Holy cow!
Don Spady
----- Original Message -----
From: "Nick Cox" <[email protected]>
To: <[email protected]>
Sent: Thursday, May 08, 2003 13:48
Subject: st: RE: a little off-topic, but a good trivia question
> 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
> > don't know about
> > 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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>
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