Which One Doesn’t Belong? at breakfast

donuts

This set required some serious leg work. The cup in the upper right was borrowed from a neighbor (thanks Facebook for facilitating!) and the square bagel at lower left required a special trip to Cosi.

The original inspiration for this set comes from a field of math called topology. Topologists study the shape of things, but not their size. To a topologist, a cube and a sphere are the same because each is a surface without edges or holes.

A standard example in topology is that a donut and a coffee cup are the same as each other. If you had a coffee cup made of soft modeling clay, it would not be very functional. But you could deform it into a donut with the right stretching and squishing. As long as you stretch and squish without puncturing or ripping, you are making equivalent things in topology.

Thinking about this got me wondering about other things that are like coffee cups and/or donuts, but in different ways.

A final thing to think about—does a coffee cup have one hole or two? Is there something different about the hole in the handle from the hole where you pour the coffee? Should they both rightly be called holes? What do you think?