In his book Mathematical Delights Ross Honsberger tells about a letter Professor Liong-shin Hahn received from a mathematics teacher. The latter posed to his student the following problem:
Given a 5×5 square grid
Find five circles so that they pass through each of the 25 grid points at least once.
One of the students reported the following solution:
explaining that a straight line is nothing but a circle with an infinite radius. When the teacher insisted that the task was to find circles with finite radii, the student surprised the teacher with another diagram:
To teacher’s objections the student rolled the diagram into a cylinder, making all circles of finite radius
Naturally, that was not what the teacher had in mind. But what was it?