$x, y, z$ for dimensions

Question

We tend to use $x$ for an arbitary first dimension, $y$ for one at right angles to it, $z$ for one at rigth angles to both of those ... what is the letter for $4\textrm{D}$?

Often, after $x,y,z$ come $u,v,w$ ;) – Hagen von Eitzen Jun 06 '20 at 21:35 — Hagen von Eitzen, Jun 06 '20 at 21:35

score 3 · Accepted Answer · edited Jun 06 '20 at 22:03

3

I think the letter $t$, because the fourth dimension is (usually) $\textrm{time}$ which is often symbolized with $t$. However when people use many dimensions they often use the notation $x_1, x_2, ...$ since it is easier than having to remember which letter corresponds to which dimension.

edited Jun 06 '20 at 22:03

matt

123

answered Jun 06 '20 at 21:30

michalis vazaios

1,252

score 2 · Answer 2 · answered Jun 07 '20 at 01:04

While $t$ is used in special contexts like Minkowski space (often associated with physics) where we might want to distinguish one dimension versus the others, I find that $w$ is more common and more neutral as a next letter.

For examples in programming, see here and here and the 4D vector page on Wikipedia.

For examples of the pattern $(x,y,z,w)$ in various math contexts, see these MathSE questions here (a quadruple integral) and here (a diophantine equation in four variables) and this Socratic question (solving a system of equations in four variables).

Relatedly, in complex analysis there is often a convention of using $z$ to denote the complex number $x+iy$. Then $w$ is the next letter, used for another complex number which may be written $u+iv$. This can be found in, say, "Visual Complex Analysis" by Needham.

$x, y, z$ for dimensions

2 Answers2