Math Forum Discussions

Robert Hill

Posts: 529
Registered: 12/8/04

Re: Is y = mx + b linear?
Posted: May 15, 2000 1:23 PM

Plain Text

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