[BITList] 4 squares questions

[HUGH]

John,

Assuming the figures are as regular as can be, the first two are OK, since
it's simply joining points. However, the problem asks us to produce 4 equal
areas for the third, and and 7 for the fourth.  If a class of schoolkids are
told there is no geometrical way to divide an angle into 3 equal angles,
they will stay behind and try to do it - but it's impossible.  The
subdivision of a line into 2,4,8,16, etc is possible by geometric means, so
No 3 is probably OK, but there is no geometrical way to subdivide a line
into 3, 5 , 7, etc, equal segments. So the solution to the 4th problem is
invalid.

Hugh.