Why in China do they use k instead of m for the slope of a line?
I suspect that it originated from one of the Germanic languages, where the &quot;hard c&quot; sound in English is represented with &quot;k&quot; and thus &quot;coefficient&quot; or &quot;constant&quot; would begin with a &quot;k&quot;. I tested the hypothesis with a translator and, indeed, the terms in modern German are &quot;Koeffizient&quot; and &quot;Konstante&quot;.
So why would the Chinese mathematicians borrow from German/Swedish/Danish mathematicians? It might have to do with the fact that many of the leading mathematicians in the 18th-20th century were German-speaking, e.g. Euler who lived in Germany and who in fact was the first to use &quot;a,b,c&quot; to denote constants and &quot;x,y,z&quot; to denote unknowns; Leibniz, who invented much of modern calculus; Gauss, who contributed significantly to almost every field in mathematics; and other big names such as Riemann and Cantor.
Since the Chinese academics were just opening up to the advances in mathematics at the time, it made sense that they would borrow the notation from the leading scholars of the time.
What makes me more curious is why the Americans use m for slope, which don't seem to have any linguistic explanation. I did some brief reading and this page seems to have the best (non-)answer:

&quot;J. Miller has undertaken a detailed study of the origin of the symbol m to denote slope. The consensus seems to be that it is not known why the letter m was chosen. One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for &quot;to climb&quot; is &quot;monter.&quot; However, there is no evidence to make any such connection. In fact, Descartes, who was French, did not use m (Miller). Eves (1972) suggests &quot;it just happened.&quot; &quot;

Edit: Actually, that might be wrong. I found this page which listed the common notation for slopes in many countries (based on letters from his readers). Excerpt:

In the US, Australia, Canada, Egypt, Mexico, Portugal and Philippines the notation is:     y = mx + b
In the UK, Germany, and former British colonies    y = mx + c
In Azerbaijan, China, Finland, Russia and Ukraine:     y = kx + b
In Sweden:     y = kx + m
In Slovenia:   y = kx + n

So the Germans today in fact use &quot;m&quot; like the Americans and the British. It's certainly possible that they used &quot;k&quot; in the 19th century and shifted to the more prevalent English usage later on. But based on the data above, it seems more likely that the Chinese usage came from Russia. There could be a historical explanation for this - the Chinese Communist Party adopted Soviet science education as the basis of their curriculum after the &quot;liberation&quot;.
To test this &quot;Soviet origin&quot; hypothesis, I looked at the usage in the Nationalist-ruled province of Taiwan. And voila! The Kuomintang curriculum uses m (see here, page 8). This is evidence that the use of k was probably not prevalent in China before 1949.
So, the conclusion: The use of &quot;k&quot; was probably adopted from the Russians. There is in fact an analogue of k in the Cyrillic alphabet, which looks extremely similar to the Latin k. And if you put &quot;Constant&quot; or &quot;Coefficient&quot; in a Russian translator, you'll see that they do in fact use this letter. So I stand by my theory that linguistically it comes from &quot;Constant&quot; or &quot;Coefficient&quot;, but I'd say the historical origin was Russian, not German.