Six flat pictures of everything
There is one way to photograph the whole sphere and keep every straight line straight, and it is to stop using one surface. Six flat pictures at ninety degrees cover everything, each of them a perfect pinhole, and the price is paid entirely at the seams — where a straight line does not bend but kinks, by an angle that reaches 45 degrees and is exactly zero for the lines lying in the seam's own plane.
rung 3 · curved