2. Arc length is defined as the limit of the length of a polygonal approximations to a curve. From (B), we know our approximations would approach the arc length

2. Arc length is defined as the limit of the length of a polygonal approximations to a curve. From (B), we know our approximations would approach the arc length from below. You call this "geometry"? Since when does geometry involve a function limiting and bounding process? We didn't even know what a limit was until calculus...