[Maths-Education] Re: References about the history of the symbol m for gradient of line

[maths-education@nottingham.ac.uk]

This is an esxtract of a posting by Julio Gonzalez Cabillon, the 
moderator of the History of math list.
This question appears frequently in the list, and this is one of the 
best answers I've gotten so far. The bottom line is that "m" is NOT a 
math symbol as we thought of other symbols, (e.g., "="); or at least 
that "it" does not have the same "status" if that is possible to say,

Enjoy,

Vilma Mesa.
>
>Date: Sun, 03 Sep 2000 12:59:31 -0300
>To: historia-matematica@chasque.apc.org
>From: Julio Gonzalez Cabillon <jgc@adinet.com.uy>
>Subject: Re: [HM] Slope
>Sender: owner-historia-matematica@chasque.apc.org
>Reply-To: historia-matematica@chasque.apc.org
Status: RO

In his "Earliest Uses of Symbols from Geometry" web page, list member
Jeff Miller gathered the following information:

Slope. The earliest known use of m for slope is an 1844 British
text by Matthew O'Brien entitled _A Treatise on Plane Co-Ordinate
Geometry_ [V. Frederick Rickey].

George Salmon (1819-1904), an Irish mathematician, used y = mx + b
in his _A Treatise on Conic Sections_, which was published in several
editions beginning in 1848. Salmon referred in several places to
O'Brien's Conic Sections and it may be that he adopted O'Brien's
notation. Salmon used a to denote the x-intercept, and gave the
equation (x/a) + (y/b) = 1 [David Wilkins].

Another use of m is in the 1855 edition of Isaac Todhunter's
_Treatise on Plane Co-Ordinate Geometry_, which uses y = mx + c
[Dave Cohen].

In _Webster's New International Dictionary_ (1909), the "slope form"
is y = sx + b.

In 1891, _Differential and Integral Calculus_ by George A. Osborne
has y - y' = m(x - x').

In _Analytic Geometry_ (1924) by Arthur M. Harding and George Mullins,
the "slope-intercept form" is y = mx + b.

In _A Brief Course in Advanced Algebra_ by Buchanan and others (1937),
the "slope form" is y = mx + k.

According to Erland Gadde, in Swedish textbooks the equation is usually
written as y = kx + m. He writes that the technical Swedish word for
"slope" is "riktningskoefficient", which literally means "direction
coefficient," and he supposes k comes from "koefficient."

According to Dick Klingens, in the Netherlands the equation is usually
written as y = ax + b or px + q or mx + n. He writes that the Dutch
word for "slope" is "richtingscoefficient", which literally means
"direction coefficient."

In Austria k is used for the slope, and d for the y-intercept.

It is not known why the letter m was chosen for slope; the choice may
have been arbitrary. John Conway has suggested m could stand for
"modulus of slope." One high school algebra textbook says the reason
for m is unknown, but remarks that it is interesting that the French
word for "to climb" is monter. However, there is no evidence to make
any such connection. Descartes, who was French, did not use m. In
_Mathematical Circles Revisited_ (1971) mathematics historian Howard
W. Eves suggests "it just happened."

                            ----------

As I wrote some years ago, I don't think anyone should consider or
ponder over this 'm' as a *math symbol*, at least with the same status,
say, of $e$, $i$, $0$, and so forth. Through the years, I have realized
that some of you [in the US] read too much significance into the
LETTERS  'm'  or  'b'  in  y = mx + b. I would like to say once again
that these parameters are not sacred in this context, not even in the
US books. You may find:

y = cx + d        y = nx + c    [e.g. taken from Spivak's "Calculus"]
y = mx + c        y = mx + k        y = mx + n        ...

In Uruguay the equation is usually written as

                  y = ax + b        or        y = mx + n,

and the "slope" is called "pendiente", "coeficiente angular", or
"parametro de direccion".

Regards,
Julio Gonzalez Cabillon
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>Dear members
>
>I was working with a group of high school teachers generating a concept for
>Functions, and one of them asked the group on the origin of the use 
>of m as the
>gradient of a line.  The assumption was that we can predict that c is from the
>word constant.  Almost all our sessions on mathematics teaching have a bias
>towards history.
>
>Thank you in anticipation
>
>Mthunzi Nxawe
>Rhodes University Mathematics Education Project
>PO Box 94
>Grahamstown
>6140
>
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-- 
===================================================
Vilma M. Mesa
Research Fellow and Lecturer-University of Michigan
2610 SEB, 610 East University
Ann Arbor, MI 48109-1259
Phone: 	734 647 9392
Fax:	734 936 1606
===================================================