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Day 9 | LThMath Advent Calendar

Yesterday, I spoke about topology in general. There is still one piece of information that I would like to share. It is funny, interesting and a bit of a surprise at first glance. I remember how amused I was first time I learnt about this.

A doughnut and a coffee cup

I never imagined that a doughnut and a coffee cup have anything in common. It never occured to me to look at the number of holes in a surface.


In mathematics, genus (plural genera) has a few different, but closely related, meanings. Probably the fastest, easiest and most intuitive way to introduce genus is that it is the number of "holes" of a surface. So that a sphere has genus 0 and a torus has genus 1.

Play with pledo

Topology is often described as the rubber-sheet or plasticene geometry, where distances have very little meaning. Speaking about genus to children is actually very straight forward and I believe they have a great intuition when it comes to this idea, especially if you present it using pledo, clay or any other plasticene.

I think it is a fun activity to start from a pledo doughnut and see how you can transform it into a cup (as in the sequence of images above). I would love to see photos if you have ever tried it.

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