Why m for slope?
Date: Wed, 9 Nov 1994 15:44:42 -0800 (PST) From: Mary Koch Dr. Math: My class wants me to ask you why the letter m was selected to represent slope. Mary
Date: Sat, 12 Nov 1994 07:28:39 -0500 From: Stephen Weimar Subject: Re: why "m" for slope >Date: Fri, 11 Nov 94 23:47:50 EST >Sender: email@example.com >From: EVOOLICH@mecn.mass.edu >Subject: Re: why "m" for slope > >Why call slope m has been a question that has been researched by >math historians but has not been answered definitively yet. All the >usual suggested "reasons" have proven false. One math historian has >been doing a search for a few years for the earliest use in a math book. >So the jury is still out on this question. > >Erica Voolich >firstname.lastname@example.org __________ From: "John Conway" Date: Sun, 13 Nov 94 19:38:58 EST Subject: Re: why "m" for slope? Cc: email@example.com I believe (but am not sure) that what we now call just the "slope" was once called the "modulus of slope", the word "modulus" being used in its sense of "number used to measure" (as in "Young's modulus"). Descartes' "La Geometrie" doesn't use the "m" in this connection, but I seem to remember that Euler often does. Descartes makes no use of Greek letters for parameters in his Geometrie, and most later authors have followed him in this, if we except the use of theta, phi for variable angles. This is an interesting question - I'll try to track it back. John Conway __________ Date: Mon, 19 Feb 1996 08:52:40 -0500 (EST) From: John Conway Subject: Re: GEOMETRIC TERMS When this question came up last year, it emerged that many people have been taught that it comes from the French, "monter", to climb. I think this is an "urban legend". I don't have much faith in the theory I put forward then - that this m stands for "modulus of slope". It is true that the term "modulus" has often been used for "the essential parameter determining". John Conway __________ Date: Mon, 19 Feb 1996 10:07:33 -0500 From: André Deschênes Organization: Le Petit Séminaire de Québec Subject: Re: GEOMETRIC TERMS I recently met a former Mathematics book writer, M. Risi, who wrote some books for teaching mathematics at a level that is about the same as pre-college. These books where written in French for students of Quebec province. I asked him exactly the same question as yours: "Why did you use m for slope? No French word beginning with the letter m seems to me appropriate to represent slope, and I don't know an English word either." His answer was approximately: "In our system, the first letters of the alphabet, a, b , c... represent the constants, the last letters, x, y, z represent the unknown variables and the middle letters, m, n, p... represents the parameters. When we started the explanations of slope, it was in studying the first degree equation: y = mx + b. x and y were the variables, b was fixed and considered as a constant, and what was appended to the coefficient of x as its value varied. So it was a parameter and that is why we used m." André Deschênes __________ Date: Mon, 19 Feb 1996 12:38:34 -0500 (EST) From: John Conway Subject: Re: GEOMETRIC TERMS But M. Risi plainly wasn't the first person to use "m" in this connection! It interests me that on this continent the typical form is y = mx + b, whereas in England and in "the" Continent it is y = mx + c. The latter form still seems to me to be more natural, since this "c" is like the arbitrary constants in indefinite integrals, and so it will probably be very hard to date. But the "b" usage probably originated with the author of a particular influential North American textbook, and maybe we can find out just who it was. John Conway
From: "G. A. Edgar" <firstname.lastname@example.org> Newsgroups: sci.math Subject: Re: Why "m" for slope? Date: Thu, 09 Sep 1999 06:50:26 -0400 Organization: The Ohio State University Where did this question come from? It is asked like clockwork every September. Let me just quote an answer from 1996: > Subject: Re: QUESTION: M = slope? IN GEOMETRY > Email: email@example.com > Date: 1996/12/21 > Forums: k12.ed.math > > According to one of the most eminent mathematics historians in > the US who has researched the topic, Professor Frederick > Rickey, Bowling Green University, Ohio, we do NOT know why m > was used for slope in the slope/intercept form of the > equation. Book authors who give the French connection are > WRONG. Professor Rickey says there is absolutely no proof for > the the French connection. > > Now, if someone knows another math historian with a better > reputation than Dr. Rickey who disputes Rickey's claim, please > let me know. > --- > > > Karen Dee Michalowicz Adjunct Faculty > Upper School Mathematics Chair George Mason University > The Langley School Fairfax, VA > McLean, VA > Treasurer, > HPM (History/Pedagogy of Mathematics), Americas Section > .......... > > Subject: Re: y=mx+b > Author: V. Frederick Rickey <firstname.lastname@example.org> > Date: Sat, 24 May 1997 14:56:52 -0400 > > Yes, in 1990 I did write a brief note in the HPM Newsletter about the > origin of the word slope. Since then I have pushed the first use of the > word (that I know of) back to 1850. Before that phrases such as "the > tangent of the angle between the line and the x-axis" were used. I take > this as evidence that the concept of slope had not crystalized and so name > was attached to it. Both the word "slope" and the use of the letter "m" > seem to have originated in the USA. > > Unfortunately, I am not now in a position to post a detailed reply as I am > on my way out of town. I will do so in July. > > Fred Rickey > -- Gerald A. Edgar Department of Mathematics The Ohio State University Columbus, OH 43210
Date: Tue, 3 Oct 2000 22:23:20 -0400 (EDT) From: Robby Subject: Re: why "m" for slope I came across the question in your FAQ and I just wanted to say that I think of m as standing for "move" and b for "begin." This relates to the way you graph linear equations by hand. You can use the b value to plot the "beginning" point (0,b). Then the m value instructs you where to "move" from point (0,b) to plot the next point, thus giving you the line for the equation. Just another idea (and a simple way to teach linear equations!) Robby "Math-freak" Grant
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