Letter m For Slope

harpazo

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Why is m the symbol to represent slope?
 

MarkAZ

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There are a number of ideas regarding the choice of 'm' for slope. Some are described in this compilation at Duke University.

Their final paragraph:

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."

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MarkAZ

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Using Google, I see a lot of variation around the world.

y = mx + b

y = ax + b

y = mx + c

y = kx + b

y = mx + n

y = px + q

Some European countries (and possibly others) don't say 'slope'. They say 'direction coefficient'. My favorite idea is the following.

When we pick letters of the alphabet to represent numbers, we generally pick beginning letters for constants {a,b,c,d,e} and ending letters for variables {u,v,x,y,z} and letters in the middle for parameters (k,m,n}. Slope is a parameter. So somebody picked m, and it caught on (in the US, anyway).

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MarkFL

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If it were up to me, I would use:

\(\displaystyle y=ax+b\)

Just as I would use:

\(\displaystyle y=ax^2+bx+c\)

\(\displaystyle y=ax^3+bx^2+cx+d\)

etc.

However, for an \(n\)th order polynomial, I would tend to use:

\(\displaystyle y=\sum_{k=0}^{n}\left(a_kx^k\right)\)
 
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harpazo

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Thank you everyone.