This question already has an answer here:

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, Etienne Mar 11 '14 at 18:09

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  • $\begingroup$ you can use the min() and absolute value functions $\endgroup$ – Guy Mar 11 '14 at 16:55
  • $\begingroup$ math.stackexchange.com/questions/69099/equation-of-a-rectangle $\endgroup$ – lab bhattacharjee Mar 11 '14 at 16:57
  • $\begingroup$ 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. $\endgroup$ – MPW Mar 11 '14 at 17:34

enter image description here

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.

  • $\begingroup$ The expression in the picture isn't very clear. Please format it here using MathJax $\ddot\smile$ $\endgroup$ – Shaun Mar 11 '14 at 18:02

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