Question 13
A bug (of negligible size) starts at the origin on the coordinate plane. First it moves $1$ unit right to $(1,0).$ Then it makes a $90^\circ$ turn counterclockwise and travels $\frac12$ a unit to $(1,\frac12).$ If it continues in this fashion, each time making a $90^\circ$ turn counterclockwise and traveling half as far as in the previous move, to which of the following points will it come closest?