Why Does M Mean Slope?
It is simply not obvious why the value for slope in the line intercept equation is represented with the letter "m." As a result, several theories developed in an attempt to explain why "m" is used to represent slope; math professors and mathematicians with an interest in the history of math have attempted to determine how much truth there is in each of these theories.
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Theories/Speculation
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Climbing a "slope" One popular explanation, commonly given in mathematics textbooks, is that the French word “monter”, which means “to climb”, begins with the letter m. The fact that Descartes was French seems to support this. Other sources have suggested that the longer term “modulus of slope” provides the source of the mystifying letter m in question. Other explanations are based on the fact that variations of the French or Latin words for mountain (“montaigne” or “mons”, respectively) also begin with the letter m.
History
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The letter m was first used as the designation for slope during the middle of the 1800s. Professor Fredrick Rickey of Bowling Green State University published an article in the "History and Pedagogy of Mathematics" Newsletter (1990) that traced the first use of m for slope back to 1850. He also asserts that the use of m to designate slope is a practice that began in the U.S. Eric Weisstein found that M. O'Brien was the first to represent slope with the letter m in a published work in the UK in 1844.
The most noteworthy historical fact is that Rene Descartes himself, pioneer of Cartesian geometry, did not use m to designate slope in any of his writings.
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Protocol for Assigning Letters
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The math community has a convention for how letters of the alphabet are used in equations. The letters at the beginning of the alphabet, a, b and c, are constants; those at the end of the alphabet, x, y and z, are unknown variables, and other letters from the middle of the alphabet are assigned to the parameters of an equation. This makes m a reasonable choice to be the symbol for the parameter of slope.
Other Notation
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Slope has been represented by other letters, in other countries and languages. There is no universally accepted notation for slope. M is simply one of the most common symbols, particularly in most English-speaking countries. In Sweden, for example, slope is represented by a “k”, where the “k” most likely stands for the word “koefficient” (coefficient). France and the Netherlands use the letter "a" to denote slope in the line intercept equation.
Conclusion
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The theories about why U.S. math convention uses m to represent slope are plentiful and the research has looked at them all, however, there has been no definitive reason discovered to date. Without definitive proof for any one explanation, H.W. Eves, American mathematician and author of "Great Moments in the History of Mathematics," may have provided the best explanation when he stated that, “It just happened.”
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References
- Photo Credit pencil draw graph image by Anatoly Tiplyashin from Fotolia.com woman climbing image by Marius Lazin from Fotolia.com
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Comments
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In statistics slope is essential to determine the rate of change:)
