I had to post my comment as its own post because it wouldnt let me comment on Noa's post.
M is the slope or the slant of a linear equation. I was wondering why it used to be called Modulus and was also wondering if M was always used to represent the slope in linear equations.
Amelia
Why is the letter m used for slope in equations?
ReplyDeleteThis 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?
In the last comment there were a few words that i didn't know by difintion so i decided to look them up.
ReplyDeletearbitrary-depending on individual discretion a and not fixed by law
parameter- an arbitrary constant whose value characterizes a member of a system
definitive- serving to provide a final solution or to end a situation
1.The first people to use math were the Babylonians and the Egyptians and later the Greeks
ReplyDelete2."mathematics" is a greek word which means learning, study, science and later on the definition narrowed to a mroe techincal meaning- mathematical study