Prof. Dr Daniel Grieser
Institute of Mathematics

• Photos from the lecture

Anyone who has ever blown soap bubbles will be familiar with them: those iridescent spheres, sometimes small, sometimes large – and always round. Or have you ever seen a square soap bubble? Why is that? The soap bubble solves a mathematical problem that has fascinated people for over 2,000 years: how do you enclose a certain volume of air with the smallest possible surface area? In this lecture, we’ll explore the mathematics of the smallest surfaces, as well as its little sister, the mathematics of the shortest paths: where should three friends meet so that, in total, they walk as little as possible from home to the meeting point? Which direction should you fly from Oldenburg to take the shortest route to China? Perhaps you’d like to have a go at this beforehand – ideally not on a map of the world, but on a globe!

Host: Carola Schede

Wednesday, 11 March 2009
, 4.30 pm to 5.30 pm
Audimax, lecture centre

Here are some web links where you can find out more about soap bubbles, minimal surfaces (often referred to as minimal surfaces) and the shortest paths:

Lots about soap bubbles (the chemistry of the soap film, where the colours come from, how to make a good soap bubble solution, etc.)

‘Palast der Seifenhäute’ is a lovely film about soap films. You can find information about it here, including how to order a copy of the video. You can watch some clips from the video for free here.

Here are some pictures of double bubbles. These are two soap bubbles joined together. As you can see, the resulting structure is made up of spherical segments. However, it is much more difficult to understand why the configuration shown in the pictures actually results in the smallest surface area than it is in the case of a single bubble. Although mathematicians have been thinking about soap bubbles for over 150 years, they only managed to solve this problem 9 years ago!
And here are a few more pictures of multiple soap bubbles and similar phenomena.

You can find the puzzle sheet here. You can find the solutions here.

Note on the bee problem in the puzzle sheet: Reflect the bee at the edge of the forest and the beehive by the river.

Do you have any questions, or would you like to write to me about the lecture? My email address is

And now, have fun with soap bubbles, spheres, circles, rectangles …
Yours, Daniel Grieser