@snacks it depends whether u consider different lines to be different shapes . but like , yea

a circle is a very different shape than a sttaight line

@snacks nope , actually

u can only see it globally by embedding it in 2d space , but it exists perfectly fine as a 1D shape . topology , and such

@snacks the circle is a line , it has no surface area

the line , however , subdivides 2d space in 2 subspaces , and one of them has a finite surface area

@snacks imagine yourself as a 1D observer , there is substancial difference between a circle and a straight line . namely , in one case you will find yourself back at the beginning eventually

also , imagine a curved geometry , for example , spherical geometry : here , “straight lines” are just closed loops

@snacks shapes exist regardless of the space one os embedding them in , thats the big takeaway here