Bubbles are fun, and what's more, there is loads of maths involved in them! But before all that, how about making some yourself?  

We had a biggest bubble competition in my year 7 class today as part of a data handling unit of work - students were in teams of 4-6 and we found averages, range etc

It was the most fun way I've ever taught data handling - see the pics on the right!

Here's some pics when I went to a local primary school to show them the maths behind bubbles.

Bubbles make interesting shapes when you dip different frames into soapy water.

The video on the right shows what happened when we dipped a tetrahedron and cube into soapy water to liven up a year 13 saturday revision session!

Here is a still image from the video.

Can you explain why we get a cube in the middle? Why is it a bit bendy?  

What will happen when you dip different shapes into the water?

This page aims to answer some of these questions...

The best way to understand what is going on is to look at what happens when two or more bubbles meet.  Here are some pictures - click on them to read the captions: 

I have modelled what happens when two bubbles meet on this geogebra online file.  You don't need geogebra on your computer to view it.  Please be patient - it might take a while to load up.  For information on the maths, read the document on the right.  

Plateau was a blind scientist who experimented with bubbles and found  that a maximum of only 3 soap films (faces) ever meet at an edge (once the bubbles have stablised).  Try it for yourself! 

As a consequence only 4 edges meet at any point.  So although the films (faces) meet at 120 degrees, the edges meet at a different angle.  Can you guess what this is going to be?  

Well, if you dip a tetrahedron into soapy water, you can see clearly what happens!  The angle between the edges is our old friend the tetrahedral angle, 109 and a bit degrees!

This explains why the cube in the middle of the cube is bendy.  At a vertices, the (tangents to the) edges meet at angles of 109 degrees, not 90 degrees! 

On the right is a brilliant video from BBC program The Code that explains all this with the help of Tom Noddy, a bubble magician! Another video of him appearing on a chat show is below.

His website contains lots more videos, practical projects and more on the science of bubbles.

Bubbles seek to find the arrangement that minimises surface area and energy.  Further to Plateau's work in this, this topic was studied mathematically by Sophie Germain, and is currently an area of great development in molecular biology and chemistry. The fact that bubbles must meet in the way they do was only proved in the 1970s! 

This principle can be seen in not only soap bubbles but more generally in nature.  The wings of a dragonfly are a nice example, as are bee hives.  A lovely explanation of this phenomena is given in the classic book On Growth and Form by D'Arcy Thompson.