# st: RE: a little off-topic, but a good trivia question

 From "Nick Cox" <[email protected]> To <[email protected]> Subject st: RE: a little off-topic, but a good trivia question Date Thu, 8 May 2003 20:48:21 +0100

```Christopher W. Ryan
>
> My teenage daughter's math teacher has posed a riddle to
> her class:  why is the
> letter "m" traditionally used (at least here in the US, I
> elsehwere) to indicate the slope of a line on a graph?  Is
> there some
> underlyinig meaning, or a historical convention?

See http://members.aol.com/jeff570/geometry.html:

Slope. The earliest known use of m for slope appears in Vincenzo
Riccati�s
memoir De methodo Hermanni ad locos geometricos resolvendos, which is
chapter
XII of the first part of his book Vincentii Riccati Opusculorum ad res
Physica,
& Mathematicas pertinentium (1757):

Propositio prima. Aequationes primi gradus construere. Ut Hermanni
methodo
utamor, danda est aequationi hujusmodi forma y = mx + n, quod semper
fieri
posse certum est. (p. 151) The reference is to the Swiss mathematician
Jacob
Hermann (1678-1733). This use of m was found by Dr. Sandro Caparrini
of the
Department of Mathematics at the University of Torino.  In 1830,
Traite
Elementaire D'Arithmetique, Al'Usage De L'Ecole Centrale des
Quatre-Nations:
Par S.F. LaCroix, Dix-Huitieme Edition has y = ax + b [Karen Dee
Michalowicz].

Another use of m occurs in 1842 in An Elementary Treatise on the
Differential
Calculus by Rev. Matthew O'Brien, from the bottom of page 1: "Thus in
the
general equation to a right line, namely y = mx + c, if we suppose the
line..."
[Dave Cohen].

O'Brien used m for slope again in 1844 in 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].

Karen Dee Michalowicz has found an 1848 British analytic geometry text
which
has y = mx + h.

The 1855 edition of Isaac Todhunter's Treatise on Plane Co-Ordinate
Geometry
has y = mx + c [Dave Cohen].

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

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

In 1921, in An Introduction to Mathematical Analysis by Frank Loxley
Griffin,
the equation is written y = lx + k.

In Analytic Geometry (1924) by Arthur M. Harding and George W.
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
"richtingsco�ffici�nt", which literally means "direction coefficient."

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

According to Julio Gonz�lez Cabill�n, in Uruguay the equation is
usually
written as y = ax + b or y = mx + n, and slope is called "pendiente,"
"coeficiente angular," or "parametro de direccion."

According to George Zeliger, "in Russian textbooks the equation was
frequently
written as y = kx + b, especially when plotting was involved. Since in
Russian
the slope is called 'the angle coefficient' and the word coefficient
is spelled
with k in the Cyrillic alphabet, usually nobody questioned the use of
k. The
use of b is less clear."

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."

<end of quotation>

Nick
[email protected]

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