  A mathematical donut is a rectangle of integral side length with a smaller
rectangle (called the hole of the donut), also of integral side length,
strictly inside it and with sides of the rectangles parallel to each other,
where the area of the larger rectangle is twice that of the smaller. Necessary
and sufficient conditions are determined for when the hole of the donut can be
rotated $90^{\circ}$ and a donut still exists, and a complete classification of
all square or square-holed donuts is given, with the square donut
classification being intimately related to Pythagorean triples.
