# Does a square have an equation? [duplicate]

can you model a square in an equation ?

like a circle for example $r^2 = x^2 + y^2$

and lets say we have a square with: centered at $(3,3)$

$2 \leq x \leq 4$ and $2 \leq y\leq 4$

can we somehow make an equation for that square ?

## marked as duplicate by Ross Millikan, Steven Stadnicki, user66733, user63181, EtienneMar 11 '14 at 18:09

• You can regard the square as the limiting set of the graphs of $$|x-3|^p + |y-3|^p=1$$ as $p\rightarrow +\infty$. Unfortunately, you can't really write $|x-3|^{\infty} + |y-3|^{\infty}=1$ without rigorously defining the symbols used. – MPW Mar 11 '14 at 17:34
In general, $\left|(x - h) + (y - k) \right|+\left| (x - h) - (y - k) \right|=r$ describes a square centered at (h,k) and having side length r.
• The expression in the picture isn't very clear. Please format it here using MathJax $\ddot\smile$ – Shaun Mar 11 '14 at 18:02