the word "polynomial"
> and the corresponding context, and a misunderstanding arises.

The earliest usages of "linear" were surely geometrical:
linear measure, etc. (W.W. Sawyer says that "straight line"

The earliest usage of "linear" in algebra was presumably in the phrase
"linear equation". And this got its name because (if it's in two
variables) its graph is a straight line - whether through the origin or not.

So whilst, if one takes the current usage as given, the older
usage is a "burden", one could take a more etymological point
of view and blame the "burden" on those who changed the word's meaning.

From this point of view, the people who were in too much of a hurry,
and who introduced the potential for confusion, were those who first
abbreviated "homogeneous linear transformation" by omitting "homogeneous".

--
Robert Hill

Date Subject Author
5/14/00 John Prussing
5/14/00 Pertti Lounesto
5/15/00 The Kellys
5/14/00 Virgil Hancher
5/15/00 William L. Bahn
5/15/00 Zdislav V. Kovarik
5/15/00 Pertti Lounesto
5/15/00 John Prussing
5/15/00 G. A. Edgar
5/15/00 Robert Hill