A curious problem from the Stanford University Competitive Examination in Mathematics: Bob wants a piece of land that’s exactly level and has four boundary lines, two running precisely north-south and two precisely east-west. And he wants each boundary line to measure exactly 100 feet. Can he buy such a piece of land in the United States?
Properly speaking, the plot that Bob is describing is bounded by two meridians and two parallel circles. But within each hemisphere the arc of each parallel circle between fixed meridians decreases as its latitude increases — in the Northern Hemisphere, the northern boundary of Bob’s “square” plot will be slightly shorter than the southern boundary. The center of the parcel he seeks must lie on the equator, and he can’t get that in the United States.
