Besides being the first and last letters of the alphabet, why do we like abc and xyz so much?

In algebra, both abc and xyz are used, and occasionally pqr as well. Why those specifically? And for vectors, one of the notations is ij. Why is that? And in programming, it is a convention to use loops with ijk as the index. Why not something like cde (for count) or tuv(tally)? Why index? And in coordinates, we use xyz. Why is that? Why not abc? What about ijk, pqr, etc.? Also, why is y and z flipped in some 3D programs, and why is in some 2D programs, up is negative y rather than positive?

Finally, why do these kind of triplet letter combinations always use the Latin alphabet? Why aren’t there any conventions that use Cyrillic, Greek, Arabic, or the Latin letters with cool hats? Is it because English became the dominant language? That can’t be the only reason, as we still use some Greek symbols for some things like pi, phi, alpha(for angles as well as the particle), beta, gamma (rays), etc. The Greeks figured out things like coordinates, algebra, etc., so why Latin letters? Is it because of the Romans?

  • howrar@lemmy.ca
    9·
    3 days ago

    abc and xyz make sense because they lie on opposite ends of the alphabet, so if you need more variables for either sets, there’s a lot more room to maneuver. If you’re looking for the history of these variables in the context of Cartesian coordinates, I’d start with looking at Descartes’ work. This whole system originated from him, so if he used xyz, then that must be where it came from.

    I’ve seen p and q used in various contexts. For example, they could be probability distributions (e.g. KL(p|q)), they could be two points. In these scenarios, we just use p because it’s the first letter of whatever they represent, and q comes after while looking similar so it suggests that they’re the same type of mathematical object.

    For indexing, it’s what we commonly use just because we call it an index. You’re not counting or tallying things. It’s a reference to a location in memory. But if you are counting, then c makes perfect sense and I’ve definitely used it in that context. I’ve also used t for indexing if that index represents time. But if there’s no other meaning associated with it, then it’s just an index, hence i.