Astounding Science Fiction/Volume 54/Number 06/Purely Coincidence, No Doubt

Purely Coincidence, No Doubt

 

The following series of figures is almost certainly familiar to you:

 

 

This series of figures are all—including #6, despite appearances—single figures, produced by simple geometry. They are single members of a family of figures similar to the family of conic sections. Conic sections range from a straight line through hyperbola, parabola, ellipse to circle.

The above figures are toroidal sections; they don't come from a biology text, but can be produced at home with a knife and a doughnut. #1 and #2 are produced by cutting the doughnut in a plane parallel to the plane of the doughnut. #3 through #6 are produced by cuts varying distances from the axis of the doughnut's hole—#6 being the intersection of the plane passed through the axis, of course. #6 looks for all the world like two separate entities, but recognizing it as simply the cut surfaces of a doughnut, it's evident that it's actually a single figure.

A smoke-ring would show the same characteristics, of course, but being highly dynamic, retaining its structure only by reason of its dynamic movement, it can't be sectioned without dissolution.