1
$\begingroup$

Can I transform an implicit function of a cylinder to explicit form?

Lets say we have a cylinder

$x^2 + y^2 - 1 = 0$

and we want to have it expressed as function $f(x,y,z)$.

  • 1
    You have already written it as $f(x,y,z)=0$, haven't you?2011-10-17

1 Answers 1

4

If what you want is an equation of the form $z=f(x,y)$, forget it: such a function would, by definition, give a unique value of $z$ for every pair of values $(x,y)$, but on your cylinder, a single pair $(x,y)$ may correspond to infinitely many values of $z$. That is, what would you want $f(1,0)$ to be? If what you want is $f(x,y,z)=0$, then, as lhf writes in the comments, you already have it. Think of it as $x^2+y^2+0z-1=0$, if it helps.

  • 0
    or perhaps $1\times x^2+1\times y^2+0\times z^2 - 1 =0$ to emphasise that it is an even function of all three variables2011-10-17