Ronn Blankenship wrote:
>
> (One way that our hypothetical Flatlanders could determine
> that they are
> actually living on the surface of a huge sphere rather than on a flat
> surface would be to lay out a big enough triangle and measure
> its angles
> carefully. On a plane, the sum of the angles of a triangle is always
> exactly 180 degrees. On the surface of a sphere, the sum of
> the angles of
> a triangle is always greater than 180 degrees.)
And one should, of course, read _Sphereland_ by Dionys Burger, a sequel
to _Flatland_, for the dramatic "ripped from the headlines" account of
such an undertaking.
In my pile of "projects I'd love to do but will never get around to
starting, let alone completing" there sits the idea for a second sequel,
"Fractalland" which explores fractional dimensions and chaos. And just
so I can take credit for the idea, the tale will be related by the
preeminent Flatlander researcher, Anne Octagon (granddaughter-in-law of
A. Hexagon and great-great-granddaughter-in-law of A. Square).
Joshua
