Soap bubbles are simply irresistible. As is the heading of Section 4.3 of Roberto Piazza‘s book Soft Matter, so I had to borrow it for this post. In the book, you can learn about some of the wonderful physical properties of soap bubbles. For example, I was not aware that each bubble is a double shell enclosing water in between. In this way, the hydrophilic heads of the soap molecules point inside whereas the hydrophobic tails point outside. The colours are then created by interference of light reflected from the two soap films. As water flows and evaporates between the films, colours change depending on the distance between the two films.
From a mathematical point of view, soap bubbles are interesting because they form minimal surfaces and, when restricted to plane arrangements, find Steiner trees (Scott Aaronson has an interesting take on this in NP-complete Problems and Physical Reality).
For the more bio-chemically inclined, there is a connection between the calculus of variations and protein folding. See for example James McCoy’s paper Helices for mathematical modelling of proteins, nucleic acids and polymers.
I may come back to these topics when I start reading in earnest Mariano Giaquinta’s and Stefan Hildebrandt’s epic two volume work on the Calculus of Variations (vol. 1, vol. 2). In the meantime, why waste words on things you can easily appreciate in the following videos.