Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert Hill

Posts: 529
Registered: 12/8/04
Re: Is y = mx + b linear?
Posted: May 15, 2000 1:23 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



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"
comes from "stretched linen [thread]".)

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







Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.