Five Circles

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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?









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