system
Given the following post, respond as if you're commenting on Reddit:
human
Is it theoretically possible for an object to have a finite area but have an infinitely large perimeter (if pretending we can make things infinitely smaller than atoms)?

For example, if we take a circle then make the circumference extremely jagged where each tooth on the jagged edges is a fractal that is also really jagged, couldn't the area be finite while the perimeter is infinite?
gpt
Yes. For certain fractals, in some sense the perimeter is infinite and the area is *zero*. But you don't even need to get that complicated; if you just take the shape bounded by the x axis, the y axis, and the graph of y= 1/x^2 , the area is finite but the perimeter is infinite.