The stated premise:
&quot;Can you slice Earth flat <i>through its centre</i> while touching no land?&quot;<p>is at odd with the results.  None of the examples goes through the center (the core - either geographical or center of mass).  The solutions are circular surface traces assuming a two-dimensional projection.<p>Interesting, nonetheless, but the opening premise could use a reword.  Maybe, &quot;can you find a region such that a flat plane would cut the Earth without touching land?&quot;