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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 > 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] * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: a little off-topic, but a good trivia question***From:*David Kantor <[email protected]>

**st: Re: RE: a little off-topic, but a good trivia question***From:*"Don Spady" <[email protected]>

**References**:**st: a little off-topic, but a good trivia question***From:*"Christopher W. Ryan" <[email protected]>

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