# why do they use m for slope

Q: This drives math teachers crazy, perhaps because itБs more of a language question: Why do we use the letter БmБ for the slope of a line? If you don t know, youБre in good company. Even people on the
arenБt sure. A: WeБre in good company, it seems, though we can clear up some of the nonsense found online about the use of БmБ as a symbol for slope. LetБs begin with a bit of history. The (2nd ed. ) by Eric W. Weisstein says the letter БmБ was first used in print as a symbol for slope in the mid-19th century. Weisstein traces the usage to an 1844 treatise on geometry by the British mathematician Matthew OБBrien. That may be the earliest use of the symbol in an English work, but Sandro Caparrini, a scholar at the University of Torino in Italy, has traced the usage all the way back to a 1757 work by the Italian mathematician Vincenzo Riccati. Why, you ask, did the letter БmБ become the symbol for the slope of a line instead of, say, БsБ or some other letter?

First, we ought to point out that the symbol is different in some other languages. In Swedish, for example, itБs Бk. Б The mathematician Erland Gadde has speculated that the БkБ stands for Бkoefficient,Б which is part of a longer technical word for slope in Swedish. But getting back to your question about the symbol Бm,Б one theory is that it comes from monter, which means to climb in French. Unfortunately, thereБs no evidence to support this. And the 17th-century French mathematician and philosopher Renц Descartes never used the symbol Бm,Б as many supporters of the monter theory have claimed. Other unsubstantiated speculation is that the БmБ refers to either mons, Latin for mountain, or montagne, French for mountain. One common theory is that the БmБ stands for the first word in Бmodulus of slope. Б Although the word БmodulusБ can refer to a number or function or parameter, we find no evidence that it was once commonly used with Бslope.

Б We have, however, found one explanation forБor rather comment aboutБthis БmБ business that makes sense to use. In (2003), the math historian Howard W. Eves suggests that it doesnБt matter why БmБ has come to represent slope. БWhen lecturing before an analytic geometry class during the early part of the course,Б he writes, Бone may say: БWe designate the slope of a line by m, because the word slope starts with the letter m ; I know of no better reason. Б Б Check out our books about the English language Why call slope m has been a question that has been researched by math historians but has not been answered definitively yet. Many people have been taught that it comes from the French, \”monter\”, to climb. I think this is an \”urban legend\”. Former Mathematics book writer, M. Risi answered \”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. \” But M. Risi plainly wasn\’t the first person to use \”m\” in this connection. 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. 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 French connection. 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 crystallized 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. 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.