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Why is the letter m used for slope in equations?

This question has been researched by math historians but has not yet been answered definitively.

Many people have been taught that m comes from the French monter, to climb, but this appears to be an 'urban legend.'

Although m can stand for "modulus of slope" and the term "modulus" has often been used for "the essential parameter determining," there is no definitive proof that this is the derivation of m.

M. Risi, the author of math textbooks written in French for students of Quebec province, says that in his 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... represent the parameters." When he started to explain 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 was appended to the coefficient of x as its value varied--so it was a parameter, and that is why m was selected.

Prof. John Conway points out, however, that M. Risi was not the first person to use 'm' to represent slope. Thus the jury is still out on this question.

Jeff Miller summarizes:

    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." (Earliest Uses of Symbols from Geometry)

Student Robby Grant has suggested a way of remembering m for slope and b for y-intercept:

    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.

See the full discussion from the Dr. Math archives:

Why m for slope?



What do you call the "fraction bar"?

There was quite a lengthy discussion of this on a History of Math mailing list. Different people and nationalities use different terms (variety is the spice of life).

The word solidus is used for the symbol "/" in any context. It doesn't have to be part of a fraction as in 1/2. The solidus is also called a virgule, - the two words can be used interchangeably.

When the line isn't slanted, but looks like this:

           a
         -----
          b-c

it's called a vinculum (binding). Originally a vinculum was a horizontal bar placed over two or more terms in order to indicate grouping, but according to The Words of Mathematics, An Etymological Dictionary of Mathematical Terms Used in English, by Steven Schwartzman, "some recent authors have extended the definition of vinculum to include the bar between the numerator and the denominator of a fraction, given that the fraction bar often acts as a grouping symbol."

In addition to The Words of Mathematics, Steven Schwartzman, MAA 1994, see A History of Mathematical Notation, Florian Cajori, Dover.



Tim Kurtz, formerly of St. Bonaventure University, whose service "Ask Professor Maths" provided the initial inspiration for Ask Dr. Math, adds:

The virgule or solidus is also used in the following ways:

      alternatives                and/or
      to mean "per"             miles/hour
      to delineate line breaks    Old King Cole/Was a merry old soul.



For more on math terms from the Dr. Math archives, see

Elementary Terms and Units of Measure
Middle School Terms and Units of Measure

On the Web are two excellent sources of information about math terms and symbols, regularly updated by Jeff Miller:

Earliest Uses of Mathematical Symbols
Earliest Uses of Some Words of Mathematics

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