If I said, for which value of $r$ does a circle have equal area and circumference, we could all calculate that it happens when $r=2$, but when written out, are we not saying that an area equals a length? I didn't think this was allowed because the dimensions of both sides of an equation have to be equal, right? Could someone please correct my misunderstanding please.
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
The question would not be stated like this in physics. It would then have to be formulated as
For which value of $r$ does a circle have numerically equal area and circumference?
Because you are absolutely right that there would otherwise be a dimensional issue. In mathematics, though, you'd often work on unitless numbers in which case you might hear the sentence that you wrote. But when you apply the maths to a physical scenario, then units become relevant.
